Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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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.

Geometry & Representation - Mike Roth (Queen's University)

Monday, November 26th, 2018

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

Speaker: Mike Roth (Queen's University)

Title: Generating Rays for the Eigencone (after Belkale and Piers)

Abstract:  Let G be a semisimple algebraic group. A fundamental question in the representation theory of G is knowing how to decompose the tensor product of two irreducible representations into its irreducible components, or slightly weaker, which irreducible components appear in a tensor product of two irreducible representations. The irreducible representations of G are parameterized by highest weights, vectors in ℕ^{r}, where r is the rank of G. For a highest weight λ the corresponding irreducible representation is denoted V_{λ} If one takes triples (λ, μ, ν) of highest weights such that V_{ν} appears in V_{λ} ⊗ V_{μ} then these triples generate a polyhedral cone in ℚ^{3r}, known as the eigencone (or sometimes the tensor cone). Trying to find explicit equations for the hyperplanes cutting out the eigencone is a problem with a long history, including fundamental contributions by Weyl, Gelfand, Lidskii, and Wielandt. Finally, twenty years ago, Klyachko found a set of hyperplane inequalities cutting out the eigencone in type A. Progress in the last 20 years has included finding hyperplane inequalities for the eigencones in all types, finding minimal hyperplane inequalities in all types, and finally, also finding descriptions of the linear conditions cutting out higher codimensional faces of the eigencone. Dually to their description by hyperplane inequalities, polyhedral cones may also be described by their generating rays. It is of course natural to then ask for the generating rays of the eigencone. This talk will discuss a recent paper of Belkale and Piers giving a recursive method, valid in all types, of finding generating rays for the eigencone.

Lorne Campbell Lectureship - Frank R. Kschischang (U of T)

Frank R. Kschischang

Friday, November 23rd, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 126

Speaker: Frank R. Kschischang
(Distinguished Professor of Digital Communication, University of Toronto)

Title: The Mathematics of Modems

Abstract: Virtually all practical digital communications systems in use today include some form of error-control coding scheme. In this talk, I will review the theory and development of error-correcting schemes that can achieve, with practical decoding complexity, a performance approaching the fundamental information-theoretic limits established by Claude E. Shannon over seven decades ago

Frank R. Kschischang received the B.A.Sc. degree (with honours) from the University of British Columbia in 1985 and the M.A.Sc. and Ph.D. degrees from the University of Toronto in 1988 and 1991, respectively, all in electrical engineering. He holds the title of Distinguished Professor of Digital Communication in the Department of Electrical and Computer Engineering at the University of Toronto, where he has been a faculty member since 1991. During 1997-98, he was a visiting scientist at MIT, Cambridge, MA; in 2005 he was a visiting professor at the ETH, Zurich, and in 2011 and again in 2012-13 he was a visiting Hans Fischer Senior Fellow at the Institute for Advanced Study at the Technical University of Munich.

His research interests are focused primarily on the area of channel coding techniques, applied to wireline, wireless and optical communication systems and networks. In 1999 he was a recipient of the Ontario Premier’s Excellence Research Award and in 2001 (renewed in 2008) he was awarded the Tier I Canada Research Chair in Communication Algorithms at the University of Toronto.

Received the 2010 Communications Society and Information Theory Society Joint Paper Award. He is a recipient of the 2012 Canadian Award in Telecommunications Research. He is a Fellow of IEEE, of the Engineering Institute of Canada, and of the Royal Society of Canada.

During 1997-2000, he served as an Associate Editor for Coding Theory for the IEEE Transactions on Information Theory, and from 2014 to 2016, he served as this journal’s Editor-in-Chief. In 2016, he received the Aaron D. Wyner Distinguished Service Award of the IEEE Information Theory Society.

Images from Dr. Frank Kschischang's Lecture - Nov. 23rd, 2018

Lorne Campbell Lectureship - Dr. Frank Kschischang
Lorne Campbell Lectureship - Dr. Frank Kschischang
Lorne Campbell Lectureship - Dr. Frank Kschischang
Lorne Campbell Lectureship - Dr. Frank Kschischang

Curves Seminar - Mike Roth (Queen's University)

Tuesday, November 20th, 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 $c_1(K_X)=0$.

Abstract: We will discuss Beauville’s paper giving a classification statement for (compact, complex) Kähler manifolds with vanishing first Chern class. The Hilbert scheme of points comes in to construct examples of ``irreducible holomorphic symplectic manifolds’’, one of the pieces appearing in the classification.

Number Theory - Siqi Li (Queen's University)

Tuesday, November 20th, 2018

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

Speaker: Siqi Li (Queen's University)

Title: Realizability of a set of integers as degrees of the vertices of a linear graph.

Abstract: In this talk, we consider the following problem: Let A be a non-decreasing sequence of positive integers of length n. Does there exist a graph G on n vertices v_1 to v_n such that A is the sequence formed by deg(v_1) to deg(v_n)? Furthermore, the realizability of a connected graph, simple graph and the biconnected graph for a given finite sequence of vertices degrees A is considered. The application of the above theorem involves the description of the structure for isomers in an organic chemical compound.