Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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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.

Number Theory - Steven Spallone (IISER Pune)

Wednesday, May 22nd, 2019

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

Speaker: Steven Spallone (IISER Pune)

Title: Divisibility of Character Values of Symmetric Groups

Abstract: Fix a permutation $\sigma$ in some symmetric group $S_k$, and consider it as sitting in $S_n$ for $n \geq k$. Also fix a positive integer $d$. The probability that an irreducible character $\chi$ of $S_n$ evaluated at $\sigma$ will be a multiple of $d$ approaches $100\%$ as $n$ approaches infinity. We will sketch a proof, which is joint work with Jyotirmoy Ganguly and Amritanshu Prasad.

Nonlocal problems in PDEs and geometry

May 20-24, 2019

Prof. Eleonora Cinti (Università di Bologna, Italy) will teach a 5-day mini-course aimed at graduate students and junior researchers at the intersection of Analysis and Geometry.

Dr. Cinti earned her Ph.D in 2010 and since then has worked at the Max Planck Institute in Leipzig, the Weierstrass Institute in Berlin, and various Italian universities (Pavia, Bologna, Torino). Eleonora Cinti's research focuses on nonlocal partial differential equations, geometric measure theory, and calculus of variations.

Schedule

The mini-course will be structured as follows:

  • Lecture 1 (Monday, May 20): Preliminaries: basic facts about the Laplacian and harmonic functions.
  • Lecture 2 (Tuesday, May 21): The fractional Laplacians: motivations and properties.
  • Problem Session (Wednesday, May 22).
  • Lecture 3 (Thursday, May 23): $s$-Harmonic functions and the Caffarelli-Silvestre extension theorem.
  • Lecture 4 (Friday, May 24): Geometry meets PDEs, a nonlocal phase transition model and nonlocal minimal surfaces.

Registration

If you want to attend the mini-course, please email nonlocal19@queensu.ca.

Control Theory Seminar - Prof. Melkior Ornik (UIUC)

Friday, May 17th, 2019

Time: 10:30 a.m Place: Jeffery 110

Speaker: Prof. Melkior Ornik (University of Illinois at Urbana-Champaign)

Title: Deception and Unpredictability in Stochastic Control

Abstract: In a number of adversarial scenarios, the success of an agent at achieving its objective rests on its use of a deceptive strategy: a strategy that enables the agent to progress towards its objective while manipulating the beliefs of the agent’s adversary about the nature of the agent. For instance, the agent may wish to instill incorrect beliefs about its location, identity, or objective, or it may simply wish to act seemingly unpredictably while still progressing towards its objective. In this talk, I will outline recent work on formalizing the notions of deception and unpredictability within the setting of Markov decision processes. I will begin by describing a basic approach that encodes deception through introducing a belief space for an adversary and a belief-induced reward objective, thus expressing deceptive strategies as control policies on a product state space. I will then discuss notions of unpredictability, deception, and counter-deception in scenarios with a temporal logic objective. I will relate unpredictability of an agent to the total Shannon entropy of its paths, and show that maximal unpredictability is achieved by following a policy that results in maximal total entropy of the induced Markov chain. Finally, I will express the notion of deception for temporal logic objectives using Kullback-Leibler divergence and show that optimal deceptive (for the agent) and counter-deceptive (for the adversary) policies can be synthesized as solutions of a convex optimization problem and a non-convex min-max problem, respectively. I will conclude with a brief discussion of open problems in the area of deceptive planning.

Number Theory - Anup Dixit (Queen's University)

Wednesday, May 15th, 2019

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

Speaker: Anup Dixit (Queen's University)

Title: On the distribution of the number of local prime factors of n

Abstract: Let $\omega(n)$ denote the number of distinct prime factors of $n$ and $\omega_y(n)$ denote the number of distinct prime factors of $n$ less than $y$. It was shown by Hardy and Ramanujan that typically $\omega(n)$ is $\log \log n$ up to an error term of $\sqrt{\log \log n}$. This was further generalized in the famous Erd\"{o}s-Kac theorem, which asserts that the probability distribution of $(\omega(n) - \log \log n)/(\sqrt{\log\log n})$ is the standard normal distribution.In this talk, we will prove analogous results for $\omega_y(n)$, which can be thought of as a local Erd\"{o}s-Kac theorem and describe its further implications. This is joint work with Prof. Ram Murty.

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