Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
Subscribe to RSS - Seminars

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.

Control Theory - Prof. Ashutosh Nayyar (USC)

Thursday, November 20th, 2018

Time: 10:00 a.m Place: Jeffery Hall 319

Speaker: Prof. Ashutosh Nayyar (USC)

Title: Decentralized control over unreliable communication links

Abstract: Decentralized control problems have been a topic of significant research interest due to their relevance to multi-agent systems and large-scale distributed systems.The design of optimal decentralized control strategies has been investigated under various models for inter-controller communication such as graph-based communication models and communication with delays. A common feature of much of the prior work is that the underlying communication structure of the decentralized system is assumed to be fixed and unchanging. For example, several works assume a fixed communication graph among controllers whose edges describe perfect communication links between controllers. Similarly, when the communication graph incorporates delays, the delays are assumed to be fixed and known. This is a key limitation since in many situations communication among controllers may suffer from imperfections such as random packet loss and random packet delays. These imperfections introduce a new layer of uncertainty in the information structure that is not present in the models considered in prior work. In this talk, we will describe a decentralized LQG control problem where some of the communication links suffer from random packet loss. We will first identify optimal decentralized control strategies for finite horizon version of our problem. We will then discuss the infinite horizon problem and show that there are critical thresholds for packet loss probabilities above which no strategy can achieve finite cost and below which optimal strategies can be explicitly identified.

Department Colloquium - Anne Broadbent (University of Ottawa)

Anne Broadbent (University of Ottawa)

Friday, November 16th, 2018

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

Speaker: Anne Broadbent (University of Ottawa)

Title: How to Verify a Quantum Computation?

Abstract: Experimental implementations of quantum computers are in their infancy, but already we are faced with the following conundrum: if quantum computers are exponentially more powerful than their classical counterparts, how can we verify the outcome of a quantum computation? In this context, the scientific method of "predict and verify" appears to fail dramatically: these computations are so complex that they are impossible to predict. For a solution to this problem, we turn to theoretical computer science, where it is well established that interaction dramatically increases the power of a verification process.

Dr. Anne Broadbent is an Associate Professor in the Department of Mathematics and Statistics at the University of Ottawa, where she holds the University Research Chair in Quantum Information Processing. Her research focuses on quantum complexity and cryptography and she is perhaps best known for her 2009 paper on 'Blind Quantum Computing'. Dr. Broadbent was awarded the NSERC Doctoral Prize (2009), the John Charles Polanyi Prize in Physics (2010), the Ontario Early Researcher Award (2016) and the Andre Aisenstadt Mathematics Prize of the Centre de Recherches Mathematiques (2016). She is also a CIFAR Global Scholar Alumni and an affiliate member of the Perimeter Institute for Theoretical Physics, the Institute for Quantum Computing, and the Institut Transdiscliplinaire d'Informatique Quantique.

Geometry & Representation - Yin Chen (NE Normal University, China)

Monday, November 12th, 2018

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

Speaker: Yin Chen (Northeast Normal University, China)

Title: On vector invariant fields for finite classical groups

Abstract:  In the recent work ( with David Wehlau, we found a minimal polynomial generating set for the vector and covector invariant field of the general linear group over finite fields. Our method relied on some relations between the generators for the invariant ring of one vector and one covector. The remaining case (without covectors) is more complicated. In this talk, I will present an approach to find polynomial generating sets for the vector invariant fields of the most of finite classical groups. This is a joint work with Zhongming Tang.