Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Number Theory Seminar - Richard Gottesman (Queen's University)

Wednesday, July 10th, 2019

Time: 3:30-4:30 p.m.  Place: Jeffery Hall 319

Speaker: Richard Gottesman (Queen's University)

Title: Vector-Valued Modular Forms and Modular Linear Differential Equations

Abstract: The sequence of denominators of the Fourier coefficients of a modular form on a congruence subgroup is always bounded. It has been conjectured that the converse is also true. We will consider this problem in the context of vector-valued modular forms and explain a strategy for proving such an unbounded denominator result. In this talk, we will also explain how the module structure of vector-valued modular forms leads one to study modular linear differential equations. A key point is the importance of understanding the solutions of the modular linear differential equation at all of the cusps. No previous background on vector-valued modular forms will be assumed.

Number Theory - Robert Osburn (University College Dublin)

Wednesday, June 19th, 2019

Time: 3:30-4:30 p.m.  Place: Jeffery Hall 319

Speaker: Robert Osburn (University College Dublin)

Title: Generalized Kontsevich-Zagier series via knots

Abstract: Over the past two decades, there has been substantial interest in the overlap between quantum knot invariants, q-series and modular forms. In this talk, we discuss one such instance, namely an explicit q-hypergeometric expression for the Nth colored Jones polynomial for double twist knots. As an application, we generalize a duality at roots of unity between the Kontsevich-Zagier series and the generating function for strongly unimodal sequences. This is joint work with Jeremy Lovejoy (Paris 7 and Berkeley).

Control Theory Special Seminar - Behrouz Touri (UCSD)

Monday, June 17th, 2019

Time: 2:00 p.m Place: Jeffery Hall 319

Speaker: Behrouz Touri (University of California San Diego)

Title: Stochastic Adventures in Systems and Controls

Abstract: In this talk, we visit two systems and controls problems with stochastic components. The first problem relates to the control of safety critical systems. We provide a necessary and sufficient reachability result for an open and bounded safety set. In particular, we show that a stochastic system is controllable if and only if the expected system is controllable.

The second problem relates to control of large networked systems. We prove that a conjecture of Chris Godsil on controllability of graphs is true. The conjecture asserts that the number of binary symmetric matrices A that are controllable with all-one vector to the total number of binary matrices approaches one as the dimension of A approaches infinity. We also provide a result on universality of minimal controllability of networked systems.

Bio: Behrouz Touri is an Assistant Professor of the Electrical and Computer Engineering at the University of California San Diego and an Assistant Professor of the Electrical, Computer, and Energy Engineering Department at the University of Colorado Boulder (on leave). He received his B.Sc. degree in Electrical Engineering from Isfahan University of Technology, Isfahan, Iran in 2006, his M.Sc. degree in Communications, Systems, Electronics from Jacobs University, Bremen, Germany in 2008, and his Ph.D. degree in Industrial Engineering from the University of Illinois at Urbana-Champaign in 2011. Between 2011 and 2014, he was a postdoctoral researcher with the ECE departments of the University of Illinois and Georgia Institute of Technology. His research interests include applied probability theory, distributed optimization, control and estimation, population dynamics, and evolutionary game theory. He is a recipient of American Control Council's Donald P. Eckman Award in 2018 and AFOSR Young Investigator Award 2016.

Number Theory - Ahmet Guloglu (Bilkent University)

Wednesday, June 12th, 2019

Time: 3:00-4:00 p.m.  Place: Jeffery Hall 319

Speaker: Ahmet Guloglu (Bilkent University)

Title: Cubic Characters and some applications

Abstract: I will mainly focus on cubic Hecke characters and related applications such as non-vanishing results for related L-functions, one-level density and Kummer’s conjecture.

Number Theory - Brad Rodgers (Queen's University)

Wednesday, May 29th, 2019

Time: 3:30-4:30 p.m.  Place: Jeffery Hall 319

Speaker: Brad Rodgers (Queen's University)

Title: The variance of counts of squarefrees in short intervals

Abstract: Consider the number of squarefree integers in a randomly chosen short interval. In this talk we will discuss a method for computing the variance of such a count. The estimate we arrive at improves an old result of R.R. Hall and confirms a conjecture of Keating and Rudnick in a restricted range. This is joint work with Ofir Gorodetsky, Bingrong Huang, and Maksym Radziwill.

Control Theory Seminar - Ali Pakniyat (University of Michigan)

Monday, May 27th, 2019

Time: 10:30 a.m Place: Jeffery 319

Speaker: Ali Pakniyat (University of Michigan)

Title: The Quest for Missing Component: Dualities in Hybrid Optimal Control

Abstract: We revisit the notion of feedback as a ubiquitous policy structure in systems and control theory, and argue that a feedback law purely in state is not necessarily optimal. By studying examples of deterministic and stochastic hybrid systems, we remark that a general control policy depends on both the past information and future predictions about the process and, hence, a reduction to feedback structure jointly in the state and a "dual" variable requires the pair to summarize both the past and the future. Viewing the two fundamental results in optimal control theory from a duality perspective, we show that duality relationship holds in the Minimum Principle (MP) between the finite dimensional spaces of state variations and of co-state (adjoint) processes, and in Dynamic Programming (DP) between the infinite dimensional spaces of measures and of continuous functions. We present new version of the MP and DP for deterministic and stochastic hybrid systems and illustrate their implementation on analytic and practical examples. For numerical solution methodologies, we study the three classes of (a) generally nonlinear, (b) linear quadratic, and (c) polynomial systems where, for the latter case in particular, we can employ sum-of-squares techniques.

Non-Local Operators - Ikemefuna Agbanusi

Wednesday, May 22nd, 2019

Time: 1:30 p.m.  Place: Jeffery Hall 101

Speaker: Ikemefuna Agbanusi (Colgate University / Colorado College)

Title: Non-Local Operators Everywhere

Abstract: My goal in this talk is to give another approach---along with examples, characterizations and refinements of local and non-local operators. Very loosely speaking, non-local operators are necessary if one wishes to "albegraically complete" the local ones and my goal in this talk is to explain why and show also that pretty much all the "interesting" operators are non-local.