Time: 2:00-3:30 p.m Place: Jeffery Hall 116
Speaker: Mike Roth (Queen's University)
Title: Examples of subschemes of points II
Abstract: We will use the examples from last time to study some of the global geometry of the Hilbert scheme $X^{[n]}$ when $X$ is a smooth surface, and $n=2$, $3$
Time: 10:15 a.m. Place: Jeffery Hall 422
Speaker: Siddhi Pathak (Queen's University)
Title: On the Euler-Kronecker constants.
Abstract: Values of the series $\sum_{n=1}^{\infty} A(n)/B(n)$ where A(X) and B(X) are polynomials with suitable conditions to ensure convergence, have been studied by several authors in the past. The evaluation of these series can be considered as a generalization of Euler's theorem evaluating $\zeta(2k)$. In this talk, we study elliptic analogues of these series.
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.
Time: 4:30-6:00 p.m. Place: Jeffery Hall 422
Speaker: Pei-Lun Tseng (Queen's University)
Title: Right Hilbert A-modules
Abstract: Last week, we gave a sketch of proving the GNS construction. We will start to introduce the matrices over a C*-algebra this week, which is an application of the GNS construction. Then, we will begin the new topic: Right Hilbert A-modules. We will deduce the process to construct the inner product on a right Hilbert A-module H. As long as we have the inner product, we can consider the orthogonality on H and compare the different between the scalar case and $A$-valued case.
Time: 11:30 a.m - 12:20 p.m Place: Jeffery Hall 422
Speaker: Richard Gottesman (Queen's University)
Title: Siegel Modular Forms II
Abstract: We will continue our journey into the fascinating world of Siegel modular forms.
Time: 2:00-3:30 p.m Place: Jeffery Hall 116
Speaker: Mike Roth (Queen's University)
Title: Examples of subschemes of points
Abstract: Last time we defined the ‘Hilbert Scheme of points’ of a projective variety $X$. This talk will concentrate on examples of the objects being parameterized. I.e., what is "a subscheme of $X$ with Hilbert polynomial $P(s) = m$?".
Time: 10:00 a.m. Place: Jeffery Hall 422
Speaker: Anup Dixit (Queen's University)
Title: On the Euler-Kronecker constants.
Abstract: In 2006, Y. Ihara introduced the Euler-Kronecker constant $\gamma_K$ attached to any number field $K$, which is a generalization of the Euler-Mascheroni constant. This constant surprisingly arises in several seemingly unrelated aspects of analytic number theory. Ihara studied this constant systematically and produced bounds on $gamma_K$ under GRH. In this talk, we prove unconditional bounds for $\gamma_K$ in some cases and discuss its connection to the Brauer-Siegel theorem.
Time: 10:30 a.m Place: Jeffery Hall 422
Speaker: Francesco Cellarosi (Queen's University)
Title: Central Limit Theorem via spectral method
Abstract: I will explain the Nagaev-Guivarc'h method to obtain a Central Limit Theorem for sequences of random variables coming from a large class of 1-dimensional dynamical systems, namely uniformly expanding maps of the interval. The idea is work in a suitable Banach space to establish a spectral gap for the transfer operator, and then use a perturbative argument. This talk is based on a paper by Sébastien Gouëzel.
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.
Time: 11:30 a.m - 12:20 p.m Place: Jeffery Hall 422
Speaker: Richard Gottesman (Queen's University)
Title: Siegel Modular Forms
Abstract: Siegel modular forms are a rich generalization of elliptic modular forms. The goal of this expository talk is to give an introduction to these mathematical objects.
