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Math Club

Thursday, February 9th, 2023

Time: 5:30 p.m.  Place: Jeffery Hall, Room 118

Speaker: Francesco Cellarosi (Queen's University)

Title: A converse to the intermediate value theorem?

Abstract: Continuous functions satisfy the intermediate value property: on an interval $[a,b]$ they attain every value between $f(a)$ and $f(b)$. Is the converse true? That is, does the intermediate value property imply continuity? We will see that the answer is no, and discuss some extreme counterexamples of everywhere discontinuous functions with the intermediate value property.

Algebra & Geometry Seminar

Monday, February 13th, 2023

Time: 4:30 p.m.  Place: TBA

Speaker: David Wehlau (RMC & Queen's University)

Title: Determining whether the invariants of a modular permutation representation are Cohen-Macaulay

Abstract:

Website details here: https://mast.queensu.ca/~georep/Fall%20'22.html

Probability Seminar

Wednesday, March 29th, 2023

Time: 12:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Ben Landon (U of Toronto)

Title: Local law and rigidity for unitary Brownian motion

Abstract: We establish high probability estimates on the eigenvalue locations of Brownian motion on the N-dimensional unitary group, as well as estimates on the number of eigenvalues lying in any interval on the unit circle. These estimates are optimal up to arbitrarily small polynomial factors in N. Our results hold at the spectral edges (showing that the extremal eigenvalues are within $O(N^{-2/3+})$ of the edges of the limiting spectral measure), in the spectral bulk, as well as for times near 4 at which point the limiting spectral measure forms a cusp. Our methods are dynamical and are based on analyzing the evolution of the Borel transform of the empirical spectral measure along the characteristics of the PDE satisfied by the limiting spectral measure, that of the free unitary Brownian motion. Joint work with Arka Adhikari

Probability Seminar

Wednesday, February 15th, 2023

Time: 12:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Somnath Pradhan (Queen's University)

Title: TBA

Abstract: TBA

Probability Seminar

Wednesday, February 8th, 2023

Time: 12:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Zachary Selk (Queen's University)

Title: Trapezoid Rule for Rough Paths

Abstract: Rough paths theory is an alternative theory of solving stochastic differential equations to the classical Ito theory. Rough paths have two main advantages over Ito theory. First, it can be used to solve differential equations driven by more general processes than semi-martingales. Second, it can be used to solve differential equations in a pathwise way. Furthermore the solution map is continuous - that is, given two instances of driving signals that are close the solutions are also close.

The so-called "rough integral" is a standard Riemann-Stieltjes integral with an additional "correction term" which can be viewed as encoding a kind of "iterated integral" of the driving signal against itself. This correction term can be seen as unnatural. In this talk, we show for a wide class of Gaussian processes including the fractional Brownian motion one can simply use the trapezoid rule. Joint work with Yanghui Liu and Samy Tindel.

Math Club

Thursday, February 2nd, 2023

Time: 5:30 p.m.  Place: Jeffery Hall, Room 118

Speaker: Mike Roth (Queen's University)

Title: Fractran!

Abstract: This talk will discuss fractran, a programming langage based on fractions invented by John Conway.

Math Club

Thursday, January 26th, 2023

Time: 5:30 p.m.  Place: Jeffery Hall, Room 118

Speaker: Troy Day (Queen's University)

Title: Lessons from the Covid-19 Pandemic : how to use an undergraduate degree in mathematics to influence public health policy

Abstract: The talk will share some experiences from working with the Ontario Science Table Modeling Group on COVID-19.

We will discuss two examples where relatively simple mathematical ideas had a direct impact on public health policy in the province.

Math & Stats Department Colloquium

Friday, February 10th, 2023

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

Speaker: Carolyn Abbott (Brandeis University)

Title: Big mapping class groups and their actions on hyperbolic graphs

Abstract: Given a surface with nite genus and nitely many punctures, there are two important objects naturally associated to it: a group, called the mapping class group, and an innite-diameter hyperbolic graph, called the curve graph. The mapping class group acts by isometries on the curve graph, and this action has been extremely useful in understanding the algebraic and geometric properties of mapping class groups. Nielsen and Thurston give a powerful classication of elements of a mapping class group, in which the most interesting and complex elements correspond to those with the dynamically richest actions on the curve graph. When the surface has innite genus or innitely many punctures, the mapping class group is much more complicated, and this classication no longer holds. In this talk, I will explain where the complications arise in this innite-type setting, focusing on the action of a mapping class group on an associated hyperbolic graph generalizing the curve graph. I will describe several constructions of elements which have dynamically rich actions on this graph which do not appear in the nite-type setting. This is joint work with Nick Miller and Priyam Patel.

Dr. Abbott is an Assistant Professor in the Mathematics Department at Brandeis University. Previously, she was an NSF Postdoctoral Fellow at Columbia University (2019-2021), an NSF Postdoctoral Fellow at UC Berkeley (2018-2019), and a Morrey Visiting Assistant Professor, also at UC Berkeley (2017-2018). She received her Ph.D. from the University of Wisconsin-Madison in 2017, where she studied geometric group theory under the supervision of Tullia Dymarz.

Dr. Abbott's research interests include geometric group theory and low-dimensional topology. In particular, she is interested in group actions by isometries on hyperbolic spaces, especially acylindrical actions. The kinds of groups she thinks about include hyperbolic and relatively hyperbolic groups, mapping class groups, Out(Fn), CAT(0) groups, three manifold groups, hierarchically hyperbolic groups, and many more.

Curves Seminar

Wednesday, February 1st, 2023

Time: 1:00 p.m.  Place: Jeffery Hall, Room 222 & Zoom

Speaker: Julia McClellan

Title: Introduction to Polytopes and their Lattice Points

Abstract: Before we begin to look at the rich connections between our previous discussion of projective toric varieties and polytopes, we need to study polytopes themselves and their lattice points. We will begin by developing a vocabulary to discuss polytopes and their properties. Next, we will see some examples of special classes of polytopes. Finally, we will define sums, multiples, and duals. These tools will allow us to continue our discussion towards lattice polytopes and their connection with toric varieties.

Math & Stats Department Colloquium

Friday, February 3rd, 2023

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

Speaker: Kwun Chuen Gary Chan (University of Washington)

Title: Stein shrinkage, random matrix and imaginary direction smoothing

Abstract: The Jame-Stein estimator of a multivariate mean vector and the Stein estimator of a covariance matrix are classical examples of shrinkage estimators. Conceptually very different from the majority of contemporary estimators formulated using penalization with sparsity and/or low-rank assumptions, Stein covariance estimator targets non-sparse and full-rank covariance matrices. We review recent literature in random matrix theory which are relevant in studying Stein-type shrinkage estimators and extensions, and present certain asymptotic optimality results under various loss functions. A recurring unknown quantity to be estimated is a real-direction limit of a Stieltjes transform of the limiting spectral distribution, defined on the upper complex half-plane. Moment-based estimators of such quantities are quite unstable but were used in Stein's original paper. We consider an alternative estimator by defining a smoothed loss function based on smoothed empirical spectral distribution, with an optimum in terms of a smoothed Stieljes transform, where smoothing is along the imaginary direction via a Cauchy kernel. A data-adaptive choice of the smoothing parameter is proposed due to a relationship between the imaginary part of a complex Stieltjes transform and the sample eigenvalue distribution. Some theoretical properties and numerical illustration will be discussed. This is a joint work with Sheung Chi Phillip Yam, Xiaolong Li and Yifan Shi.

Gary Chan is a professor jointly appointed in the Department of Biostatistics and Department of Health Systems and Population Health at the University of Washington. He has a broad statistical research interest on observational data, including complex designs, exposures and outcomes. He also has theoretical interest in certain semiparametric and nonparametric problems. He is a Fellow of the American Statistical Association and Institute of Mathematical Statistics. He is currently an associate editor of Journal of American Statistical Association (Theory and Methods) as well as a few statistics and public health journals.