Date
Thursday February 2, 2023Location
Jeffery Hall, Room 118Thursday, 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.
Date
Thursday January 26, 2023Location
Jeffery Hall, Room 118Thursday, 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.
Date
Friday February 10, 2023Location
Jeffery Hall, Room 234Friday, 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.
Date
Wednesday February 1, 2023Location
Jeffery Hall, Room 222 & ZoomWednesday, 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.
Date
Friday February 3, 2023Location
Jeffery Hall, Room 234Friday, 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.
Date
Wednesday January 18, 2023Location
Jeffery Hall, Room 222 & ZoomWednesday, January 18th, 2023
Time: 1:00 p.m. Place: Jeffery Hall, Room 222 & Zoom
Speaker: Calvin Fletcher
Title: Projective Toric Varieties
Abstract: We will provide a review of projective space, projective varieties and affine pieces. We will then introduce projective toric varieties and study some examples. We will also discuss the relationship between the affine cone of a projective toric variety arising from a finite set and the toric variety arising from that same finite set.
Date
Wednesday January 25, 2023Location
Jeffery Hall, Room 222 & ZoomWednesday, January 25th, 2023
Time: 1:00 p.m. Place: Jeffery Hall, Room 222 & Zoom
Speaker: Sonja Ruzic
Title: Torus and Affine Pieces of Projective Toric Varieties
Abstract: We will continue our discussion of projective toric varieties. We will describe the torus of a projective toric variety by finding its character lattice. Next, we will describe its affine pieces. Time permitting, we will start the discussion on polytopes.
Date
Friday January 27, 2023Location
Jeffery Hall, Room 234Friday, January 27th, 2023
Time: 2:30 p.m. Place: Jeffery Hall, Room 234
Speaker: Benjamin Dozier (Cornell University)
Title: Random hyperbolic surfaces and random regular graphs
Abstract: I will discuss the burgeoning field of random hyperbolic geometry. An important source of inspiration is the analogy between random hyperbolic surfaces and random regular graphs, rich objects which have been studied for many years. Both random objects tends to have good ``expansion properties'': mixing happens very quickly, they cannot be separated into big pieces by a cut of small length, and the Laplace operator has uniform spectral gap. I will end with some recent results on counting simple closed geodesics in both settings, joint with Jenya Sapir.
Date
Monday January 23, 2023Location
Jeffery Hall, Room 319Monday, January 23rd, 2023
Time: 4:30 p.m. Place: Jeffery Hall, Room 319
Speaker: Nic Fellini (Queen's University)
Title: The bipartite sieve and applications to probabilistic Galois theory
Abstract: Given a monic polynomial f of degree n in Z[x], one can ask: what is the probability that the Galois group of f is a proper subgroup of the symmetric group on n symbols? This probabilistic Galois theory question has been studied for nearly 90 years! The most "satisfying" answer to this question is due to P. Gallagher in 1973. The key part of Gallagher's proof is the use of the multidimensional large sieve. The goal of this talk is to develop a much simpler sieve--- the bipartite sieve ---to study the probabilistic Galois theory question. Time permitting, we will discuss other applications of the bipartite sieve.
Date
Monday January 16, 2023Location
Jeffery Hall, Room 319Monday, January 16th, 2023
Time: 4:30 p.m. Place: Jeffery Hall, Room 319
Speaker: M. Ram Murty (Queen's University)
Title: SOME REMARKS ON HASSE'S INEQUALITY
Abstract: Hasse's inequality regarding the number of points on an elliptic curve mod p has a colorful history. Some of this is well-known in that it led to the rapid development of algebraic geometry. But some work of Davenport in the 1930's that predate Hasse's work is not so well-known. The beauty and elegance of this work got buried in the sands of time. I will give a streamlined version of both Davenport and Hasse's works and discuss especially what Davenport's work suggests for the classical Riemann hypothesis.
