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Fall 2025

Dynamics and Bifurcations in a Predator-Prey System with Holling Functional Responses and Allee Effects

When: Sept. 26 (2:30pm), 2025 in RT 1516
Speaker: Chunhua Shan (U. Toledo)
Abstract: The transition between strong and weak Allee effects in prey populations represents a fundamental regime shift in ecology. In this talk, we examine the interplay between Holling-type functional responses and Allee effects in a predator–prey system. We demonstrate that the system exhibits complex dynamics and higher-codimension bifurcations. A new unfolding of nilpotent saddle of codimension 3 with a fixed invariant line is discovered and developed, and the existence of codimension 2 heteroclinic bifurcation is proven. Our work extends existing knowledge of predator-prey systems with Allee effects. The bifurcation analysis and corresponding diagrams allow for biological interpretations of predator–prey interactions.

Spring 2025

Single-Index based Semiparametric Batched Bandits

When: May 2 (2:30), 2025
Speaker: Sakshi Arya (CWRU)
Abstract: The multi-armed bandits (MAB) framework is a widely used approach for sequential decision-making, where a decision-maker selects an arm in each round with the goal of maximizing long-term rewards. Moreover, in many practical applications, such as personalized medicine and recommendation systems, feedback is provided in batches, contextual information is available at the time of decision-making, and rewards from different arms are related rather than independent. In order to handle the curse of dimensionality for nonparametric regressions in contextual bandit problems, we propose a novel semi-parametric bandit approach to handle sequential-decision making problems in the batched bandit setting. Here, we assume that for each arm, the relationship between the covariates and responses can be modeled in the reduced 1-dimensional subspace (effective dimension reduction subspace) based on the single-index regression framework. Consequently, we adopt an adaptive binning and successive elimination algorithm for the sequential decision-making along the estimated single-index direction. We provide optimal regret guarantees on our proposed algorithm and illustrate the performance on simulated and real datasets.

Modeling Animal Movement with Memory with Partial Differential Equations with Time-Delay

When: Apr. 4 (1:00), 2025
Speaker: Jumping Shi (College of William and Mary)
Abstract: Animal populations often self-organize into territorial structure from movements and interactions of individual animals. Memory is one of cognitive processes that may affect the movement and navigation of the animals. We will review several mathematical approaches of animal spatial movements and also introduce our recent work using partial differential equations with time-delay to model and simulate the memory-based movement. We will show the bifurcation and pattern formation for such models. It is based on joint work with Chuncheng Wang, Hao Wang, Xiangping Yan, Qingyan Shi and Yongli Song.

Computational Models of Microorganism Motility

When: Apr. 3 (1:00), 2025
Speaker: Amy Buchmann (Univ. of San Diego)
Abstract: In the field of computational biofluids, we create mathematical and computational models to study the mechanics of biological fluids within the human body, including the circulatory and respiratory systems, as well as the motility of microorganisms. The Method of Regularized Stokelets can be used to model microorganisms immersed in a viscous fluid. Using this method we can model both rigid and elastic filaments immersed in a fluid to study the coordination of flagella and cilia.

Dispersal strategy of hosts and evolution of pathogen virulence in a two-patch model with travel loss

When: Mar. 21 (1:00), 2025
Speaker: Chang-Hong Wu (National Yang Ming Chi Tung University, NYCU)
Abstract: In this talk, we investigate how migration affects the evolution and dynamics of pathogens in animal populations, using a two-strain SIR epidemic model with travel loss in patchy environments. We prove that under suitable conditions, an optimal strategy for migration rates exists, such that the host of a strain adopting this strategy wipes out the other strain. This also reveals that migration causes the dynamics to not be completely determined by the basic reproduction numbers. By considering the effects of travel loss, our results offer insights into the evolution of pathogen virulence, suggesting that lower virulence may be favored in hosts with slower migration rates if the travel loss is large. This is joint work with Bo-Sheng Chen.

An eigenfunction/eigenvalue-like approach to time-varying queues with periodic transition rates

When: Jan. 24 (2:30), 2025
Speaker: Barbara Margolius (CSU Emeritus)
Abstract: Many random phenomena exhibit periodic behavior. These include any processes influenced by the me of day or season of the year; natural phenomena like the des; automobile and air traffic; call centers, and many other random processes. In this talk we study a variety of ergodic queueing processes with periodic transition on rates. Such processes will se le into a periodic distribution on as 𝑡 → ∞. We describe a method to find this asymptotic periodic distribution on for a variety of queueing processes including: the single-server queue, the multi-server queue, the multi-server queue with catastrophes and repair, • level independent Quasi-Birth-Death process (QBD), level independent Quasi-Birth-Death process (QBD) with catastrophes and repair, fluid queues in a random environment. A birth-death process is a stochastic c process which permits one step transitions to adjacent states. A quasi-birth-death (QBD) process is a generalization on of a birth-death process that uses a two-dimensional state space described by a level and a phase. Transitions are permitted only to adjacent levels. Phase transitions within a level are permitted to any phase based on the transitions on rates specific to the model. QBD processes are used to model a variety of applications including health care systems, queueing models, communication on networks and reliability modeling.

Fall 2024

Stability and Tipping Points in Noisy Environments

When: Nov. 15 (2:30), 2024
Speaker: Karen Abbott (CWRU)
Abstract: Sudden, persistent changes in ecosystem state or configuration, known in ecology as regime shifts, are difficult to predict and a cause of great concern. A large, stable prey population may suddenly collapse to an alternative low-density state in response to a stochastic perturbation, for example, or stochasticity may trigger outbreaks in pest populations that were previously stably suppressed. To explain phenomena like these, ecologists have drawn heavily on deterministic theory that emphasizes the nonlinearities that give rise to bifurcation-induced tipping points, while marginalizing the complex role of stochasticity in driving transitions between states. In this talk, I will discuss how different types of tipping points arise, and how we can use potential functions (including their extensions, such as the quasi-potential) to derive stronger stability concepts that allow us to move beyond classical deterministic theory. Given the pervasive influence of large perturbations in nature, this view promises to yield improved insights into the factors that stabilize or destabilize ecological systems.

Colloquium Flyer for X. Wang

When: Oct. 18 (2:30), 2024
Speaker: Xueying (Snow) Wang (Washington State Univ.)

Something "Super Special": A Tale of Isogeny Graphs, Cryptosystems, and Structures in the First and Second Dimension

When: Sept 26 (1:00), 2024
Speaker: Vlad Sworski (Colorado State Univ)

Modeling the Growth, Invasion and Competition of Aedes Mosquitos

When: Sept 20 (2:30), 2024
Speaker: Shigui Ruan (Univ of Miami, FL)

Spring 2024

Grothendieck rings of towers of generalized Weyl algebras

When: April 26 2024
Speaker: Daniele Rosso (Indiana University Northwest)
Abstract: Generalized Weyl algebras (GWAs) are an important class of algebras that include as special cases many algebras that are interesting for ring theory and representation theory. Even though they are not naturally Hopf algebras, the tensor product of a weight module for a GWA with a weight module for another GWA gives a weight module over a third GWA. As a consequence we get a ring structure on the sum of Grothendieck groups of the categories of weight modules over a tower of GWAs. I will talk about some results on describing this ring structure in various settings. This is joint work with J. T. Hartwig (Iowa State University).

Examine the environmental effects on population dynamics of insects via some mathematical models and experimental data

When: April 12, 2024
Speaker: Yanyu Xiao (University of Cincinnati)
Abstract: The population dynamics of insects are highly sensitive to its age distribution and local climate. In the first part, we will model a stage-structured insect species that undergoes diapause if faced with strong intraspecific competition among larvae. In the second part, we will discuss the impact of climate effect on vector populations from lab results.

An old threat in new territory: investigating dengue emergence with mathematical modeling

When: March 29
Speaker: Michael Robert (Virginia Tech)
Abstract: Mosquito-borne diseases endemic to areas with tropical climates have been spreading in temperate regions of the world with greater frequency in recent years. Numerous factors contribute to this spread, including urbanization; increases in global travel; and changes in temperature, precipitation, and humidity patterns due to climate change. Mathematical modeling is a useful tool to examine how these different influences impact transmission and spread of arboviruses and for projecting how potential future changes in these factors could affect arbovirus dynamics. Models have been employed for years to study disease dynamics, but diseases emerging in new regions present particular challenges. Here, we discuss models developed to study the introduction, emergence, and spread of dengue fever in Argentina. Dengue, caused by a virus transmitted by Aedes aegypti mosquitoes, first emerged in temperate Argentinian cities in 2009, and multiple outbreaks of increasing incidence have occurred since. With particular focus on the role of climate in dengue emergence, we present mathematical models designed to study meteorological influences on seasonal Aedes aegypti and dengue dynamics in temperate Argentinian cities, and we show how different seasonal patterns influence the risk of outbreaks. We also investigate potential influences of climate change on risk of dengue transmission in the future. We discuss the implications of our work on dengue and mosquito mitigation strategies, and we address some of the issues and areas for improvement in modeling emerging arboviruses.

An operator learning framework for an inverse problem in Electrical Impedance Tomography

When: March 22, 2024
Speaker: Anuj Abhishek (Case Western Reserve University)
Abstract: Neural network architectures have been shown to be fairly useful in approximating an operator between two function spaces. In this talk, we will briefly review an inverse problem that arises in Electrical Impedance tomography as well as review such operator learning network architectures. We will then see how we might use similar network architectures to learn (or, approximate) a map that takes in as its input the Dirichlet to Neumann operator and outputs the corresponding conductivity function. This is based on an ongoing work with my collaborator, Thilo Strauss (Xi'an Jiaotong Liverpool University).

Free resolutions of differential operators

When: February 2, 2024
Speaker: Rachel Diethorn (Oberlin College)
Abstract: The ring of differential operators which act on a commutative ring R is a classical object that reflects important properties of R and detects singularities. In this talk, I will introduce the notion of differential operators in commutative algebra and report on recent joint work with Jeffries, Miller, Packauskas, Pollitz, Rahmati, and Vassiliadou in which we develop new homological techniques for studying differential operators. In particular, we construct minimal sets of generators (and minimal free resolutions) for the modules of differential operators in low orders in a non smooth setting. This generalizes well-known results of Bernstein, Gelfand, and Gelfand and of Vigue from the 1970's.

Fall 2023

Honors Senior Project Presenations

When: December 8, 2023
Speaker: Rosalia and Joshua (CSU Honors Students)

Super Multiset RSK and the Restriction Problem

When: October 20, 2023
Speaker: Alexander Wilson (VAP at Oberlin College)
Abstract: Diagram algebras like the Temperley-Lieb algebra, the partition algebra, and more recently the multiset partition algebra are associative algebras whose product is given by a combinatorial operation on graph-theoretic diagrams. Because they occur naturally as centralizer algebras of the symmetric group, they have been used to approach long-standing questions about the representation theory of the symmetric group like the Kronecker and restriction problems. In this talk, I will introduce a generalization of the RSK algorithm, which has proven useful in studying certain diagram algebras associated to the 𝐺𝐿 representation $\bigwedge\nolimits^{r}V$, and I will discuss how these methods can be used to reframe the problem of restricting 𝐺𝐿 representations to 𝑆

Special Colloquium on Quantum Computing

When: October 13 @ 4:00PM in WH401
Speaker: Hakan Doga (Postdoc Mathematician at IBM Research, CCF)
Abstract: This lecture will provide a general overview of quantum computing, define some fundamental concepts with an emphasis on the mathematical model for quantum computing. I will conclude the lecture by presenting a project that I am working on that explores the use of quantum computing for protein conformation prediction problem. This is a joint research project with the Cleveland Clinic.

Framework for the Theory of Higher Order Convex Bodies

When: September 29, 2023
Speaker: Michael Roysdon (VAP at CWRU)
Abstract: We develop the basic theory of “higher–order” convex bodies beginning with a result of Schneider from 1970 concerning the Rogers-Shephard inequality. Building upon Schneider’s work, we develop the notion of the higher order L_p-projection body and L_p centroid body. If time permits, we will discuss proofs of the associated affine isoperimetric inequalities: Petty projection inequality, Zhang’s projection inequality, and Busemann-Petty Centroid inequality. In particular, we discuss two interesting consequences of our results that are surprisingly new to the literature: 1) A version of the Busemann random simplex inequality for the mean width, but where the random simplex is replaced by a random polytope and where the vertices of the random polytope need not be i.i.d. 2) A extremal volume inequality for operator norms between Banach spaces. This talk in based on joint works, and ongoing works, with Julian Haddad, Dylan Langharst, Eli Putterman, and Deping Ye.

Plücker-type Inequalities for Mixed Areas and Intersection Numbers of Curve Arrangements

When: September 15, 2023
Speaker: Gennadiy Averkov (Brandenburgische Technische Universitat)
Abstract: Any collection of n compact convex planar sets 𝐾,….,𝐾defines a vector of (n/2) mixed areas V(Ki, Kj ) for 1 ≤ i < j ≤ n. We show that for n ≥ 4 these numbers satisfy certain Plücker-type inequalities. Moreover, we prove that for n = 4 these inequalities completely describe the space of all mixed area vectors (V(Ki,Kj) : 1 ≤ i < j ≤ 4). For arbitrary n ≥ 4 we show that this space has a semi-algebraic closure of full dimension. As an application, we show that the pairwise intersection numbers of any collection of n tropical curves satisfy the Plücker-type inequalities. Moreover, in the case of four tropical curves, any homogeneous polynomial relation between their six intersection numbers follows from the corresponding Plücker-type inequalities.

Spring 2023

A (larger) taxonomy of Dedekind-finite rings and reflexive rings.

When: February 10, 2023
Speaker: Steve Szabo (Eastern Kentucky University)
Abstract: A taxonomy of Dedekind finite rings and reflexive rings will be given including connections between ring properties defined on elements and those defined on ideals. Symflexive (symmetrically-reflexive) rings will be introduced (formerly, ideal-symmetric) showing their natural place in the given taxonomy. The ring classes of prime, semiprime, symflexive and reflexive form a chain by inclusion. Characterizations of Morita context rings of each of these types will be given showing their close connections. Other topics relating to the taxonomy will also be discussed as time permits.

Misc.

When: Feb 15, 17, 24, 2023
Speaker: TT Stats Job Candidate Interviews

Algebraic Curves and Codes

When: March 3
Speaker: Luciane Quoos (Instituto de Matematica, Universidade Federal do Rio de Janeiro)
Abstract: In the early eighties tools from algebraic geometry were applied by V. Goppa to construct linear codes using algebraic curves over finite fields. Nowadays these codes are called algebraic geometry codes (AG codes) and have been an area of intense research in the last decades. The AG codes are closely related to maximal curves, since the explicit construction of algebraic geometry codes over maximal curves provides codes with good parameters. In this talk we are going to introduce AG codes and some special families.

Symmetric Monomial Ideals

When: March 10
Speaker: Alexandra Seceleanu (Dept. of Mathematics, Univ. of Nebraska-Lincoln)
Abstract: Monomials are single term polynomials in several variables and ideals are a convenient way of organizing them into algebraic structures. The talk will illustrate quite literally, by means of pictures, how monomials build bridges between algebra, geometry and combinatorics. We will explore this idea by focusing on what it means for a monomial ideal to exhibit symmetry with respect to a few different groups. This leads to the notion of symmetric strongly sifted ideals, which we study in joint work with Alessandra Costantini.

Deep learning for real-time probabilistic traffic congestion prediction

When: March 24, 2023
Speaker: Pedro Gerum (CSU Business)
Abstract: Transportation systems depend on timely and accurate traffic congestion predictions to provide travelers with a reliable and satisfactory experience. However, most current models fail to account for unexpected situations and produce forecasts with limited information. Moreover, these models usually rely on extensive preprocessing to achieve relative accuracy. This research provides new probabilistic deep learning architectures geared specifically for traffic density forecasting that extend state-of-the-art methods. We address the quantile-crossing issue to ensure correct forecasts and perform an extensive experimental study using two distinct data sets. We verify that the proposed models are significantly more general, reliable, and accurate than traditional time-series models. The results suggest that the proposed models are (1) general across data sets without the need for preprocessing; (2) capable of capturing non-recurrent events that impact congestion; and thus (3) produce dynamic, accurate, and correct distributions of traffic density. The proposed deep learning regressors are the clear winners against traditional methods. They produce valid non-parametric distributions that can be directly used for congestion mitigation practices, unlike the other standard regressors.

Benefits of Simplification, Compression, and Reconstruction of 3D Objects using Chain Codes and Helical Paths

When: March 31, 2023
Speaker: Osvlado Tapia Dueñas (Visiting Scholar at CSU from Autonomous University of Aguascalientes)
Abstract: This presentation will explore the application of chain codes and helical paths in compression and simplification techniques for 3D objects and medical images. In the first part, we will explore the compression of medical images using chain codes to encode contour information into sequential codes and helical paths to order the resulting chain codes. In the second part, we will discuss the use of chain codes to compress 3D objects and context-free grammar to reduce the amount of information even more to obtain a simplified point cloud. We will also explore the application of helical paths in simplifying point clouds of 3D objects by ordering them in regions that compose the shape. Finally, we will present a method to reconstruct the 3D mesh from the simplified point cloud. This presentation will provide insights into the implementation and benefits of chain codes and helical paths in compression and simplification techniques for various applications.

MRSD Codes and Anticodes in the sum-rank metric

When: April 7 (1:00pm), 2023
Speaker: Eduardo Camps-Moreno (Visiting Scholar at CSU)
Abstract: Let F be a finite field and V a F-vector space. Let d be a norm over V. A linear space C<V is called a d-code if all the elements of C has norm at least d. C is called a r-anticode if the elements of C has norm at most r. In this talk we will discuss bounds on the dimensions of codes and anticodes in the sum-rank metric and we will provide characterization of optimal codes (called MSRD) and optimal anticodes.

A Confluence of Coding Theory, Combinatorics, and Commutative Algebra

When: April 14, 2023
Speaker: Sudhir R. Ghorpade (Indian Institute of Technology Bombay)
Abstract: We will outline some interactions between linear error correcting codes, combinatorial structures known as matroids, and certain notions and results in commutative and homological algebra. In particular, we will discuss a relatively recent work of Johnsen and Verdure where they associate a fine set of invariants, called Betti numbers, to linear codes. These are obtained by considering certain Stanley-Reisner rings corresponding to linear codes and studying the graded minimal free resolutions of these rings. It turns out that these Betti numbers determine several important parameters of linear codes such as generalized Hamming weights and generalized weight enumerators. However, computing Betti numbers is usually a hard problem. But it is tractable if the free resolution is "pure". We will review these developments and then outline an intrinsic characterization of purity of graded minimal free resolutions associated with linear codes. Further, we will discuss a characterization of (generalized) Reed-Muller codes that admit a pure resolution. We shall then turn to rank metric codes, which have been of some current interest, and discuss appropriate analogs of generalized Hamming weights in the context of rank metric codes. Motivated by a quest for a suitable definition of Betti numbers and minimal free resolutions associated with rank metric codes, we revisit a classical notion in combinatorial topology known as shellability, and then discuss its "q analogs" and some computations of homology. The talk is based on joint works with (i) Prasant Singh, (ii) Rati Ludhani, (iii) Trygve Johnsen, and (iv) Rakhi Pratihar and Tovohery Randrianarisoa. An attempt will be made to keep the prerequisites at a minimum.

Masking, maintenance and mimicry: the interplay of cell-intrinsic and cell-extrinsic effects in evolutionary games

When: April 21, 2023
Speaker: Rowan Barker-Clarke (CCF, Theory Division)
Abstract: Biological evolution is a stochastic yet inevitable process that lies at the heart of cancer, and thus underlies treatment resistance. Modelling the evolutionary processes underlying resistance is fundamental to both understanding and treating complex diseases, particularly in the interest of engineering solutions that avoid the evolution of multi-drug resistance entirely. There is a need for evolutionary theory and modelling that incorporates both biological stochasticity and the interactions between cells within tumors. Through the lens of experimental biology and a simple two species system, we frame cell-cell interactions in our mathematical approach as cell-extrinsic, growth-rate modifying, frequency-dependent interactions. In this way, we show the extent to which the presence of these ecological interactions can modify the evolutionary trajectories that would be predicted from cell-intrinsic properties alone. We show that these interactions can modify evolution in such ways as to mask, mimic, or maintain the results of cell intrinsic fitness advantages. This work has implications for the interpretation and understanding of evolution; a result which may explain an abundance of apparently neutral evolution in cancer systems and heterogeneous populations in general. In addition, the derivation of an analytical result for stochastic, ecologically dependent evolution paves the way for treatment approaches involving genetic and ecological control.

Wiggling and Paddling: Exploring Tomopteris Swimming Performance

When: April 28, 2023
Speaker: Nick Battista (The College of New Jersey, Mathematics)
Abstract: The soft-bodied, midwater polychaete Tomopteris is an interesting swimmer. Not only do Tomopteris swim continuously throughout their life, they also perform two modes of locomotion simultaneously: metachronal paddling and bodily undulation. Tomopteris have two rows of flexible legs (parapodia) positioned on opposite sides of its body. Although each row performs a metachronal beating pattern, they paddle out of phase to one another. Both of these paddling behaviors occur in concert with lateral bodily undulation. The undulation appears to further displace the parapodia, assisting the metachronal paddling process. We created a self-propelled, fluid-structure interaction model of a Tomopteris to explore how these two modes of locomotion synergize to generate effective swimming. In particular, we studied performance holistically over a 6D parameter space (leg length, leg number, paddling amplitude, undulation amplitude, body width, and fluid scale) with our sights on investigating higher-dimensional parameter spaces. In today's talk, I will describe how we approach studying Tomopteris swimming, through a blend of computational fluid dynamics and machine learning techniques.

Maximum Zeros and Generalized Hamming Weight

When: May 5, 2023
Speaker: Eliseo Sarmiento Rosales (Visiting Scholar at CSU, Prof Instituto Politécnico Nacional, Mexico)
Abstract: This talk explores the relationship between the maximum number of zeros of polynomials over finite fields and generalized Hamming weights. We examine various methods employed to solve these problems and provide bounds for computing the maximum number of zeros in some cases.

Title: TBA

When: Zhishen Shuai (Univ. of Central Florida)
Speaker: May 19 (10 am), 2023

Fall 2022

Jordan Decompositions of Tensors and Applications to Quantum Information

When: October 14, 2022
Speaker: Luke Oeding (Auburn University)
Abstract: The Jordan normal form for matrices is a powerful classification tool as it provides a test to determine which matrices are similar (in the same orbit), and whether one orbit contains another or not. One wonders what a natural generalization to hypermatrices (tensors) would look like. We focus on the algebraic structure of Jordan decompositions, expanding on an idea of Vinberg to combine a tensor space and a natural Lie algebra acting on it into an auxiliary algebra. Viewed as endomorphisms of this algebra we associate adjoint operators to tensors. We show that the group actions on the tensor space and on the adjoint operators are consistent, which endows the tensor with a Jordan decomposition. We utilize aspects of the Jordan decomposition to study orbit separation and classification in examples that are relevant for quantum information. This is joint work with Frederic Holweck (UTBM)

Representations of Special Classes of Linear Codes

When: October 21, 2022
Speaker: Henry Chimal-Dzul (Notre Dame Univ.)
Abstract: Dr. Chimal-Dzul obtained his PhD in Mathematics at Ohio University in 2021. His first job as a postdoc was at the University of Zurich where he worked with the prestigious Applied Algebra Group of Professor Joachim Rosenthal. Currently, he is a visiting assistant professor at University of Notre Dame. His lines of research are ring and module theory and their applications to coding theory and cryptography.

Explorations in Resources for Linear Algebra Courses

When: October 28, 2022
Speaker: Paul Zachlin (Lakeland) and Anna Davis (Ohio Dominican)
Abstract: In 2018, the Ohio Open Ed Collaborative (OOEC) sponsored the development of a Linear Algebra OER that meets the Ohio Transfer Module standards. The text was developed using the interactive XIMERA platform. The first edition of the text became available in January 2019 and since then has been used by multiple instructors at several institutions. Based on experience and feedback, two of the original authors returned to the project in 2022 to improve and expand the text. In this presentation we will highlight new additions to the text, such as many new GeoGebra interactives, and discuss how this text can be customized, re-mixed, and used in the classroom.

ZPD Algebras and Related Questions

When: November 4, 2022
Speaker: Hayden Julius (YSU, former student at CSU)
Abstract: An algebra is called zero product determined (zpd) if every bilinear map that vanishes on zero product pairs must be implemented by a linear transformation. Zpd algebras arose from the study of certain preserver problems in algebra and analysis concerning linear transformations preserving zero divisor structure. In this talk we will motivate zpd algebras, provide a few examples, and discuss some recent related results where the role of the zero element is generalized.

Pulsing Xeniid Corals Modeling and SImulation:  Mixing, Photosynthesis, and Muscle Contraction

When: November 18, 2022
Speaker: Matea Santiago (U. Arizona)
Abstract: Sessile Xeniid corals rhythmically pulse their tentacles by actively contracting their muscles. The behavior is unusual in that it doesn't seem to enhance feeding. Rather, experimental results have indicated that the pulsing facilitates the photosynthesis of their symbiotic algae by mixing the fluid to advect photosynthesis' waste, oxygen, away from the tentacles. This work seeks to use modeling and numerical simulation to understand this unique behavior using various methods and approaches. I will first discuss my thesis work which uses the classic immersed boundary method to numerically simulate the elastic coral tentacles' interaction with the surrounding fluid in two dimensions. The simulated velocity field is then used to find the Poincaré map, and the fluid mixing is quantified using the map's manifolds. I also coupled a photosynthesis model, where the tentacles act as an oxygen source. This project has progressed to fully three-dimensional simulations using IBAMR, an open-source, adaptive, parallelizable implementation of the immersed boundary finite element method. In this newer work, coral pulsing is driven by muscle contraction rather than prescribed motion, allowing for emergent behavior.

Spring 2022

Honors Project Presentation - Location Julka Hall 338

When: April 26, 2022
Speaker: Katherine Sammon

Roles of Cellular Anisotropy and Heterogeneity in Life

When: April 29, 2022
Speaker: Qixuan Wang (UC Riverside)
Abstract: Cells can be structurally anisotropic, and they can be heterogeneous due to either genetic or environment clues. Cellular anisotropy and heterogeneity might lead to interesting behaviors of both an individual cell and a collection of cells. In this talk we will discuss the roles of cellular anisotropy and heterogeneity in two systems. In the first part, we will discuss how anisotropic flagella bending rigidity affects the flagellar beating dynamics. Flagellar beating is controlled by molecular motors that exert forces along the length of the flagellum and are regulated by a feedback mechanism coupled to the flagellar motion. We build on previous work on sliding-controlled motor feedback to develop a fully three-dimensional description of flagellar beating, accounting for both bending and twist. We show that with isotropic bending, three dimensional spiral modes are spontaneously generated beyond a critical molecular activity. On the other hand, when a bias in the bending directions presents, the three-dimensional spiral modes give way to planar beating. In the second part, we will discuss how hair follicle heterogeneous responses to signals regulate the follicle temporal growth dynamics. Hair follicles are mini skin organs rich of stem cells, and they undergo cyclic growth. The growing phase – anagen of a hair follicle is tightly controlled by a group of epithelial transient amplifying (TA) cells. Using an interdisciplinary approach combined of multi-scale modeling and lineage tracing experiments, we show that cellular heterogeneity based on cell division generations generates the clonal drift phenomenon that prolongs the anagen.

Reserved for Honors Project Presentations

When: May 6, 2022
Speaker: B. Kovacic, J. Rausch, R. Schonhuitt (CSU)

Misc.

When: March 8 - April 1, 2022
Speaker: Candidate Interviews

Fall 2021

Structure of Codes for the Sum-Rank Metric

When: October 15, 2021
Speaker: Alberto Ravagnani (Eindhoven)
Abstract: I will discuss the fundamental properties of error-correcting codes in the sum-rank-metric space. These are linear spaces of matrix tuples (of mixed size) endowed with the sum-rank distance. The new results I will present include upper bounds for the size of sum-rank-metric codes, existence results, and duality properties.

Degree bounds for invariant skew polynomials

When: October 22, 2021
Speaker: Francesca Gandini (Kalamazoo College)
Abstract: When we consider the action of a finite group on a polynomial ring, an invariant is a polynomial unchanged by the action. A famous result of Noether states that in characteristic zero the maximal degree of a minimal generating invariant is bounded above by the order of the group. Our work establishes that the same bound holds for invariant skew polynomials in the exterior algebra. Our approach to the problem relies on a theorem of Derksen that connects invariant theory to the study of ideals of subspace arrangements. We reduce the problem to establishing a bound on the Castelnuovo Mumford regularity of intersections of linear ideals in the exterior algebra, which we prove using tools from representation theory. We also examine another result from classical invariant theory, Weyl’s Polarization Theorem, and show that this result does not hold in the exterior algebra but also provide an alternative bound that does hold in this context.

Spring 2021

Triangles and Princesses and Bears! Oh My!

When: January 29, 2021
Speaker: David Duncan (JMU)
Abstract: Several years ago, a friend of mine, Ben Schmidt, came across an interesting math puzzle in an old Russian puzzle book. The puzzle involves three princesses and three bears, with the bears allowed to move according to certain rules. Upon investigating these rules, we discovered unexpectedly rich mathematical structures making connections with dynamics, mathematical biology, and even quantum mechanics! In this talk, I will describe the puzzle, its solution, and some of the math that has come out of our study.

Mechanisms Underlying Spatiotemporal Patterning in Microbial Collectives: A Model's Perspective

When: February 26, 2021
Speaker: Bhargav Karamched (Florida State)
Abstract: We describe a spatial Moran model that captures mechanical interactions and directional growth in spatially extended populations. The model is analytically tractable and completely solvable under a mean-field approximation and can elucidate the mechanisms that drive the formation of population-level patterns. As an example, we model a population of E. coli growing in a rectangular microfluidic trap. We show that spatial patterns can arise because of a tug-of-war between boundary effects and growth rate modulations due to cell-cell interactions: Cells align parallel to the long side of the trap when boundary effects dominate. However, when cell-cell interactions exceed a critical value, cells align orthogonally to the trap’s long side. This modeling approach and analysis can be extended to directionally growing cells in a variety of domains to provide insight into how local and global interactions shape collective behavior. As an example, we discuss how our model reveals how changes to a cell-shape describing parameter may manifest at the population level of the microbial collective. Specifically, we discuss mechanisms revealed by our model on how we may be able to control spatiotemporal patterning by modifying cell shape of a given strain in a multi-strain microbial consortium.

Mathematics of Digital Image Interpolation

When: March 12, 2021
Speaker: Seongjai Kim (Mississippi State)
Abstract: Digital zooming is a method of magnifying the size of digital photographic or video images. It is usually accomplished employing interpolation methods, with no adjustment of the camera's optics. However, the resulting images hardly gain optical resolution and may involve interpolation artifacts such as ringing (aliasing), blurring, and image halo. Various interpolation methods have been proposed in order to minimize interpolation artifacts, particularly by avoiding the interpolation evaluation across the edges. This talk will begin with basic principles in interpolation. Then we will consider mathematical image interpolation methods such as the curvature interpolation methods (CIMs) and the sharp edge-enhancing diffeomorphism (SEED), which outperform state of-the-art interpolation methods. These mathematical image interpolation methods minimize interpolation artifacts and enhances the optical resolution (super-resolution) as well, by avoiding the interpolation evaluation across the edges and trying to sharpen the image in the normal direction of the edges. Various numerical examples will be shown to verify the claim.

Spectra of commutative BCK-algebras

When: March 26, 2021
Speaker: Matt Evans (Oberlin College)
Abstract: BCK-algebras are the algebraic semantics of a non-classical logic. Like for commutative rings, there is a notion of a prime ideal in these algebras, and the set of prime ideals is a topological space called the spectrum. By work of Stone (and later, Priestley), there is a close connection between these spectra and distributive lattices with 0. In this talk I will discuss some recent results on the interplay between commutative BCK algebras, their spectra, and distributive lattices.

Discussion of Online Homework Systems for Future

When: April 9, 2021
Speaker: Department of Math/Stat Faculty

Research Talks

When: April 12 - 16, 2021
Speaker: Job Candidates

Honors Undergraduate Research Presentations

When: April 30, 2021
Speaker: K. Ball and S. Alfaro (CSU Math)

Fall 2020

Using Topology to Measure Dynamics of Time-Varying Systems

When: September 18, 2020
Speaker: Lori Ziegelmeier (Macalester College)
Abstract: A time-varying collection of metric spaces as formed, for example, by a moving school of fish or flock of birds, can contain a vast amount of information. There is sometimes a need to simplify or summarize the dynamic behavior, and recently, topological tools have been applied to this purpose. One such method is a crocker plot, a 2-dimensional image that displays the (non-persistent but varying with scale) topological information at all times simultaneously. We use this method to perform exploratory data analysis and investigate parameter recovery via machine learning in the collective motion model of D’Orsogna et al. (2006). Then, we use it to choose between unbiased correlated random walk models of Nilsen et al. (2013) that describe motion tracking experiments on pea aphids. Finally, we discuss an extension of the crocker plot that is persistent and equivalent to the information in a persistence diagram at each point in time, and hence, inherits the nice stability properties of persistent homology.

A Mathematical Model for the Pest Control on a Broccoli Crop

When: October 9, 2020
Speaker: Sandra Elizabeth Delgadillo Aleman and Roberto Ku Carrillo
Abstract: In this work we propose an ode model that aims to abstract the most important characteristics of the larvae pest called Diamond Back Moth (DBM) that affects the broccoli crop. DBM is a major plague because it feeds on the broccoli leaves, affecting its growth and causing economical losses. For this reason, it is important to have a mathematical and in-silico model that allows us a more efficient pest control based on the DBM growth dynamics. Our model considers two control mechanisms used for farmers to reduce the DBM population. They are a) the biological pesticides which consist of a toxin that kills the DBM larvae, and b) other biological control such as insects which are natural predators or parasites DBM eggs. These two pest control strategies are far less toxic than the chemical pesticides. In our model, we assume exponential growth, and also, that there is migration from the surroundings at a constant rate. Finally, we use the data provided by a local company that uses the biological pesticide Bacillus thuringiensis and the Diadegma and trichogramma wasp to control the growth of the DBM. The provided data were used to determine the parameters of our model. We present the solutions of the adjusted model. Such solutions approximate the data sets and show an advance in this direction.

Q-Borel Ideals

When: October 16, 2020
Speaker: Eliseo Sarmiento Rosales (National Polytechnic Institute, Mexico)
Abstract: Fix a poset Q on {x1,...,xn}. A Q-Borel monomial ideal I ⊆ K[x1,...,xn] is a monomial ideal whose monomials are closed under the Borel-like moves induced by Q. A monomial ideal I is a principal Q-Borel ideal, denoted I = Q(m), if there is a monomial m such that all the minimal generators of I can be obtained via Q-Borel moves from m. We study powers of principal Q-Borel ideals, we show that all powers of Q(m) agree with their symbolic powers, and that the ideal Q(m) satisfies the persistence property for associated primes.

A Wasserstein Norm for Signed Measures

When: October 23, 2020
Speaker: Magali Tournus (Ecole Centrale Marseille, France)
Abstract: We introduce the optimal transportation interpretation of the Kantorovich norm on the space of signed Radon measures with finite mass, based on a generalized Wasserstein distance for measures with different masses. With the formulation and the new topological properties, we obtain for this norm, we prove existence and uniqueness for solutions to non-local and non-linear transport equations with source terms, when the initial condition is a signed measure. I will make this talk pedagogical, explain using examples what is the Wasserstein distance, and explain why it is a big challenge to study partial differential equations in Wasserstein spaces.

Using randomness and learning to calculate Gröbner bases in a novel way

When: October 30, 2020
Speaker: Sara Jamshidi Zelenberg (Lake Forest College)
Abstract: We know how to solve a system of linear equations--the majority of college educated people have been exposed to Gaussian elimination at one point in their life. To solve a system of polynomial equations, however, can be very tricky. The current method is to understand the ideal generated by the polynomial system and calculate that ideal's Gröbner basis (BG). The method for calculation is analogous to Gaussian elimination and is referred to as Buchberger's (BOOK-burger) algorithm. Other approaches to the problem, like the F4 and F5 algorithms, can be thought of as different varieties of Buchberger's algorithm. Improvements on the current algorithm are difficult to achieve as the method is difficult to distribute and can become wildly complex. In this talk, we discuss potential improvements using ML predictions with some preliminary results. There is growing interest in determining if we can improve the computation when predictions are possible.

Equations and Syzygies for Varieties of Binary Forms

When: November 6, 2020
Speaker: Claudiu Raicu (Univ. of Notre Dame)
Abstract: The space of binary forms of degree d has a natural stratification given by the factorization pattern of a form, which is indexed by the partitions of d. For instance, those binary forms that are d-th powers of a linear form trace out a rational normal curve. Those that factor as a^(d-1) * b, with a,b linear forms, describe the tangent developable of the rational normal curve, etc. It is an interesting open problem to describe the defining equations of the closures of the factorization strata, as well as their higher syzygy modules. I will discuss some of the known results and recent work on this problem, based on a beautiful interaction between geometry and the representation theory of SL_2.

Mathematical Modeling of Colon Cancer Progression

When: November 13, 2020
Speaker: Arkadz Kirshtein (UMass Amherst)
Abstract: Every colon cancer has its own unique characteristics, and therefore may respond differently to identical treatments. In a recent article we develop a data driven mathematical model for the interaction network of key components of the immune microenvironment in colon cancer. We estimate the relative abundance of each immune cell from gene expression profiles of tumors, and group patients based on their immune patterns. Then we compare the tumor sensitivity and progression in each of these groups of patients and observe differences in the patterns of tumor growth between the groups. In this talk I will explain methods used for modeling, immune pattern estimation, and sensitivity analysis of the resulting system. Then I will present the results of the model and its analysis. This is a Joint work with Leili Shahriyari, Wenrui Hao, Shaya Akbarinejad, Trang Le, and Rachel Aronow.

A Computational Model for Metabolism and Circadian Clock

When: November 20, 2020
Speaker: Mehrshad Sadria (U. Waterloo)
Abstract: Ageing is associated with impairments in a number of regulatory processes, including in energy deregulation that affects multiple metabolic pathways and in the circadian rhythms. In the management of metabolic stress and ageing mechanisms, key proteins such as mTORC, AMPK, and sirtuins are known to play an essential role. An impairment in these mechanisms is commonly associated with cellular ageing and degenerative diseases. To understand the complex interactions of ageing‐related signalling pathways and environmental signals, and the impacts on lifespan and health span, we developed a computational model of ageing signalling pathways. The model can be used as an essential component to simulate gene manipulation, therapies (e.g., rapamycin and wortmannin), calorie restrictions, and chronic stress, and to assess their functional implications on longevity and ageing‐related diseases.

Monomials, convex bodies, and optimization

When: December 4, 2020
Speaker: Alexandra Seceleanu (U. Nebraska-Lincoln)
Abstract: Monomials are deceivingly simple algebraic expressions that consist of products of variables. However, when monomials are grouped together to form monomial ideals, they can be responsible for creating intricate patterns. For example, any hypergraph, as well as any collection of linear spaces spanned by standard basis vectors in a Euclidean space of arbitrary dimension can be encoded by monomial ideals. In this talk, we give monomial ideals geometric shape as we associate to them certain convex geometric bodies, namely the classical Newton polyhedron and the more modern symbolic polyhedron. We consider two linear optimization problems having these convex bodies as feasible sets and use them to establish a relationship between combinatorial commutative algebra and discrete optimization. This is based on joint work with the participants of the 2020 Polymath REU.

Mathematics Honors Senior Project

When: December 7, 2020
Speaker: Elisabeth Helmick (CSU Math Honors Student)

Spring 2020

Computationally predictive models of integrated cerebral metabolism, electrophysiology and hemodynamics

When: January 31, 2020
Speaker: Daniela Calvetti, Case Western Reserve University
Abstract: Understanding the energetic requirements of brain cells during resting state and during high neural activity is a very active research area where mathematical models have contributed significantly by providing a context for the interpretation of the experimental results. We recently proposed novel computational predictive models that connect cerebral electrophysiological activity, cellular metabolism and hemodynamic response via a system of double feedback mechanisms based on energy demand and production. In addition to the difficulty of interfacing the modeling paradigms for the different brain functions, many computational challenges had to be addressed, mostly due to the very different characteristic times at which the electrical, metabolic and hemodynamic events occur. Computed experiments with these models for different protocols, that include awake resting state, transitions between resting state and neural activation and ischemic episodes, as well as cortical spreading depression episodes, show that the model predictions are in good agreement with experimental observations.

COSHP Teaching Award Luncheon

When: February 7, 2020 @ 12:00-1:30PM in the Student Center
Speaker: COSHP Teaching Award Luncheon

Differential Equations and Monodromy Problems

When: February 14, 2020
Speaker: Sachin Gautam, Ohio State University
Abstract: Differential equations were introduced in the mathematical world by Newton and Leibniz, around the turn of the 18th century. Ever since, they have been studied from various perspectives, and contributed to the development of many beautiful theories. The notion of monodromy was introduced by Weierstrass in the latter half of the 19th century. It has been used in the works of many mathematicians as a powerful machinery to produce invariants of differential equations. Recent developments in mathematical physics, enumerative geometry and representation theory have discovered numerous new families of differential equations. The problem of computing their monodromy has led to fruitful new directions of research. In this talk I will give an overview of some of these topics of interest, and a sample of connections they have uncovered, a lot of them still conjectural.

Maximizing Flow over Space Networks using Temporal Graphs and Sheaves

When: February 21, 2020
Speaker: Robert Short, John Carroll University
Abstract: With the increased presence of humans in space, there is an increased need for understanding how networking can work in interplanetary environments. Unlike Earth networks, the dynamics of planet motion and motion of objects in space causes several difficulties in translating traditional networking theory to space networks. The new networking theory relevant to space networks often gets the name "Delay/Disconnection Tolerant Networking" or "DTN" due to the delays and disconnections inherent to space networks. The flexible nature of this networking theory has made finding mathematical frameworks that are effective at describing or comparing DTN models more challenging than anticipated. The goal of this work is to argue for a mathematical foundation for DTN models that allows us to effectively compare different properties. To this end, we have constructed models of proposed space networks and computed the maximum amount of information flow over each network using our techniques. The key tool that we introduce to the literature is the Temporal Flow Network, a time-varying graph that allows us to model known delays/disconnections effectively. In addition, we point to the theory of sheaves as a means of introducing consistency into data flow over space networks. In this talk, we will describe the problems of DTN and why Temporal Flow Networks are an effective model for a typical space network. We will also discuss how sheaves may be useful in translating traditional networking tools into a DTN framework.

A Study on Systemic Risk in the Chinese Commercial Banks

When: March 20, 2020 (POSTPONED due to Extended Spring Break from COVID19)
Speaker: Hong Mei Li, Liaoning University (China)
Abstract: The services of the commercial banks, to a greater or less extent, have become more complicated as the structure changes in banking for the past few decades. These led the commercial banks facing many types of risks. Banks are nodes of the whole financial system. Once the crisis occurs on any link in the system, it will affect the stability of the whole system. And then through the contagion and expansion of the risk, the systemic risk will break out. This implies that there is no single commercial bank immune from the systemic risk. With this background in mind, we study, in this project, the ability of the systemic risk faced by commercial banks (mainly focus on the Chinese commercial banks) using the SRISK methodology to measure the systemic risk of Chinese commercial banks.

Title: TBD

When: March 27, 2020 (POSTPONED due to suspension from face-to-face activities from COVID19)
Speaker: Steve Szabo, Eastern Kentucky University

Title: TBD

When: April 10, 2020 (POSTPONED due to suspension from face-to-face activities from COVID19)
Speaker: Claudiu Raicu, Notre Dame University

Science Research Day

When: April 17, 2020 (POSTPONED due to suspension from face-to-face activities from COVID19)
Speaker: COSHP/COE Faculty

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Fall 2019

From Nerve Net to Vortex Ring: A Computational Modeling Approach to Medusan Biomechanics

When: September 20, 2019
Speaker: Alex Hoover, U. Akron
Abstract: In order for an organism to have an robust mode of locomotion, the underlying neuromuscular organization must be adaptable in a changing environment. In jellyfish, the activation and release of muscular tension is governed by the interaction of pacemakers with the underlying motor nerve net that communicates with the musculature. This set of equally-spaced pacemakers located at bell rim alter their firing frequency in response to environmental cues, forming a distributed mechanism to control the bell's muscular contraction. The relative simplicity of the jellyfish nervous system presents mathematicians with the opportunity to examine an intriguing multi-scale, multi physics system with many potential applications to soft-body robotics and tissue engineered pumps. In this talk, we explore the control of medusan neuromuscular activation in with a model jellyfish bell immersed in a viscous fluid and use numerical simulations to describe the interplay between active muscle contraction, passive body elasticity, and fluid forces. The fully-coupled fluid structure interaction problem is resolved using an adaptive and parallelized version of the immersed boundary method (IBAMR). This model is then used to explore the interplay between the speed of neuromechanical activation, fluid dynamics, and the material properties of the bell.

Gelfand-type Problems for Turbulent Jets

When: September 27, 2019
Speaker: Peter Gordon, Kent State University
Abstract: In this talk I will discuss the model of auto-ignition (thermal explosion) of a free round reactive turbulent jet. This model falls into the general class of Gelfand-type problems and constitutes a boundary value problem for a certain semi-linear elliptic equation that depends on two parameters: 𝛼 characterizing the flow rate and 𝜆 (Frank Kamentskii parameter) characterizing the strength of the reaction. Similar to the classical Gelfand problem, this equation admits a solution when the Frank-Kametskii parameter 𝜆 does not exceed some critical value 𝜆𝛼 and admits no solutions for larger values of 𝜆. I will discuss the sharp asymptotic behavior of the critical Frank-Kamenetskii parameter in the strong flow limit 𝛼 ≫ 1. I will also give a detailed description of the extremal solution (i.e., the solution corresponding to 𝜆∗) in this regime. This is a joint work with Fedor Nazarov and Vitaly Moroz.

New Functional Polarity Inequalities

When: October 4, 2019
Speaker: Dan Florentin, CSU
Abstract: Several functional analogs of fundamental geometric inequalities have appeared in recent decades, beginning with the works of Prekopa and Leindler in the 1970's. In this talk I will, after discussing the method of functionalization of geometry, present new functional extensions of the Brunn-Minkowski inequality and their consequences. I will also discuss functional counterparts of the Blaschke-Santalo inequality, regarding the Mahler volume of a convex body.

Discrete Morse Theory and Topological Complexity of Unordered Graph Configuration Spaces

When: October 18, 2019
Speaker: Steven Scheirer, Ashland Univ.
Abstract: The topological complexity of a space X, denoted by TC(X), is related to the problem of motion planning within the space X. More specifically, TC(X) can be viewed as the minimum number of "continuous rules" that are required to describe how to move between any two points in X. In this talk, we will be interested in the topological complexity of unordered graph configuration spaces. We will discuss an approach to studying these spaces using discrete Morse theory and use this approach to determine the topological complexity for certain classes of graphs.

Modeling the Long-term Effects of Thermoregulation on Human Sleep

When: October 25, 2019
Speaker: Alicia Prieto Langarica, Youngstown State Univ.
Abstract: It has long been believed that there is a strong connection between human sleep and energy exertion. The link between human sleep and energy exertion has long been regarded as part of the reasoning for why we need sleep. Perhaps though, the underlying link is more complex than previously believed. In this paper, we describe a mathematical model of human sleep--wake behavior, which supports a recent unifying theory for the function of sleep among all species. The model incorporates thermoregulatory functions and how temperature affects the stages of sleep and its effect on metabolic processes. Solutions of the model are computed for dingle night and average night simulations; Measurements obtained from the simulations as well as the dynamics of the model are discussed.

Stock Price Fluctuations and Productivity Growth

When: November 15, 2019
Speaker: Phuong Ngo, CSU Economics
Abstract: We study the relationship between stock prices and fluctuations in total-factor productivity (TFP). We document a strong predictability of lagged stock price growth on future TFP growth at medium horizons. To explore the sources of this co-movement, we develop a one-sector real business model augmented to allow for (i) endogenous technology through R&D and adoption, and (ii) exogenous shocks to the risk premium. Model simulations produce predictability patterns quantitatively similar to the data. A version of the model with exogenous technology produces no predictability of TFP growth. Decomposing historical TFP, we show that the predictability uncovered in the data is fully driven by the endogenous component of TFP. This finding suggests that fluctuations in risk premia impact TFP growth through their effect on the speed of technology diffusion instead of responding to exogenous fluctuations in future TFP.

Reed-Muller codes with application to quantum computation and information retrieval

When: November 22, 2019
Speaker: Felice Manganiello, Clemson University
Abstract: In recent years communication problems have evolved based on the needs of the society. In this talk we will consider two very distinct modern communication problems. The first one is the problem of achieving universal fault-tolerant quantum computation and the second is of multiparty information retrieval. Although these two problems are completely different, there is a family of classical linear codes that adapts to the needs of both. Reed-Muller (RM) codes are a well-known family of classical linear codes based on the evaluation of multivariate polynomials over finite fields. They have been extensively studied throughout the years and have been previously used in deep space communication. Their advantageous algebraic properties make them a good candidate for many applications. This is a talk aimed to a broad audience. We will introduce RM codes and learn some of their most important algebraic properties. We will then see how RM codes can help in achieving universal fault-tolerant quantum computation, one of the most vital theoretical aspects of quantum information processing, and how their local properties make them employable for problems of multiparty information retrieval.

Spring 2019

Linking influenza virus infection to risk of cardiovascular events: a mechanistic approach

When: February 22, 2019
Speaker: Zachary McCarthy, York University
Abstract: There is heavy burden associated with influenza including all-cause hospitalization as well as severe cardiovascular and cardiorespiratory events. Influenza induced cardiac events are associated with multiple biological pathways in a human host. To study the contribution of influenza virus infection to cardiovascular events, we develop a dynamic model which incorporates the immune response, inflammatory system, and blood coagulation. We synthesize these biological systems and integrate them into a cohesive modelling framework to study their connections to blood clotting. The primary outcome of this model is a blood clot of an artery or blood vessel resulting from influenza virus infection. We show the dynamics of the resulting model and demonstrate how clot severity depends on initial prothrombin levels. We also utilize our model and clinical data to inform a threshold level of the inflammatory cytokine TNFα which causes tissue factor induction and subsequent blood clotting. This model may be used to aid epidemiological study and also explore how individual biological components contribute to blood clotting events. Overall, the model can potentially identify individuals at risk of clotting based on their circulating prothrombin levels and may guide how future vaccines should be designed to optimally interact with the immune system.

Mathematics predicts discontinuities in dynamics of living cells

When: March 22, 2019
Speaker: Mykhailo Potomkin, Penn State University

On the nonabelian tensor product of cyclic groups of p-power order

When: March 29, 2019
Speaker: Luise-Charlotte Kappe, Binghamton University
Abstract: Let G and H be groups which act on each other and each of which acts on itself by conjugation, then the actions are compatible if (gh)g' = g(h(g-1 g')) and (hg)h' = h(g(h-1 h')) for g,g'∈G and h,h'∈H. Compatible actions play a very important role in determining the nonabelian tensor product. The nonabelian tensor product, G⊗H, was introduced by Brown and Loday in 1984. The nonabelian tensor product is the group generated by g⊗h with two relations gg'⊗h = (gg'⊗gh)(g⊗h) and g⊗hh' = (g⊗h)(hg⊗hh') for g,g'∈G and h,h'∈H, where G and H act on each other in a compatible fashion and act on themselves by conjugation. In 1987, Brown et al. gave an open problem in determining whether the tensor product of two cyclic groups is cyclic. Visscher in 1998 has shown that the nonabelian tensor product is not necessarily cyclic, but he only focused on the case of cyclic groups of 2-power order where the action is of order two. In this paper, the compatibility and the nonabelian tensor product of cyclic groups of order p2 with the actions of order p are determined.

Mathematical Modeling of Resistance to Anti-Cancer Drugs

When: April 5, 2019
Speaker: Nara Yoon, Cleveland Clinic (LRI)
Abstract: Cancer treatments, including drug therapies, eventually fail due to the resistance induced by the treatments. In this talk, I will discuss several recent projects about drug resistance. In one project, we explored underlying process of resistance development. It has been conventionally assumed that the evolution of tumor cells (from sensitive to resistant types) occur by a single process of ‘driver’ mutation. However,our experimental data and modeling study do not support this. Instead, we have observed that the effect of the drug seems to change cell types gradually over time. I will talk about this new hypothesis, along with the utilized data,model and analysis. Another topic of interest are effective drug regimens that could prevent or mitigate the onset of resistance. We have focused on sequential application of drugs where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. Based on drug cycles linked by the relationships of collateral sensitivity, we have (i) built a mathematical model, (ii) found the optimal way to switch drugs, and (iii) analyzed clinical meaning and implementation of our optimal therapy, all of which will be discussed in the talk.

Fluid-Structure Interactions with Biological Applications

When: April 12, 2019
Speaker: Longhua Zhao, CWRU

Title: TBD

When: April 26, 2019
Speaker: Adam Van Tuyl, McMaster University

Title: TBD

When: May 3, 2019
Speaker: Prayat Poudel, Centre College (KY)

Coding and dominant point detection for shape-of-objects

When: May 7, 2019
Speaker: Hermilo Sánchez-Cruz, Universidad Autónoma de Aguascalientes

Fall 2018

Chaos and Levy walks in swarming bacteria

When: November 2, 2018
Speaker: Gil Ariel, Bar Ilan University (Israel)
Abstract: Bacterial swarming is a collective mode of motion in which cells migrate rapidly over surfaces. Swarming is typically characterized by densely packed groups moving in coherent patterns of whirls and flows. Recent experiments showed that within such dense swarms, bacteria are performing super-diffusion that is consistent with Levy walks – random processes in which the Gaussian central limit theorem fails. We present a simple model of a spheroidal, self-propelled particle, moving in the effective, vortex-like flow generated by all other bacteria. Mathematically, the model presents a new mechanism for Levy walks in chaotic maps that are reversible but not volume preserving. Levy walking emerges from sticking close to regular, fractal-like areas with multiscale periodicities. A bifurcation separates a chaotic, super-diffusive regime and a regular, ballistic one. Biologically, it explains how cells can fine-tune the geometric properties of their trajectories.

Title: TBD

When: November 30, 2018
Speaker: Semyon Alekser, Tel Aviv University (Israel)

Honors Project Presentations (if needed)

When: December 7, 2018
Speaker: CSU Math Honors Students

Spring 2018

Graphical Presentations of Tensor Categories

When: February 16, 2018
Speaker: Ryan Vitale, Indiana University

Galois Groups in Enumerative Geometry and Applications

When: March 19, 2018
Speaker: Frank Sottile, Texas A&M University

Continuous and Discrete Energy Based Methods for Accurate Force Computations on Shells in the Immersed Boundary Method

When: March 30, 2018
Speaker: Wanda Strychalski, CWRU

Registries-based Population Size Estimation: An Algebraic Statistics Perspective

When: April 6, 2018
Speaker: Ann Johnston, Penn State University

Monodromy in classical and quantum mechanical systems 

When: April 10, 2018
Speaker: Mark Hamilton, Mount Allison University (Canada)

Spring 2017

Deblurring Images with Mathematical Models

When: April 21st, 2017
Speaker: Malena Espanol, Univ. of Akron

Towards a new digital homotopy

When: April 7th, 2017
Speaker: Nick Scoville, Ursinus College (PA)

Advances in phase reduction: discontinuous, stochastic, and singular oscillators

When: February 3rd, 2017
Speaker: Peter Thomas, Case Western Reserve University 

Fall 2016

Resolution of the Priority Dispute on the Special Theory of Relativity; Einstein, Poincare, Lorentz, Larmor, and Voigt

When: December 2, 2016
Speaker: Jon C. Freeman, NASA Glenn Research

Gas Transport and Applications to Materials Processing

When: November 4, 2016
Speaker: Andrew Jones, Florida A&M University

Spring 2015

Coin Tossing and Fubini's Nightmare

When: April 10, 2015
Speaker: Ali Tahzibi, University of Sao Paulo at Sao Carlos, Brazil

Topological Complexity: A product formula

When: February 4, 2015
Speaker: Paul-Eugene Parent, University of Ottawa

Fall 2014

Independence of polarization in geometric quantization

When: November 21, 2014
Speaker: Mark Hamilton, Mount Allison University

Spring 2014

STEMM Education: Fostering School University Connections

When: May 13, 2014
Speaker: Linda Gojak, National Council of Teachers of Mathematics

Phase Transitions in Random Cech complexes

When: April 2, 2014
Speaker: Omer Bobrowski, Duke University

A Transformation Class for Spatio-temporal Survival Data With a Cure Fraction

When: February 7, 2014
Speaker: Sandra Hurtado, Weill Cornell Medical College

Envelopes for Matrix-valued Regressions

When: February 5, 2014
Speaker: Shanshan Ding, University of Pennsylvania

Multivariate Analysis of Neural Spike Trains: Skellam Process with Resetting and Its Applications

When: February 3, 2014
Speaker: Reza Ramezan, University of Waterloo

Topological Complexity of Groups

When: January 31, 2014
Speaker: Mark Grant, Newcastle University, UK

Some Ideas from Combinatorics, Commutative Algebra and Topology in the Realm of Algebraic Geometry

When: January 29, 2014
Speaker: Jose Gonzalez, University of British Columbia

Multiplicities and Distinguishing Singularities

When: January 27, 2014
Speaker: Javid Validashti, University of Illinois at Urbana-Champaign

Fall 2013

The Mathematics of Life: Decisions, Decisions

When: November 22, 2013
Speaker: Jim Keener, University of Utah

Spring 2013

A mathematical view of fish migration

When: April 26, 2013
Speaker: Alethea Barbaro, Case Western Reserve University

Reconstructing manifolds and functions from noisy point samples

When: March 29, 2013
Speaker: Vidit Nanda, University of Pennsylvania

Enhanced surveillance on food-borne disease outbreaks: Dynamics of cross-contamination in biocidal wash procedure

When: March 1, 2013
Speaker: Dan Munther, Centre for Disease Modeling, York University

Mathematical Modeling of Immune-Modulated Tumor Growth

When: February 27, 2013
Speaker: Kathleen Wilkie, Tufts University School of Medicine

Analysis of RNA structures by using geometric shape descriptors

When: February 22, 2013
Speaker: Christian Laing, Wilkes University

Fall 2012

Closing the memory gap in stochastic functional differential equations-CANCELED

When: November 27, Tuesday, 2:50 PM, 2012
Speaker: Flavia C. Sancier-Barbosa, Wittenberg University

Some remarks on the hyperelliptic moduli of genus 3

When: November 16, 2012
Speaker: Tony Shaska, Oakland University

Generalized Cyclic Convolutional Codes

When: November 2, 2012
Speaker: Steve Szabo, Eastern Kentucky University

Spring 2012

Edge Ideals, Path Ideals, and the Linear Strand

When: April 27, 2012
Speaker: Rachelle Bouchat, Slippery Rock University

Closed range composition operators on Besov type spaces

When: April 13, 2012
Speaker: Maria Tjani, University of Arkansas

The Future of Introductory Statistics Courses and the Common Core State Standards in K-12

When: March 30 @ 4 PM, MC 136, 2012
Speaker: Christine Franklin, The University of Georgia

Topology and Robotics

When: March 9, 2012
Speaker: Mark Grant, The University of Nottingham

K3 surfaces, quantum black holes and a sporadic simple group

When: February 10, 2012
Speaker: John Duncan, Case Western Reserve University

Fall 2011

Topological Invariants Associated with Quantum Groups

When: December 2, 2011
Speaker: Qi Chen, Winston-Salem State University

Ehrhart theory in practice

When: November 4, 2011
Speaker: Benjamin Nill, Case Western Reserve University

Statistics and healthcare fraud investigations

When: October 14, 2011
Speaker: Don Edwards, University of South Carolina

Models of the Honey Bees Nest Site Selection Process

When: September 30, 2011
Speaker: Partha Srinivasan, Cleveland State University

On statistics related to trauma

When: September 16, 2011
Speaker: Michael Nowak, Northern Ohio Trauma System, Metro Hospital

Spring 2011

Characterization of Lie maps and other questions connecting Lie algebra and Ring Theory

When: May 4, 2011
Speaker: Mikhail Chebotar, Kent State University

Ranks of Polynomials

When: April 22, 2011
Speaker: Zach Teitler, Boise State University

Convex bodies and algebraic varieties

When: April 1, 2011
Speaker: Kiumars Kaveh, University of Pittsburgh

Minkowski length of polytopes

When: April 22, 2011
Speaker: Jenya Soprunova, Kent State University

Fall 2010

Manifold calculus of functors

When: December 3, 2010
Speaker: Victor Turchin, Kansas State University

Effective methods in geometry of polynomial mappings

When: November 5, 2010
Speaker: Janusz Adamus, The University of Western Ontario

The invariants of n points on the line, and spatial polygons

When: October 21, Thursday, 2010
Speaker: Benjamin Howard, University of Michigan

Sprig 2010

Resolution of Certain Binomial Ideals

When: April 8, Thursday, 2010
Speaker: Hema Srinivasan, University of Missouri, Columbia

A Model for Functional Genome-wide Association Studies of Dynamic Traits

When: April 2, 2010
Speaker: Rongling Wu, Pennsylvania State University

Pattern Formation of Glioma Cells Outside the Tumor Spheroid Core

When: March 26, 2010
Speaker: Yangjin Kim, University of Michigan - Dearborn

A Survey of Ghost Symmetry

When: March 5, 2010
Speaker: David Richter, Western Michigan University

Configuration Spaces of Hard Discs

When: February 26, 2010
Speaker: Matthew Kahle, Stanford University

Fluid Mechanics

When: February 12, 2010
Speaker: Andrew Resnick, Cleveland State University, Physics

Jump to year: 2009 | 2008 | 2007

Fall 2009

Next-Generation Sequencing Data Analysis and a Maximization Problem

When: November 20, 2009
Speaker: Shuying Sun, Case Comprehensive Cancer Center

When is normal normal? Approximation results for random measures

When: November 13, 2009
Speaker: Elizabeth Meckes, Case Western Reserve University

The Mathematics of Digital Entertainment - an Industry Perspective

When: October 16, 2009
Speaker: Sean Chang, Dreamworks

Mathematical Approaches on Some Image Processing and Analysis Problems

When: October 2, 2009
Speaker: Weihong Guo, Case Western Reserve University

Spring 2009

Fully Nonparametric Bayesian Analysis in Regression Model with Serially Correlated Errors

When: March 13, 2009
Speaker: Tanujit Dey, The College of William and Mary

H-Linked Graphs

When: February 27, 2009
Speaker: Mike Ferrara, The University of Akron

Spring 2008

Sequences with good correlation properties

When: May 1, 2008
Speaker: K.T. Arasu, Wright State University

Simulation of blood flow in a compliant vessel by the immersed boundary method

When: April 18, 2008
Speaker: Sookkyung Lim, University of Cincinnati

Graphs on surfaces and knot theory

When: April 11, 2008
Speaker: Sergei Chmutov, Ohio State University

Classification of Orthogonal Arrays by Integer Programming

When: March 21 @ 4 PM - 5 PM, 2008
Speaker: Dursun Bulutoglu, Air Force Institute of Technology

Conditional Servo/Integral Action in Nonlinear Control

When: March 7, 2008 In Stilwell Hall 103
Speaker: Hassan K. Khalil, Michigan State University

Fall 2007

On the local equatorial characterization of Zonoids

When: November 30, 2007
Speaker: Dima Ryabogin, Kent State University

Mathematical Foundations of Computer Generated Digital Entertainment

When: November 21, 2007 in RT 502
Speaker: Sean Chang, Dream Works Animation

Tropical Elimination Theory

When: November 16, 2007
Speaker: Jenia Tevelev, University of Massachusetts

Solving Lattice Point Problems Using Rational Generating Functions

When: November 8, 2007
Speaker: Kevin Woods, Oberlin College

Automorphisms of polynomial and free algebras

When: October 19, 2007
Speaker: Ualbai Umirbaev, Eurasian National University

Spring 2007

Geometric and Topological methods in protein structure analysis

When: April 20, 2007
Speaker: Yusu Wang, Ohio State Univesity

Graded Resolutions, Multiplicity and Graphs

When: April 13, 2007
Speaker: Hema Srinivasan, University of Missouri, Columbia

Adventures in Teaching with Technology

When: March 30, 2007
Speaker: Webster West, Texas A & M University

Numerical Methods for Partial Differential Equations

When: March 2, 2007
Speaker: C.L. Chang, Cleveland State University

The Lights Out Game: A Domination Problem with Parity Constraints

When: February 23, 2007
Speaker: Johannes Hatzls, University of Waterloo

The Busemann-Petty problem for arbitrary measures

When: February 16, 2007
Speaker: Artem Zvavitch, Kent State University

The Ups and Downs of Large High-Altitude Balloons

When: February 9, 2007
Speaker: Frank Baginski, George Washington University