2017-2018
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 (stinga@iastate.edu)
Fall 2017
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September 5
Speaker: Tin-Yau Tam
Auburn University
Title: Orbital geometry - from matrices to
Lie groups
September 12
Speaker: Dennis Kriventsov
Courant Institute (NYU)
Title: Spectral optimization and free
boundary problems
September 19
Speaker: Deanna Haunsperger
Carletton College
Title: Stories from Math Horizons
October 3
Speaker: Hien Nguyen
Iowa State University
Title: Mean curvature flow, its long-time
existence, self-similar surfaces, and some related
problems
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
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
October 12 (Room: Carver 202)
Speaker: Bernard Lidicky
Iowa State University
Title: Flag algebras and applications
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
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
October 24
Speaker: Tathagata Basak
Iowa State University
Title: From sphere packing in R^24 to a
monster manifold via hyperbolic geometry
October 26 (Room: Carver 001)
Speaker: Songting Luo
Iowa State University
Title: Mathematical modeling and simulation
of wave-matter interactions
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
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) -
November 14
Speaker: Yong Zeng
National Science Foundation
Title: Bayesian inference via filtering
equations for financial ultra-high frequency data
[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
[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.]
Spring 2018
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
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.
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!
Abstract: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 https://projecteuclid.org/euclid.aos/1498636874
January 17 (4:10pm -- Carver 268)
Michael Catanzaro
University of Florida
Title: Topological data analysis and a geometric approach to multiparameter persistent homology
Abstract: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 (4:10pm -- Carver 268)
Zahra Aminzare
Princeton University
Title: Synchronization patterns in networks of nonlinear dynamical systems
Abstract:The analysis of synchronization in networks of nonlinear systems is important in a variety of research fields in science and engineering as well as in mathematics. In the human nervous system, synchronization can be beneficial, allowing for production of a vast range of behaviors such as generation of circadian rhythms and emergence of organized bursting in pancreatic beta-cells; or detrimental, causing disorders such as Parkinson’s disease and epilepsy.
In realistic networks that feature heterogeneous nodes and nonuniform coupling structure, complex patterns of synchronization emerge. Finding the conditions that foster synchronization in networked systems is critical to understanding a wide range of biological and mechanical systems. In this talk I introduce several synchronization patterns and identify when synchronization occurs and explain its dependance on parameters such as network structure, coupling weights, and intrinsic nodal dynamics.
As a real application of synchronization in biological settings, I show synchronous phenomena in central pattern generators (CPGs). CPGs are sophisticated circuits that can generate complex locomotor behaviors and even switch between different gaits. I discuss the mechanism of gait transition in an oscillator model of CPGs in insects.
January 24 (4:10pm -- Carver 268)
Yoonsang Lee
Lawrence Berkeley National Laboratory
Title: Uncertainty Quantification of Physics-constrained Problems
Abstract:Observation data along with mathematical models play a crucial role in improving prediction skills in science and engineering. In this talk we focus on the recent development of uncertainty quantification methods, data assimilation and parameter estimation, for Physics-constrained problems that are often described by partial differential equations. We discuss the similarities shared by the two methods and their differences in mathematical and computational points of view and future research topics. As applications, numerical weather prediction for geophysical flows and parameter estimation of kinetic reaction rates in the hydrogen-oxygen combustion are provided.
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 29 (4:10pm -- Carver 268)
Mark Kempton
Harvard University
Title: Quantum walks on graphs
Abstract:Algebraic and spectral techniques in graph theory have recently found important application in quantum information theory via the study information transfer through networks of interacting qubits. Of particular interest is the problem of determining when a quantum state can be transferred perfectly through such a network, and this has been shown to be modeled by a so-called "quantum walk" on a graph. I will discuss results on perfect and approximately perfect state transfer in this context in perturbations of various classes of graphs.
January 31 (4:10pm -- Carver 268)
Thomas Fai
Harvard University
Title: The Lubricated Immersed Boundary
Method
Many real-world examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen, involve the near-contact of elastic structures separated by thin layers of fluid. The separation of length scales between these fine lubrication layers and the larger elastic objects poses significant computational challenges. Motivated by the challenge of resolving such multiscale problems, we introduce an immersed boundary method that uses elements of lubrication theory to resolve thin fluid layers between immersed boundaries. We apply this method to two-dimensional flows of increasing complexity, including eccentric rotating cylinders and elastic vesicles near walls in shear flow, to show its increased accuracy compared to the classical immersed boundary method. We present preliminary simulation results of cell suspensions, a problem in which near-contact occurs at multiple levels, such as cell-wall, cell-cell, and intracellular interactions, to highlight the importance of resolving thin fluid layers in order to obtain the correct overall dynamics.
February 2 (4:10pm -- Carver 268)
Alexey Miroshnikov
University of California Los Angeles
Title: Inference of demographic histories
for populations of variable size
Studying the demographic histories of humans or other species and understanding their effects on contemporary genetic variability is one of the central tasks of population genetics. The genealogical relationship of a sample of several individuals is commonly modeled by the ancestral recombination graph (ARG). The ARG has a very complex structure and using it for inference is computationally prohibitive. In this talk I will present novel Hidden Markov Models used to approximate the ARG and an effective computational methodology for inference of demographic histories based on these models.
February 7 (4:10pm -- Carver 268)
Joey Iverson
University of Maryland
Title: Optimal line packings from finite
group actions
February 8 (4:10pm -- Pearson 2105)
Achilles Beros
University of Hawaii, Manoa
Title: The complexity of algorithmic teaching and learning
Abstract:I will discuss some recent contributions to the research program I initiated with my thesis in 2013: classifying models in algorithmic learning theory according to their arithmetic complexity. Specifically, I will discuss the complexity of models of teaching. I will discuss the connections between algorithmic learning theory, grammatical inference and machine learning as well as the way research in the applied and theoretical research influence one another in the study of machine intelligence.
February 13
Daphne Der-Fen Liu
California State University, Los Angeles
Title: From
Integral
Sequences with Forbidden Differences to Graph
Coloring Problems
Sequences with special patterns possess phenomenal properties. For instance, the Fibonacci sequence is directly related to the Golden Ratio and appears frequently in nature. In the early 70’s Cantor and Gordon introduced the parameter called density of integral sequences with forbidden differences. For a given set of positive integers D, a D-sequence is a sequence of integers such that the difference between any two terms does not fall in D. The maximum density of such a D-sequence is called the density of D, denoted by m(D). The parameter m(D) is closely related to the parameter k(D) involved in the so called "lonely runner conjecture" [Wills 1967, and Bienia et al. 1998], and coloring parameters of distance graphs introduced by Eggleton, Erdös, Skilton in mid-80’s. (For a set of positive integers D, the distance graph generated by D has all integers as the vertex set, and two vertices are adjacent if their absolute difference falls in D.)
We introduce close connections among the above parameters, and show how these connections are used to solve some open problems in these areas. In addition, we discuss recent results and open problems.
February 19 (4:10pm -- Carver 268)
David Sivakoff
Ohio State University
Title: Stochastic Dynamics on Graphs
Abstract:Many physical and intangible structures, such as the internet and collaboration networks, can be abstracted as graphs. With the goal of understanding the various processes that take place on these structures, such as the spread of a virus or the cultivation of an idea, we study stochastic processes on graphs. I will discuss a few of these models, and outline some directions for future discovery.
February 20 (4:10pm -- Pearson 2105)
Megan Bernstein
Georgia Institute of Technology
Title: Progress in showing cutoff for
random
walks on the symmetric group
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
Title: Two Women in Mathematics who helped create a Path for Others
Abstract:
April 3
Anthony Bonato
Ryerson University
Title: Graph Searching Games and Probabilistic Methods
Abstract:The intersection of graph searching and probabilistic methods is a new topic within graph theory, with applications to graph searching problems such as the game of Cops and Robbers and its many variants, Firefighting, graph burning, and acquaintance time. Graph searching games may be played on random structures such as binomial random graphs, random regular graphs or random geometric graphs. Probabilistic methods may also be used to understand the properties of games played on deterministic structures. A third and new approach is where randomness figures into the rules of the game, such as in the game of Zombies and Survivors. We give a broad survey of graph searching and probabilistic methods, highlighting the themes and trends in this emerging area. The talk is based on my book (with the same title) co-authored with Pawel Pralat published by CRC Press.
April 10
Shelby Nicole Wilson
Morehouse College
Title: An ODE mixed-effect model of
vascular tumor growth with anti-angiogenic treatment
Abstract:
April 17
Vladimir Sverak
University of Minnesota
Title: Calculations and theory for the
Navier-Stokes equations and their simpler models -
some recent examples
Numerical calculations can give important hints for theoretical PDE analysis. In this talk, we will discuss a few examples of calculations related to new theorems for PDEs of incompressible fluid mechanics.
April 24
Daniel Erman
University of Wisconsin-Madison
Title: Big polynomials rings
There is a meta-principle in algebra that limits of free objects tend to be free themselves. We will consider this principle in the context of polynomial rings, taking the limit as the number of variables goes to infinity. I will then discuss how the principle sheds light on some famous conjectures in algebraic geometry and commutative algebra, such as Stillman’s Conjecture on projective dimension and Hartshorne’s Conjecture on complete intersections. This is joint work with Steven Sam and Andrew Snowden.