Iowa State University

Department of Mathematics Colloquium   2019-2020

Tuesdays 4:10pm in Carver 268 Tea and cookies starting at 3:45pm in Carver 404

The ISU Department of Mathematics Colloquium is organized by Pablo Raúl Stinga (stinga@iastate.edu)

Spring 2020 None at this time.

Upcoming in Fall 2020 October 6 Maria Chudnovsky (Princeton University) Title: Abstract:

Past Fall 2019 September 10 Jason McCullough (Iowa State University) Title: On the degrees of complexity of algebraic varieties Abstract: Given a system of polynomial equations in several variables, there are several natural questions regarding its associated solution set (algebraic variety): What is its dimension? Is it smooth or are there singularities? How is it embedded in affine/projective space? Free resolutions encode answers to all of these questions and are computable with modern computer algebra programs. This begs the question: can one bound the computational complexity of a variety in terms of readily available data? I will discuss two recently solved conjectures of Stillman and Eisenbud-Goto, how they relate to each other, and what they say about the complexity of algebraic varieties. September 17 Steve Butler (Iowa State University) Title: On the mathematics of juggling Abstract: The mathematics of juggling focuses on the exploration of constrained periodic patterns, including enumeration and transitions between patterns. We will look at the mathematics of juggling with an emphasis on some of the more recent results that have emerged in this area. A few "practical" applications will also be demonstrated. September 24 Alicia Carriquiry (Iowa State University) Title: Statistics, mathematics and the fair administration of justice Abstract: In criminal proceedings, we often wish to know whether the suspect was the source of the evidence at the crime scene. The prosecutor and the defense propose competing hypothesis: the defendant is the source of the evidence or someone else is the source of the evidence. The task of the forensic scientist is to determine whether the evidence favors the prosecutor's or the defense's propositions. We focus on pattern evidence (latent prints, tool marks, etc) and discuss approaches to quantify the similarity between two images. If two items are similar, does that indicate same source? We use firearms examination for illustration. October 1 James Dibble (University of Iowa) Title: Riemannian manifolds with no conjugate points Abstract: Riemannian manifolds with no conjugate points or no focal points are natural generalizations of those with nonpositive sectional curvature, but they are defined using synthetic conditions about geodesics rather than strict curvature bounds. In this talk, it will be shown that the foundational theorems of Eells-Sampson and Hartman about maps from manifolds with nonnegative Ricci curvature into those with nonpositive sectional curvature, initially proved using the heat flow and the Bochner identity for harmonic maps, generalize to targets with no focal points by an essentially geometric, rather than analytical, argument. The extent to which other classical splitting theorems generalize to manifolds with no conjugate points will also be discussed, along with recent results about their fundamental groups and applications to other questions to Riemannian geometry. October 8 David Herzog (Iowa State University) Title: On the large-time behavior of singular stochastic Hamiltonian systems Abstract: We discuss the problem of convergence to equilibrium in two stochastic differential equations used in statistical sampling algorithms. In each system, the equilibrium probability distribution has an explicit density which is known up to a normalization constant. Moreover, each density is of the Boltzmann-Gibbs form. In the context of the algorithm, this form is exploited in order to take samples from a wide array of probability distributions by running the stochastic dynamics "long enough" started from conveniently chosen prior distributions. However, outside of a particular class of target distributions, very little is known about how fast the stochastic dynamics converges to this equilibrium. This talk will cover joint work with my collaborators to bridge this gap, ultimately resolving a challenge posed by Denis Talay at an AIM conference in 2007 about convergence to equilibrium for the singular, Lennard-Jones potential. October 15 Genetha Gray (Intel) Title: Mathematics of the Workforce Abstract: Advances in technology are challenging traditional concepts of the when, where, and how of work. Employees no longer spend their entire career at one job. The Bureau of Labor Statistics reports that the average tenure of current workers is 4.6 years and that this number decreases with employee age. In 2018, Gallup reported that 43% of US workers are remote at least sometimes. Moreover, as measured by FlexJobs in 2018, the math and economics job category had the highest growth in remote job opportunities. Finally, it should be noted that the fourth industrial revolution has created a high demand and a shortage of some critical skills and highlighted the need for employers to have the ability to respond to transformation by employing people with a wide range of skills that can be readily adapted to the new areas. To respond to these new realities, companies have turned to the practice of people analytics, a data-driven approach to managing the workforce. In this talk, we will describe how people analytics has matured and give some examples of problems and studies in this space. We will focus on the data-driven nature of the work and the mathematical tools required to find insights. October 24 (Thursday - Carver 0018) Bill Johnson (Texas A&M University) Title: Some 20+ year old problems about Banach spaces and operators on them. Abstract: The title is self-explanatory; no abstract needed! October 29 No colloquium November 5 Ryan Martin (Iowa State University) Title: Extremal functions and symmetrization Abstract: In this talk we will discuss the connections between symmetrization and extremal functions of graphs that exclude both a triangle and some fixed bipartite graph. In some cases the extremal number can be determined asymptotically. The techniques arise from the study of the edit distance problem. This preliminary work is joint with Zhana Berikkyzy and Felix Lazebnik. November 12 Talea Mayo (University of Central Florida) Title: Statistical data assimilation for hurricane storm surge modeling applications Abstract: Coastal ocean models are used for a variety of applications, including the simulation of tides and hurricane storm surges. As is true for many numerical models, coastal ocean models are plagued with uncertainty, due to factors including but not limited to the numerical discretization of continuous processes, uncertainties in specified boundary and initial conditions, and the approximation of meteorological conditions and hydrodynamics. Quantifying and reducing these uncertainties is essential for developing reliable and robust storm surge models. Statistical data assimilation methods are often used to estimate uncertain model states (e.g. storm surge heights) by combining model output with uncertain observations. We have used these methods in storm surge modeling applications to reduce uncertainties resulting from coarse spatial resolution. While state estimation is beneficial for accurately simulating the surge resulting from a single, observed storm, larger contributions can be made with the estimation of uncertain model parameters. In this talk, I will discuss applications of statistical data assimilation methods for both state and parameter estimation in coastal ocean modeling.  Past Spring 2020 January 28 Pablo Seleson (Oak Ridge National Laboratory) Title: Computational fracture modeling with peridynamics Abstract: Fracture prediction is an ongoing challenge in materials science and computational science and engineering. Peridynamics offer a new framework for computational modeling of fractures which overcomes this challenge through governing equations that naturally represent material discontinuities. Peridynamics is a nonlocal reformulation of classical continuum mechanics suitable for material failure and damage simulation. This presentation will discuss computational and modeling aspects of peridynamics with applications. We will begin by providing an overview of the peridynamic theory of solid mechanics, its computational features, and its capabilities in modeling crack propagation in isotropic and anisotropic media, including brittle glass and steel, fiber-reinforced composites, and polycrystalline ceramics. We will then present recent advances in modeling highly anisotropic media in peridynamics with a specialization to two-dimensional and planar elasticity problems. February 20 (Thursday) Gabriel Khan (University of Michigan) Title: Complex geometry and optimal transport Abstract: In this talk, we consider the Monge problem of optimal transport, which seeks to find the most cost-efficient movement of resources. In particular, we study the regularity (i.e. continuity/smoothness) of the optimal plan. Building off work of Brenier, Gangbo-McCann, Ma-Trudinger-Wang and others, this question is equivalent to finding a priori estimates on a class of degenerate elliptic Monge-Ampere equations. In joint work with Jun Zhang, we show that this question is actually connected to complex geometry, and in particular the curvature of certain Kahler metrics. Apart from the geometric considerations, this work has applications to mathematical finance. More specifically, we address a question about pseudo-arbitrages, which are investment strategies which beat the market almost surely in the long run. February 25 Michelle Manes (NSF - University of Hawaii at Manoa) Title: Complex multiplication in arithmetic geometry and arithmetic dynamics Abstract: The theory of complex multiplication in arithmetic geometry involves both the arithmetic of elliptic curves and orders in imaginary quadratic fields. It has a distinguished history, and in fact was the subject of Dick Gross' AMS Colloquium Lectures at JMM in 2019. His talked started with Euler's work on elliptic integrals in 1751 and continued through research from the past 20 years. The field of arithmetic dynamics is the study of number theoretic properties of iterated functions. The field draws inspiration from dynamical analogues of theorems and conjectures in classical arithmetic geometry. In this talk I will give a bit of background in the ideas from arithmetic geometry that inspire much of the current work in arithmetic dynamics, with a focus on attempts (by myself and others) to develop a "dynamical" theory of complex multiplication.