Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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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.

Department Colloquium - Dennis K. J. Lin (Penn State University)

Dennis K. J. Lin (Penn State University)

Friday, November 9th, 2018

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

Speaker: Dennis K. J. Lin (Penn State University)

Title: Ghost Data.

Abstract: As natural as the real data, ghost data is everywhere -- it is just data that you cannot see. We need to learn how to handle it, how to model with it, and how to put it to work. Some examples of ghost data are (see, Sall, 2017):
a) Virtual data -- it isn't there until you look at it;
b) Missing data -- there is a slot to hold a value, but the slot is empty;
c) Pretend data -- data that is made up;
d) Highly Sparse Data -- whose absence implies a near zero, and
e) Simulation data -- data to answer ``what if.''
For example, absence of evidence/data is not evidence of absence. In fact, it can be evidence of something. More Ghost Data can be extended to other existing areas: Hidden Markov Chain, Two-stage Least Square Estimate, Optimization via Simulation, Partition Model, Topological Data, just to name a few. Three movies will be discussed in this talk: (1) ``The Sixth Sense'' (Bruce Willis) -- I can see things that you cannot see; (2) ``Sherlock Holmes'' (Robert Downey) -- absence of expected facts; and (3) ``Edge of Tomorrow'' (Tom Cruise) -- how to speed up your learning (AlphaGo-Zero will also be discussed). It will be helpful, if you watch these movies before coming to my talk. This is an early stage of my research in this area--any feedback from you is deeply appreciated. Much of the basic idea is highly influenced via Mr. John Sall (JMP-SAS).

Dennis K. J. Lin (Penn State University): He is a university distinguished professor of supply chain and statistics at Penn State University. His research interests are quality assurance, industrial statistics, data mining, and response surface. He has published more than 200 SCI/SSCI papers in a wide variety of journals. He currently serves or has served as associate editor for more than 10 professional journals and was co-editor for Applied Stochastic Models for Business and Industry. Dr. Lin is an elected fellow of ASA, IMS and ASQ, an elected member of ISI, a lifetime member of ICSA, and a fellow of RSS. He is an honorary chair professor for various universities, including a Chang-Jiang Scholar at Renmin University of China, Fudan University, and National Chengchi University (Taiwan). His recent awards including, the Youden Address (ASQ, 2010), the Shewell Award (ASQ, 2010), the Don Owen Award (ASA, 2011), the Loutit Address (SSC, 2011), the Hunter Award (ASQ, 2014), and the Shewhart Medal (ASQ, 2015). Last year, he was awarded the SPES Award at the 2016 Joint Statistical Meeting.

Curves Seminar - Mike Roth (Queen's University)

Tuesday, November 6th, 2018

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

Speaker: Mike Roth (Queen's University)

Title: Local description of the Hilbert scheme when $n=2$, II.

Abstract: We will finish the discussion of local descriptions of the quotient by a finite group, and use them to give local pictures of $X^{[n]}$, $\operatorname{Sym}^n(X)$, the universal family over $X^{[n]}$, and the maps between them when $X$ is a smooth surface and $n=2$.

Number Theory - Brad Rodgers (Queen's University)

Tuesday, November 6th, 2018

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

Speaker: Brad Rodgers (Queen's University)

Title: Integers in short intervals representable as sums of two squares.

Abstract: Consider the set S of integers that can be represented as a sum of two squares. How are the elements of S distributed? In particular, how many elements fall into a random "short interval". (The definition of short interval will be given in the talk.) For very short intervals elements of S seem to be laid down at random, but I will discuss evidence that this ceases to be the case for longer short intervals. In particular, I will discuss a function field analogue of this problem and a connection to z-measures, an object first investigated in the context of asymptotic representation theory. This is joint work with O. Gorodetsky.

Geometry & Representation - Steven Spallone (Indian Institute)

Monday, November 5th, 2018

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

Speaker: Steven Spallone (Indian Institute of Science Education and Research)

Title: Spinoriality of Orthogonal Representations of Reductive Groups

Abstract:  Let G be a connected semisimple complex Lie group and $\pi$ an orthogonal representation of G. We give a simple criterion for whether $\pi$ lifts to the spin group Spin(V), in terms of its highest weights. This is joint work with Rohit Joshi.

Department Colloquium - Thomas Koberda (University of Virginia)

Thomas Koberda (University of Virginia)

Friday, November 2nd, 2018

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

Speaker: Thomas Koberda (University of Virginia)

Title: Algebra versus regularity for group actions on one-manifolds.

Abstract: I will survey some results concerning the algebraic structure of finitely generated groups which admit faithful actions on compact one-manifolds. I will concentrate on continuous, $C^1$, and $C^2$ actions, and on the various algebraic restrictions imposed by regularity requirements. Of particular interest will be nilpotent groups, right-angled Artin groups, mapping class groups of surface, and Thompson's groups F and T. Time permitting, I will indicate some recent progress.

After obtaining his undergraduate at the University of Chicago, Thomas Koberda got his Ph.D.~from Harvard in 2012, then went to Yale as an NSF and Gibbs assistant professor before joining the University of Virginia in 2015. Thomas achievements have been recognized by a Sloan Research Fellowship and the Kamil Duszenko Prize of 2017.