Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Number Theory - Siddhi Pathak (Queen's University)

Tuesday, January 15th, 2019

Time: 1:00-2:00 p.m.  Place: Jeffery Hall 422

Speaker: Siddhi Pathak (Queen's University)

Title: Dedekind zeta function at odd positive integers.

Abstract: Let $\zeta(s)$ denote the Riemann zeta-function. Thanks to Euler's evaluation and Lindemann's theorem on transcendence of $\pi$, we understand that $\zeta(2k)$ is transcendental for any positive integer $k$. However, the arithmetic nature of the values of $\zeta(s)$ at odd positive integers remains a mystery. Recently, significant progress was made concerning the irrationality of these values, with perhaps the most remarkable theorem being that infinitely many of $\zeta(2k+1)$ are irrational, which was shown by T. Rivoal in 2000.

Similarly, one can inquire regarding the arithmetic nature of values of the Dedekind zeta-function $\zeta_K(s)$ attached to a number field $K$. When $K$ is totally real, the values $\zeta_K(2k)$ were proven to be algebraic multiples of powers of $\pi$ by Siegel and Klingen, independently. But this question remains unsolved in all other cases. In this talk, we discuss how our current knowledge allows us to deduce certain irrationality results for $\zeta_K(2k+1)$, where $K$ is an imaginary quadratic field. This is joint work with Prof. M. Ram Murty.

Number Theory - Anup Dixit (Queen's University)

Tuesday, January 8th, 2019

Time: 1:00-2:00 p.m.  Place: Jeffery Hall 422

Speaker: Anup Dixit (Queen's University)

Title: Large values on the 1-line for a family of L-functions.

Abstract: A classical problem in analytic number theory is to understand the values of L-functions in the critical strip. It is well-known that $|\zeta(1+it)|$ takes arbitrarily large values when $t$ runs through the real numbers. In 2006, Granville and Soundarajan conjectured that there exists arbitrarily large $t$ such that $|\zeta(1+it)|$ satisfies a certain lower bound. We discuss recent progress towards this conjecture and also generalize it to a family of L-functions. This is joint work with K. Mahatab.

Geometry & Representation - Alistair Savage (University of Ottawa)

Monday, January 7th, 2019

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 319

Speaker: Alistair Savage (University of Ottawa)

Title: Universal categories

Abstract:  Universal constructions are ubiquitous in mathematics.  For example, the polynomial ring is uniquely characterized by a universal property for commutative rings.  Other examples include free monoids, free groups, and tensor algebras.  In this mainly expository talk we will discuss an analogous, but somewhat less well known, concept on the level of categories.  In particular, we will see how one can define categories that are determined by universal properties.  Examples include the Temperley--Lieb category (the free monoidal category on a self-dual object), the Brauer category (the free symmetric monoidal category on a self-dual object), and the oriented Brauer category (the free symmetric monoidal category on a pair of dual objects).  We will discuss intuitive diagrammatic descriptions of these categories and how these universal constructions allow one to easily find deep symmetries in a wide range of categories.

Control Theory Seminar - Prof. Andy Lamperski

Monday, December 3rd, 2018

Time: 10:00 a.m Place: TBA

Speaker: Prof. Andy Lamperski

Title: Optimal Control with Noisy Time and Communicative Actions

Abstract: This talk will cover two topics: 1) Control and estimation with noisy time, and 2) communication via control actions. 

In most control analysis, time is assumed to be perfectly known.  However, in many important scenarios ranging from robotics, biological motor control, and transportation systems, timing information is not known perfectly. In the first part of the talk, we will examine problems of optimal control and estimation when time is imperfectly measured. For optimal control, we will show that under some clock noise models, dynamic programming principles can be obtained. In the linear quadratic case, explicit solutions can be computed. For estimation, we will present the problem of estimating time from sensor data. In particular, we will examine how control can influence the accuracy of time estimates, and we will discuss the estimation of time from multiple sensors with inaccurate time-stamps. 

The second part of the talk will focus on communication with control actions. This communication strategy is known as signaling. While most signaling problems are mathematically challenging, humans routinely signal during cooperative movements. The second part of the talk will present a tractable problem that models salient features of human signaling strategies. The problem consists of a signaler that reaches towards an unspecified target, and an observer that decides on the target location based on movement measurements. The optimal control scheme reproduces qualitative phenomena observed in human reaching experiments.

Geometry & Representation - Kaveh Mousavand (UQAM)

Monday, December 3rd, 2018

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 319

Speaker: Kaveh Mousavand (UQAM)

Title: $\tau$-tilting finiteness of special biserial algebras

Abstract:  $\tau$-tilting theory, recently introduced by Adachi-Iyama-Reiten, is an elegant generalization of the classical tilting theory which fixes the deficiency of the tilting modules with respect to the notion of mutation. In this talk, I view $\tau$-tilting finiteness of algebras as a natural generalization of the representation finiteness property. The natural question then becomes: For which families of algebras does $\tau$-tilting finiteness imply representation finiteness?

First I introduce a reductive method that can be applied to certain families of algebras to reduce this, a priori, intractable problem to a subfamily with nice features. Then, as an interesting class of algebras, I consider the special biserial algebras and for every minimal representation infinite member of this family, I give a full answer to the above question and show. As a corollary, we conclude that a gentle algebra is $\tau$-tilting finite if and only if it is representation finite.

Department Colloquium - Kexue Zhang (Queen's University)

Kexue Zhang (Queen's University)

Friday, November 30th, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Kexue Zhang (Queen's University)

Title: Input-to-State Stability of Impulsive Systems with Time-Delay

Abstract: Impulsive systems are dynamical systems subject to state jumps at a sequence of discrete-time moments. These systems are often modelled by impulsive differential equations, and have applications in a wide variety of areas, including network synchronization and epidemic dynamics. Time-delay is an essential part of most practical scenarios of impulsive systems. For instance, time-delay is unavoidable in sampling and transmission of the impulse information. In this talk, I will given an overview of the fundamental theory of impulsive functional differential equations, which provide the mathematical building blocks for studying impulsive time-delay systems. I then discuss the stability of the evolution of these systems, where I will focus on the input-to-state stability problem. As an application, impulsive synchronization of time-delay systems will be studied. This is joint work with Xinzhi Liu (Waterloo).

Kexue Zhang obtained his Ph.D. degree in the Department of Applied Mathematics, University of Waterloo,Canada in 2017. He is currently a Coleman Postdoctoral Fellow at Queen's University. His research interests include hybrid systems and control, differential equations on time scales, and their various applications on complex dynamical networks.

Probability Seminar - Sang-Gyun Youn (Queen's University)

Thursday, November 29th, 2018

Time: 4:30-6:00 p.m.  Place: Jeffery Hall 422

Speaker: Sang-Gyun Youn (Queen's University)

Title: Some questions on Jones-Wenzl projections in view of quantum information theory.

Abstract:  It is very natural to study separability or PPT property of quantum states in view of quantum information theory and the need to study those properties for so-called Jones-Wenzl projections has emerged in recent years. In this talk, I am going to introduce the notions of separability, PPT property and Jones-Wenzl projections.

Free Probability and Random Matrices Seminar Webpage:

Curves Seminar - Mike Roth (Queen's University)

Tuesday, November 27th, 2018

Time: 2:00-3:30 p.m Place: Jeffery Hall 116

Speaker: Mike Roth (Queen's University)

Title: Beauville’s results on classification of Kähler manifolds with $c_1(K_X)=0$, II.

Abstract: We will continue the discussion of Beauville’s paper, focussing on the structure theorem for simply connected Kähler manifolds with $c_1(K_X)=0$.

Number Theory - Sonja Ruzic

Tuesday, November 27th, 2018

Time: 10:00-11:00 a.m.  Place: Jeffery Hall 422

Speaker: Sonja Ruzic

Title: Presentation of the paper "Maxima for Graphs and a New Proof of a Theorem of Turan", by T.S. Motzkin and E.G. Straus.

Abstract: In this talk we consider the following problem: Given a graph G with vertices 1, 2, ..., n, let S be the simplex in $\mathbb{R}^n$ given by the set $x={x_1, x_2, ..., x_n | \sum_{i=1}^{n}x_i=1, x_i \geq 0 \forall I}$. What is $\max_{x \in S} \sum_{(i, j)\in G}x_ix_j?$ Furthermore, a proof of a theorem of Turan, which gives an upper bound to the number of edges of a graph G which contains no complete subgraph of order k, will be presented.