Mathematics Department Colloquium


Spring 2018

Tuesdays 4:10 p.m. in Carver 205 - Tea and cookies starting at 3:45 p.m. in Carver 404

The ISU Department of Mathematics Colloquium is organized by

Pablo Raúl Stinga (


January 17 (4:10pm -- Carver 268)

Michael Catanzaro

University of Florida

Title: Topological data analysis and a geometric approach to multiparameter persistent homology

The prevalence of ever-increasing sources of data demands the development of new tools for analysis.  Topological data analysis (TDA) provides one such toolbox, relying on geometric and topological methods to highlight features of data that are not apparent using other approaches.  A central idea of TDA is to determine the features that persist across multiple scales. These persistent features can be completely described and conveniently visualized due to a structure theorem closely related to the structure theorem for finitely generated abelian groups. In this talk, I will discuss a generalized version of persistence inspired by a parameterized form of Morse theory, and discuss how it can be used in practice.


January 19 (4:10pm -- Carver 268)

Rana Parshad

Clarkson University

Title: Finite Time Blow-Up and "Ecological" Damping: Applications to Invasive Species Control

In this talk I will present some recent finite time blow-up results in heat and wave equations, as a lead into studying certain explosive invasive populations, such as the Burmese python in South Florida. I will next introduce the idea of "ecological" damping as a means of controlling such invasive populations. These novel controls have the advantage of avoiding non-target effects due to classical chemical and biological control. I will conclude with future directions in the biological control of invasive species.

January 22

Zahara Aminzare

Princeton University



January 24

Yoongsang Lee

Lawrence Berkeley National Laboratory



January 26 (4:10pm -- Carver 268)

Amy Veprauskas

University of Louisiana at Lafayette

Title: Changes in population outcomes resulting from phenotypic evolution and environmental disturbances

We develop an evolutionary game theoretic version of a general nonlinear matrix model that includes the dynamics of a vector of mean phenotypic traits subject to natural selection. For this evolutionary model, we use bifurcation analysis to establish the existence and stability of a branch of positive equilibria that bifurcates from the extinction equilibrium when the inherent growth rate passes through one. We then present an application to a daphnia model to demonstrate how the evolution of resistance to a toxicant may change persistence scenarios. We show that if the effects of a disturbance are not too large, then it is possible for a daphnia population to evolve toxicant resistance whereby it is able to persist at higher levels of the toxicant than it would otherwise. These results highlight the complexities involved in using surrogate species to examine toxicity. Time permitting, we will also consider a nonautonomous matrix model to examine the possible long-term effects of environmental disturbances, such as oils spills, floods, and fires, on population recovery. We focus on population recovery following a single disturbance, where recovery is defined to be the return to the pre-disturbance population size. Using methods from matrix calculus, we derive explicit formulas for the sensitivity of the recovery time with respect to properties of the population or the disturbance.

January 31

Thomas Fai

Harvard University



February 13

Daphne Der-Fer Liu

University of South Carolina, Columbia



February 15 (4:10pm -- Pearson 2105)

Megan Bernstein

Georgia Institute of Technology

Title: Progress in showing cutoff for random walks on the symmetric group

Abstract:  Cutoff is a remarkable property of many Markov chains in which they rapidly transition from an unmixed to a mixed distribution. Most random walks on the symmetric group, also known as card shuffles, are believed to mix with cutoff, but we are far from being able to proof this. We will survey existing cutoff results and techniques for random walks on the symmetric group, and present three recent results: cutoff for a biased transposition walk, cutoff with window for the random-to-random card shuffle (answering a 2001 conjecture of Diaconis), and pre-cutoff for the involution walk, generated by permutations with a binomially distributed number of two-cycles. The results use either probabilistic techniques such as strong stationary times or diagonalization through algebraic combinatorics and representation theory of the symmetric group. Results include joint work with Nayantara Bhatnagar, Evita Nestoridi, and Igor Pak.

March 20

Susan Kelly

University of Wisconsin - La Crosse



April 10

Shelby Nicole Wilson

Morehouse College



April 17

Vladimir Sverak

University of Minnesota




January 8 (4:10pm -- Carver 268)

Leili Shahriyari

Mathematical Biosciences Institute - The Ohio State University

Title: Discovering effective cancer treatments through Computational models

Carcinogenesis is a complex stochastic evolutionary process. One of the key components of this process is evolving tumors, which interact with and manipulate their surrounding microenvironment in a dynamic spatio-temporal manner. Recently, several computational models have been developed to investigate such a complex phenomenon and to find potential therapeutic targets. In this talk, we present novel computational models to gain some insight about the evolutionary dynamics of cancer. Furthermore, we propose an innovative framework to systematically employ a combination of mathematical methods and bioinformatics techniques to arrive at unique personalized targeted therapies for cancer patients.

January 10 (4:10pm -- Carver 268)

Claus Kadelka

Institute of Medical Virology, University of Zurich, Switzerland -- Division of Infectious Diseases and Hospital Epidemiology, University Hospital Zurich, Zurich, Switzerland

Title: Computational HIV Vaccinology and the Robustness of Gene Regulatory Networks


My talk will be split into two parts: first, my current work in computational HIV vaccinology; and second, robustness analyses of gene regulatory networks (GRNs).

HIV broadly neutralizing antibodies (bnAbs) are the major hope for an effective HIV vaccine and therapy development, but are only elicited at low frequency in natural HIV infection. We recently conducted a systematic survey of bnAb activity in 4,484 HIV-1 infected individuals, and identified several viral and disease parameters associated with bnAb development, as well as antibody binding patterns predictive of bnAb existence. Through phylogenetic HIV sequence analysis, we further identified more than 300 likely transmission pairs, and exhibited, for the first time, that parts of the HIV antibody response are heritable.

The second part of my talk focuses on the development and analysis of time- and state-discrete dynamical system models (generalized Boolean networks) to better understand GRNs and their surprisingly high robustness to noise and perturbations. My research aims to identify the mechanisms underlying this robustness, by relating network topology to network dynamics. I will characterize the class of canalizing functions, which is well-suited to model the interactions in GRNs, and the occurrence of these functions buffers GRNs against noise.

January 12 (4:10pm -- Carver 268)

Erica Rutter

Center for Research in Scientific Computation -- North Carolina State University

Title: Modeling and Estimating Biological Heterogeneity in Spatiotemporal Data

Heterogeneity in biological populations, from cancer to ecological systems, is ubiquitous. Despite this knowledge, current mathematical models in population biology often do not account for inter-individual heterogeneity.  In systems such as cancer, this means assuming cellular homogeneity and deterministic phenotypes, despite the fact that heterogeneity is thought to play a role in therapy resistance. Glioblastoma Multiforme (GBM) is an aggressive and fatal form of brain cancer notoriously difficult to predict and treat due to its heterogeneous nature.  In this talk, I will discuss several approaches I have developed towards incorporating and estimating cellular heterogeneity into partial differential equation (PDE) models of GBM growth. In particular, I will discuss the use of random differential equations for modeling purposes and the Prohorov metric framework for estimating parameter distributions from data.

January 16

Philip Ernst

Rice University

Title: Yule's "Nonsense Correlation" Solved!

In this talk, I will discuss how I recently resolved a longstanding open statistical problem. The problem, formulated by the British statistician Udny Yule in 1926, is to mathematically prove Yule's 1926 empirical finding of "nonsense correlation". We solve the problem by analytically determining the second moment of the empirical correlation coefficient of two independent Wiener processes. Using tools from Fredholm integral equation theory, we calculate the second moment of the empirical correlation to obtain a value for the standard deviation of the empirical correlation of nearly .5. The "nonsense" correlation, which we call "volatile" correlation, is volatile in the sense that its distribution is heavily dispersed and is frequently large in absolute value. It is induced because each Wiener process is "self-correlated" in time. This is because a Wiener process is an integral of pure noise and thus its values at different time points are correlated. In addition to providing an explicit formula for the second moment of the empirical correlation, we offer implicit formulas for higher moments of the empirical correlation. The full paper is currently in press at The Annals of Statistics and can be found at


Fall 2017



September 5

Speaker: Tin-Yau Tam

Auburn University

Title: Orbital geometry - from matrices to Lie groups

Abstract: Given an $n\times n$ matrix $A$, the celebrated Toeplitz-Hausdorff theorem asserts that the classical numerical range $\{x^*Ax: x\in {\mathbb C}^n: x^*x=1\}$ is a  convex set, where ${\mathbb C}^n$ is the vector space of complex $n$-tuples and $x^*$ is the complex conjugate transpose of $x\in {\mathbb C}^n$. Schur-Horn Theorem asserts that the set of the diagonals of Hermitian matrices of a prescribed eigenvalues is the convex hull of the orbit of the eigenvalues under the action of the symmetric groups. These results are about unitary orbit of a matrix. Among interesting generalizations, we will focus our discussion on those in the context of Lie structure, more precisely, compact connected Lie groups and semisimple Lie algebras. Some results on convexity and star-shapedness will be presented.

September 12

Speaker: Dennis Kriventsov

Courant Institute (NYU)

Title: Spectral optimization and free boundary problems

Abstract: A classic subject in analysis is the relationship between the spectrum of the Laplacian on a domain and that domain's geometry. One approach to understanding this relationship is to study domains which extremize some function of their spectrum under geometric constraints. I will give a brief overview of some of these optimization problems and describe the (very few) explicit solutions known. Then I will explain how to approach these problems more abstractly, using tools from the calculus of variations to find solutions. A key difficulty with this approach is showing that the solutions (which are a priori very weak) are actually smooth domains, which I address in some recent work with Fanghua Lin. Our method revolves around relating spectral optimization problems to certain vector-valued free boundary problems of Bernoulli type.

September 19

Speaker: Deanna Haunsperger

Carletton College

Title: Stories from Math Horizons

Abstract: In this talk, Deanna will talk about becoming involved in the Mathematical Association of America as an editor of Math Horizons, some of the cool mathematics she learned in this process, and opportunities for participating in the national mathematical community.

October 3

Speaker: Hien Nguyen

Iowa State University

Title: Mean curvature flow, its long-time existence, self-similar surfaces, and some related problems

Abstract: For curves in the plane, the curvature at a point measures how fast the direction is changing. If each point moves perpendicularly to the loop at a speed equal to the curvature, the resulting flow is called the curve shortening flow. To visualize this flow, one can think of the loop as the edge of a thin layer of ice floating on water. Corners will round out instantly; skinny offshoots disappear fast; inlets fill in; and flat edges move slowly. If the ice layer is circular, it will shrink while remaining circular and disappear eventually. This last example is called a self-similar solution because its shape does not change under the flow. In higher dimensions, because so many paths go through a point, one considers the mean curvature, which is an average of all the curvatures of all the curves through a point, and defines the mean curvature flow.

In this talk, I will explore the properties of the mean curvature flow and some classical results. I will then present more recent development about its long-time existence and self-similar surfaces. In particular, I will focus on the gluing techniques and talk about the main steps and difficulties for gluing pieces of surfaces in order to construct new self-similar solutions.

October 5 (Room: Carver 018)

Speaker: Michael Young

Iowa State University

Title: Polychromatic colorings of hypercubes and integers

Abstract: Given a graph G which is a subgraph of the n-dimensional hypercube Q_n, an edge coloring of Q_n with $r\ge2$ colors such that every copy of G contains every color is called G-polychromatic. Originally introduced by Alon, Krech and Szabó in 2007 as a way to prove bounds for Turán type problems on the hypercube, polychromatic colorings have proven to be worthy of study in their own right. This talk will survey what is currently known about polychromatic colorings and introduce some open questions. In addition, there are some natural generalizations and variations of the problem that will also be discussed. One generalization will be polychromatic colorings of the integers, which we use to prove a conjecture of Newman.

October 10

Speaker: Jack H. Lutz

Iowa State University

Title: Who asked us? How the theory of computing answers questions that weren't about computing

Abstract: It is rare for the theory of computing to be used to answer open mathematical questions whose statements do not involve computation or related aspects of logic. This talk discusses recent developments that do exactly this. After a brief review of algorithmic information and dimension, we describe the point-to-set principle (with N. Lutz) and its application to two new results in geometric measure theory. These are (1) N. Lutz and D. Stull's strengthened lower bound on the Hausdorff dimensions of generalized Furstenberg sets, and (2) N. Lutz's extension of the fractal intersection formulas for Hausdorff and packing dimensions in Euclidean spaces from Borel sets to arbitrary sets.

October 12 (Room: Carver 202)

Speaker: Bernard Lidicky

Iowa State University

Title: Flag algebras and applications

Abstract: We give a short introduction to flag algebras and we discuss several of its applications. Flag algebras is a method, developed by Razborov to attack problems in extremal combinatorics. Razborov formulated the method in a general way which made it applicable to various settings. In this talk we give a brief introduction of the basic notions used in flag algebras and demonstrate the method on Mantel's theorem. Then we discuss applications of the flag algebras in different settings. In particular, we mention applications to crossing numbers, iterated extremal structure and Ramsey numbers.

October 13 (Room: Carver 202)

Speaker: Ralph McKenzie

Vanderbilt University

Title: P or NP-complete: a very successful application of general algebra to a fundamental graph homomorphism problem

Abstract: With any finite relational structure A we have a computational problem: input a finite structure B of the same signature as A; accept B if and only if there is a homomorphism from B to A. The CSP-dichotomy conjecture of Feder and Vardi states that given any template A (a finite relational structure), the described computational problem either admits a polynomial-time algorithm, or is NP-complete. Feder and Vardi proved that this general conjecture is equivalent to the restricted conjecture where the template is simply a di-graph.
It was observed by Bulatov, Jeavons and Krokhin about year 2000 that study of the polymorphism algebra of the template offers a natural and promising approach to the corresponding CSP problem. There are now two algebraic proofs of the dichotomy conjecture in circulation that are being read and checked by experts in this new field. Whether or not one of these proofs is accepted as valid, the observation of Bulatov, Jeavons and Krokhin has led over the intervening years to great progress in understanding the classification of general CSP problems, while producing an impressive body of deep results in finite universal algebra. 
My talk will sketch developments in both directions, new algorithms for large families of CSP problems, and surprising algebraic results offering unexpected insight into the diversity of deep structures in finite algebras.

October 17

Speaker: Emille Lawrence

University of San Francisco

Title: Topological symmetry groups of graphs in S^3

Abstract: The study of graphs embedded in S^3 was originally motivated by chemists’ need to predict molecular behavior. The symmetries of a molecule can explain many of its chemical properties, however we draw a distinction between rigid and flexible molecules. Flexible molecules may have symmetries that are not merely a combination of rotations and reflections. Such symmetries prompted the concept of the topological symmetry group of a graph embedded in S^3. We will discuss recent work on what groups are realizable as the topological symmetry group for several families of graphs, including the Petersen family and Möbius ladders. 

October 24

Speaker: Tathagata Basak

Iowa State University

Title: From sphere packing in R^24 to a monster manifold via hyperbolic geometry

Abstract: Last year it was proved that the Leech lattice provides the densest way to pack spheres in 24 dimensional Euclidean space. We shall talk about the infinite complex reflection group G whose special properties are borrowed from the Leech lattice. The group G acts naturally on the unit ball in complex thirteen dimensional vector space preserving a negative curvature metric. Let Y be the part of the ball on which G acts freely. The monstrous proposal conjecture states that the fundamental group of the quotient Y/G maps onto a close cousin of the monster simple group and this leads to a construction of a 12 dimensional complex manifold with a natural monster action. We shall descibe generators and relations for the fundamental group of Y/G providing strong evidence for this conjecture. Part of this is joint work with Daniel Allcock. There are two main ingredients in the proofs: (1) making use of a still poorly understood analogy between complex reflection groups and Weyl groups of complex simple Lie algebras and (2) making use of special properties of the Leech lattice. Along the way we shall explain how this project leads us to some other work of independent interest: like constructing new arithmetic lattices in U(n,1) or explicit uniformization of hermitian symmetric spaces by automorphic forms.

October 26 (Room: Carver 001)

Speaker: Songting Luo

Iowa State University

Title: Mathematical modeling and simulation of wave-matter interactions

Abstract: Simulating wave-matter interactions is important for various practical applications. Depending on the wavelengths and the matter sizes, different models (PDE models) are required and/or applied. For each model, effective numerical methods are highly desirable for applications. I will talk about some problems rising from nano optics, kinetic theory, and high frequency wave propagation that cover a wide range of scales, along with discussion of the numerical methods.  

October 31

Krishna Athreya

Iowa State University

Title: On the sums of powers of the likelihood function of random walks on the integer lattice in d dimension

Abstract: In their classic book on problems in analysis written around 1925 (republished in the US in 1945 and 1970) Polya and Szego give the asymptotics of sums of powers of binomial coefficients as n goes to infinity. In this talk we prove an analog of their result for sums of powers of probabilities involving random walks on the integer lattice in d dimension. We deduce some results for the binomial and multinomial probabilities. We also outline some open problems.

November 7

Speaker: Alicia Prieto Langarica

Youngstown State University

Title: A mathematical model of the effects of temperature on human sleep patterns

Abstract: Sleep is on of the most fundamental, across species, and less understood processes. Several studies have been done on human patients that suggest that different temperatures, such as room temperature, core body temperature, and distal skin temperature, have an important effect on sleep patterns, such as length and frequency of REM bouts. A mathematical model is created to investigate the effects of temperature on the REM/NonREM dynamics.  Our model was based on previous well-established and accepted models of sleep dynamics and thermoregulation models.
[Authors: Selenne Bañuelos (California State University Channel Islands) - Janet Best (The Ohio State University) - Gemma Huguet (Universitat Politecnica de Catalunya) - Alicia Prieto Langarica (Youngstown State University) - Pamela B. Pyzza (Ohio Wesleyan University) - Markus Schmidt (Ohio Sleep Medicine Institute) - Shebly Wilson (Morehouse College)]

November 14

Speaker: Yong Zeng

National Science Foundation

Title: Bayesian inference via filtering equations for financial ultra-high frequency data

Abstract: We propose a general partially-observed framework of Markov processes with marked point process observations for ultra-high frequency (UHF) transaction price data, allowing other observable economic or market factors. We develop the corresponding Bayesian inference via filtering equations to quantify parameter and model uncertainty. Specifically, we derive filtering equations to characterize the evolution of the statistical foundation such as likelihoods, posteriors, Bayes factors and posterior model probabilities. Given the computational challenge, we provide a convergence theorem, enabling us to employ the Markov chain approximation method to construct consistent, easily-parallelizable, recursive algorithms. The algorithms calculate the fundamental statistical characteristics and are capable of implementing the Bayesian inference in real-time for streaming UHF data, via parallel computing for sophisticated models. The general theory is illustrated by specific models built for U.S. Treasury Notes transactions data from GovPX and by Heston stochastic volatility model for stock transactions data. This talk consists joint works with B. Bundick, X. Hu, D. Kuipers and J. Yin.
[Bio. Yong Zeng serves as a program director in Division of Mathematical Sciences DMS at National Science Foundation. He is also a professor in the Department of Mathematics and Statistics at University of Missouri - Kansas City.]

December 5

Speaker: Oyita Udiani

National Institute for Mathematical and Biological Synthesis (NIMBioS)

Title: Mathematical models of social advocacy on networks

Abstract: Members of the public hold opposing positions on a multitude of social issues. For example, although there is scientific consensus that climate change is occurring and driven by human activity, a sampling of popular media makes it clear that opposing discourses are alive and well in the United States. As with many social issues, there are several organizations working to affect policy on climate change through grassroots advocacy. Achieving success depends on a number of factors, but none is perhaps more important than understanding how to design campaigns for persuading and mobilizing stakeholders within communities of interest. In this talk, I will introduce a theoretical framework to study this question using models of adaptive influence on networks. Examples discussed include campaigns to convert skeptics (maximizing prevalence of beliefs) vs. mobilize converts (maximizing extremism of beliefs).
[Bio. Oyita Udiani is an applied mathematician and NSF postdoctoral fellow at NIMBioS. His research develops models to study questions related to the organization of social and biological systems.]

Fall 2018


October 16

Vlad Vicol

University of Minnesota