Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Department Colloquium

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.

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.

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.

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.

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.

Department Colloquium - Camille Horbez (CNRS-Universite Paris Sud)

Camille Horbez (CNRS-Universite Paris Sud)

Friday, October 19th, 2018

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

Speaker: Camille Horbez (CNRS – Universite Paris Sud)

Title: Mostow-type rigidity and normal subgroups of automorphisms of free groups.

Abstract: The talk is based on a recent joint work with Richard D. Wade. Let Out(Fn) be the outer automorphism group of a finitely generated free group. In 2007, Farb and Handel proved that when n is at least 4, every isomorphism between two finite-index subgroups of Out(Fn) extends to an inner automorphism of Out(Fn). This rigidity statement, asserting that Out(Fn) has no more symmetries than the obvious ones, can be viewed as an analogue of the Mostow rigidity theorem for lattices in Lie groups, or of a result of Ivanov for mapping class groups of surfaces. We recently gave a new proof of Farb and Handel's theorem, which enabled us to also understand the symmetries of some natural normal subgroups of Out(Fn). In my talk, I will emphasize the analogies between Out(Fn), arithmetic groups and mapping class groups, and will present some general ideas behind these rigidity phenomena.

Camille Horbez obtained his Ph.D in at the Universite de Rennes in 2014, and after a year at the University of Utah, he became a Charge de Recherches for the CNRS at the Universite de Paris Sud (Orsay). In 2017, Camille was selected to give a Cours Peccot, a semester long course given at the College de France by a mathematician less than 30 year old.

Department Colloquium - Undergrad Summer Project Presentations

Undergrad Summer Project Presentations

Friday, October 12th, 2018

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

Undergraduate Summer Project Presentations

This week colloquium will consists of five short presentations by:

  • Riley Becker - On the Size of Diophantine $m$-tuples.
  • Fernando Camacho Cadena & Troy Giorshev - On a Construction of Surfaces with Distinct Hilbert Metrics and Identical Length Spectra.
  • Sean Monahan - The Cartan determinant conjecture.
  • Shikai Liu - The fluctuations of the Kesten-McKay law.
  • Linke Li - Kalman Filter and its variation.
  • Riley Becker - On the Size of Diophantine m-tuples.

    Riley Becker
    On the Size of Diophantine $m$-tuples.

  • Fernando Camacho Cadena & Troy Giorshev - On a Construction of Surfaces with Distinct Hilbert Metrics and Identical Length Spectra.

    Fernando Camacho Cadena & Troy Giorshev
    On a Construction of Surfaces with Distinct Hilbert Metrics and Identical Length Spectra.

  • Sean Monahan - The Cartan determinant conjecture.

    Sean Monahan
    The Cartan determinant conjecture.

  • Shikai Liu - The fluctuations of the Kesten-McKay law.

    Shikai Liu
    The fluctuations of the Kesten-McKay law.

  • Linke Li - Kalman Filter and its variation.

    Linke Li
    Kalman Filter and its variation.

Department Colloquium - Aaron Smith (Queen's University)

Aaron Smith, Queen's University

Friday, October 5th, 2018

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

Speaker: Aaron Smith (Queen's University)

Title: Mixing and the Glass Transition.

Abstract: Supercooled liquid forms when a liquid is cooled below its usual freezing temperature without entering a crystalline solid phase. As supercooled liquids continue to get colder, they exhibit something called the glass transition: they remain disordered, but start to otherwise behave much like solids. This glass transition is important for many materials, including rubbers and colloids, but is not theoretically well-understood. In this talk I will introduce a simple model for the glass transition that is easy to understand but difficult to study. I will then introduce two related families of models, introduced by physicists, that seem to give similar "glassy" behaviour. Finally, I will present some heuristics and recent results on the relaxation and mixing behavior of these two models. My results in this talk are from joint and ongoing work with Paul Chleboun, Alessandra Faggionato, Fabio Martinelli, Natesh Pillai and Cristina Toninelli.

Aaron Smith works in the areas of applied probability, with a focus on Markov chain Monte Carlo and related methods from computational statistics or statistical physics. He also has interest in in data mining and machine learning. He obtained his Ph.D. at Stanford in Mathematics, and was an undergraduate student at Queen's University. He held short-term appointments at Federal government of Canada, Brown University (applied math), and Harvard (statistics). He is currently an assistant professor in the Department of Mathematics and Statistics at the University of Ottawa.

Department Colloquium - Jon Chaika (University of Utah)

Jon Chaika, University of Utah

Friday, September 28th, 2018

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

Speaker: Jon Chaika (University of Utah)

Title: Horocycle orbits in strata of translation surfaces.

Abstract: Ergodic theory is concerned with describing the long term behavior of orbits as time evolves. Ratner, Margulis, Dani and many others, showed that the horocycle flow have strong measure theoretic and topological rigidity properties that allow a good understanding of every such orbit. Eskin-Mirzakhani and Eskin-Mirzakhani-Mohammadi, showed that the action of $SL(2,\mathbb{R})$, and its upper triangular subgroup, on strata of translation surfaces have similar rigidity properties. We will describe how some of these results fail for the horocycle flow on strata of translation surfaces. In particular, 1) There exist horocycle orbit closures with fractional Hausdorff dimension; 2) There exist points which do not equidistribute under the horocycle flow with respect to any measure; 3) There exist points which equidistribute under the horocycle flow with respect to a measure, but they are not in the topological support of that measure. No familiarity with these objects will be assumed and the talk will begin with motivating the subject of dynamics and ergodic. This is joint work with John Smillie and Barak Weiss.

Jon Chaika works in the field of Dynamical systems. He did his undergraduate at the University of Iowa, obtained his Ph.D. from Rice, then went to the University of Chicago before coming to the University of Utah.

Department Colloquium - Boris Levit (Queen's University)

Boris Levit, Queen's University

Friday, September 21st, 2018

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

Speaker: Boris Levit (Queen's University)

Title: Optimal Cardinal Interpolation in Approximation Theory, Nonparametric Regression, and Optimal Design

Abstract: For the Hardy classes of functions analytic in the strip around real axis of a size $2\beta$, an optimal method of cardinal interpolation has been proposed within the framework of Optimal Recovery. It will be shown that this method, based on the Jacobi elliptic functions, is also optimal according to the criteria of Nonparametric Regression and Optimal Design. In a stochastic non-asymptotic setting, the maximal mean squared error of the optimal interpolant is evaluated explicitly, for all noise levels away from $0$. A pivotal role is played by the interference effect, in which the oscillations exhibited by the interpolant's bias and variance mutually cancel each other. In the limiting case $\beta \rightarrow \infty $, the optimal interpolant converges to the well known Nyquist-Shannon cardinal sampling series.