Department of

Mathematics


Seminar Calendar
for Doob Colloquium events the year of Thursday, September 14, 2017.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2017           September 2017          October 2017    
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Wednesday, February 1, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, February 1, 2017

Modular forms, quantum field theory, and algebraic topology

Dan Berwick-Evans (UIUC)

Abstract: Modular forms appear in a wide variety of contexts. For example, they arise in physics as partition functions of two dimensional quantum field theories and in algebraic topology as the coefficient ring of elliptic cohomology. A long-standing conjecture suggests that these two appearances of modular forms are related. After explaining the ingredients, I’ll describe some recent progress.

Wednesday, February 8, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, February 8, 2017

Stability and wall-crossing in algebraic geometry

Rebecca Tramel (UIUC)

Abstract: I will discuss two notions of stability in algebraic geometry: slope stability of vector bundles on curves, and Bridgeland stability for complexes of sheaves on smooth varieties. I will try and motivate both of these definitions with questions from algebraic geometry and from physics. I will then work through a few detailed examples to show how varying our notion of stability affects the set of stable objects, and how this relates to the geometry of the space we are studying.

Wednesday, February 22, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, February 22, 2017

Topology in dimensions 1, 2 and 3

Mark Bell (UIUC)

Abstract: We will look at some of the surprising connections between low-dimensional manifolds. In particular, we will focus on the classification problem, which aims to build a periodic table of all manifolds up to homeomorphism. To tackle some of the difficulties of doing this in dimension 3, we will resort to looking at lower dimensional submanifolds and how they sit inside.

Wednesday, March 1, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, March 1, 2017

Quotient spaces, Lie theory and quantization

Ivan Contreras (UIUC)

Abstract: We encounter quotient spaces everywhere in mathematics: circles, cohomology groups, moduli spaces. And sometimes physicists come up with interpretations of such spaces in terms of the symmetries of a given theory. In this talk I will explain how a 2 dimensional topological field theory, called the Poisson sigma model, produce interesting symplectic quotient spaces and its quantization produce deformations of Poisson brackets.

Wednesday, March 8, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, March 8, 2017

What is the mollification of the Riemann zeta-function?

Nicolas Robles (UIUC)

Abstract: We explain how to compute mean value integrals of the Riemann zeta-function involving a special type of Dirichlet polynomial called a mollifier. This process will allows us to compute an explicit proportion of the zeros of the Riemann zeta-function on the critical line, namely that more than 2/5 of them satisfy the Riemann hypothesis.

Wednesday, March 29, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, March 29, 2017

Apollonian Circle Packings and Beyond: Number Theory, Graph Theory and Geometric Statistics

Xin Zhang (UIUC)

Abstract: An Apollonian circle packings (ACP) is an ancient Greek construction obtained by repeatedly inscribing circles to an original configuration of three mutually tangent circles. In the last decade, the surprisingly rich structure of ACP has attracted experts from different fields: number theory, graph theory, homogeneous dynamics, to name a few. In this talk, I’ll survey questions and the progress on this topic and related fields.

Wednesday, April 5, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, April 5, 2017

Vertex algebras, chiral algebras, and factorization algebras

Emily Cliff (UIUC)

Abstract: The definition of a vertex algebra was formulated by Borcherds in the 1980s to solve algebraic problems, but these objects turn out to have important applications in mathematical physics, especially related to models of 2d conformal field theory. In the 1990s, Beilinson and Drinfeld gave geometric formulations of the definition, which they called chiral algebras and factorization algebras. These different approaches each have advantages and disadvantages: for example, the definition of a vertex algebra is more concrete and has so far been better studied; on the other hand, the geometric approach of chiral algebras and factorization algebras allows for transfer of knowledge between the fields of geometry, physics, and representation theory, and furthermore admits natural generalizations to higher dimensions. In this talk we will introduce all three of these objects; then we will discuss the relationships between them, especially focusing on how information from any one approach can lead to new understanding in the others.

Wednesday, April 12, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, April 12, 2017

First order logic and Sub-riemannian spheres.

Erik Walsberg (UIUC)

Abstract: I will discuss a connection between sub-riemannian geometry and first order model theory. Researchers in sub-riemannian geometry have essentially been working on the following: are sub-riemannian spheres definable in an o-minimal expansion of the ordered field of real numbers? (O-minimality is an important and popular topic in model theory developed in large part by UIUC's own Lou van den Dries). It also seems that some model theorists have been trying to construct the kind of structure that the geometers are looking for. As far as I can tell neither side was really aware of what the other was doing until now. I will try to explain some of this. No knowledge of logic or sub-riemannian geometry is necessary.

Wednesday, April 26, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, April 26, 2017

Merit Program for Emerging Scholars

Jennifer McNeilly (UIUC)

Abstract: The Merit Program at the University of Illinois has helped with the retention and recruitment of underrepresented students in STEM fields for nearly three decades. With this talk, I will briefly review the history of the program and describe how it is structured in our department. I will also describe the teaching methods used (based on Dr. Uri Treisman’s collaborative learning model) and share some examples/data to demonstrate the program’s success. The goals will be to both introduce the Merit Program to those who are unfamiliar with it and also share a few teaching and TA training ideas which could be useful in a variety of settings.

Wednesday, May 3, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, May 3, 2017

Quantitative Mostow Rigidity: Relating volume to topology for hyperbolic 3-manifolds

Rosemary Guzman (UIUC)

Abstract: A celebrated result of Mostow states that if M, N are two closed, con- nected, orientable, hyperbolic n-manifolds which are homotopy equivalent in dimensions $n\geq 3$, then M, N are equivalent up to isometry. This unique geometric-topological relationship has been the framework for many important results in the field, including notable results providing lower bounds on the volume of M, and results relating volume to homology (Culler-Shalen). In this talk, we will focus on the case where the fundamental group of M has a property, $k-$free, for $k\geq5$, and discuss current work toward an improvement on the volume bound from the current known bound of 3.44 which holds for $k\geq 4$. This is joint work with Peter Shalen.

Wednesday, September 13, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, September 13, 2017

Panel: Writing Grant Applications

Philipp Hieronymi, Vera Hur, Jennifer Mcneilly, Alexander Yong (UIUC)

Abstract: Postdocs, lecturers and faculty in general must face oftentimes the task of writing applications for grants: NSF, travel grants, teaching reduction, etc. The idea of this panel is to bring together some members of our faculty, with recognized success in grant applications, to share their thoughts on the subject and to answer questions from the audience.

Wednesday, September 27, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, September 27, 2017

Applications of Mining Public Genome Data to Recover Statistical Trends using Geometric Combinatorics

Ruth Davidson (UIUC)

Abstract: Websites such as TreeBASE.org and datadryad.org provide public access to a wealth of genomic data released with peer-reviewed biological publications. Phylogenomics-the recovery of the common evolutionary history of a group of taxa from short gene samples recovered from long genomes-is a basic area of research that gives rise to many quantitative methods for mining data for evolutionary signals. In turn, myriad fields such as ecology, medicine, and linguistics consume these methods; thus improved methods have very broad scientific impact. We present a publication (joint work with MaLyn Lawhorn, Joseph Rusinko, and Noah Weber) that provides a baseline framework, built on geometric combinatorics, for studying statistical trends in genomic data. Further, we will outline future research directions that will (1) build on this framework to inform the development of new theory and methods for model-testing, and (2) improve the understanding of trends in phylogenomic data in the systematic biology, computer science, statistics, and mathematics communities.

Wednesday, October 4, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, October 4, 2017

Instability of Steep Ocean Waves and Whitecapping

Sergey Dyachenko (UIUC)

Abstract: Wave breaking in deep oceans is a challenge that still defies complete scientific understanding. Sailors know that at wind speeds of approximately 5m/sec, the random looking windblown surface begins to develop patches of white foam (’whitecaps’) near sharply angled wave crests. We idealize such a sea locally by a family of close to maximum amplitude Stokes waves and show, using highly accurate simulation algorithms based on a conformal map representation, that perturbed Stokes waves develop the universal feature of an overturning plunging jet. We analyze both the cases when surface tension is absent and present. In the latter case, we show the plunging jet is regularized by capillary waves which rapidly become nonlinear Crapper waves in whose trough pockets whitecaps may be spawned.

Wednesday, October 11, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, October 11, 2017

An overview of the theory of the Riemann zeta-function

Siegfred Baluyot (UIUC)

Abstract: This will be a motivated survey of some of the main lines of inquiry in the theory of the Riemann zeta-function. After a brief introduction to zeta and its connection to the prime numbers, we will discuss some of the advances in the subject that were made in recent decades.

Wednesday, October 18, 2017

3:00 pm in 243 AH,Wednesday, October 18, 2017

The Maxwell Bloch Equations in the Presence of Damping

Katelyn Leisman (UIUC)

Abstract: The Maxwell Bloch equations model the resonant interaction of an electric field with a two level medium. Typically, two relaxation terms are necessary to best model the physics, but in certain cases they can be ignored. In this talk, I will show numerical solutions with varying amounts of the relaxation terms. We find that when the relaxation terms are small relative to the size of the initial soliton pulse, the solution is a damped soliton. As the relaxation increases, the ripples of radiation accelerate away from the dying original pulse, forming a new precursor pulse. When the relaxation is very large, the original pulse dies almost instantaneously and the precursor pulse accelerates to the speed of light. In the limiting case of large relaxation, the equations accurately model experimental results measuring the total pulse delay of a laser pulse propagating through a beam of ruby.

Wednesday, October 25, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, October 25, 2017

Bott-Samelson varieties and combinatorics

Laura Escobar (UIUC)

Abstract: Schubert varieties parametrize families of linear spaces intersecting certain hyperplanes in C^n in a predetermined way. In the 1970’s Hansen and Demazure independently constructed resolutions of singularities for Schubert varieties: the Bott-Samelson varieties. In this talk I will describe their relation with associahedra. I will also discuss joint work with Pechenick-Tenner-Yong linking Magyar’s construction of these varieties as configuration spaces with Elnitsky’s rhombic tilings. Finally, based on joint work with Wyser-Yong, I will give a parallel for the Barbasch-Evens desingularizations of certain families of linear spaces which are constructed using symmetric subgroups of the general linear group.

Wednesday, November 8, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, November 8, 2017

Panel: Applying for academic jobs

Rui Fernandes, Rick Laugesen, Anush Tserunyan, and Alexander Woo (UIUC and University of Idaho)

Abstract: The idea of this panel is to bring together some members of our faculty to share their thoughts on applying for academic jobs and to answer questions from the audience.

Wednesday, November 29, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, November 29, 2017

Minimal mathematical models of human and animal dynamical systems

Sara Clifton (UIUC and University of Idaho)

Abstract: Minimal mathematical models are used to understand complex phenomena in the physical, biological, and social sciences. This modeling philosophy never claims, nor even attempts, to fully capture the mechanisms underlying the phenomena, and instead offers insights and predictions not otherwise possible. Here, we build and explore minimal dynamical systems models to understand three complex animal and human systems. First, we incorporate the assumptions of Zahavi's handicap principle into a mathematical model of ornament evolution and show that this existing hypothesis is sufficient to explain the previously puzzling observation of bimodally distributed ornament sizes in a variety of species. Second, we propose a 'return-to-setpoint' model of chronic pain dynamics in sickle cell disease patients with the goal of offering personalized, data-driven recommendations for treating chronic pain. Third, we present a conceptual model of restaurant competition that predicts the existence of a critical gratuity rate threshold at which restaurant owners will disallow tipping to maximize their profits. Because of their simplicity, these models of complex human and animal systems offer new connections between existing ideas, give optimized solutions with limited data, and provide qualitative predictions of future events.