Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Probability Seminar - Pei-Lun Tseng (Queen's University)

Thursday, October 18th, 2018

Time: 4:30-6:00 p.m.  Place: Jeffery Hall 422

Speaker: Pei-Lun Tseng (Queen's University)

Title: Right Hilbert A-modules, Part II

Abstract:  For the last talk, we gave some motivating examples and the definition of right A-module. We will begin this talk by showing some properties of A-valued pre inner product, and then we will deduce the process to construct a right Hilbert A-module. Next, we will introduce the operators on right Hilbert A-modules, and proving some properties of the corresponding adjoint operators.

Free Probability and Random Matrices Seminar Webpage:

CYMS Seminar - Noriko Yui (Queen's University)

Thursday, October 18th, 2018

Time: 11:30 a.m - 12:20 p.m Place: Jeffery Hall 422

Speaker: Noriko Yui (Queen's University)

Title: Four-dimensional Galois representations arising from certain Calabi--Yau threefolds Part II

Abstract: We consider the (irreducible) four-dimensional Galois representations arising from certain Calabi--Yau threefolds over ${\bf{Q}}$ with all the Hodge numbers of the third cohomology groups equal to $1$. There are many examples of (families) of such Calabi--Yau threefolds. The modularity/automorphy of such Calabi--Yau threefolds will be the main topic of discussion. There are two venues to be considered. In one venue, we ought to count the number of rational points over finite fields of these Calabi--Yau threefolds to concoct their L-series. In the other venue, we ought to construct some modular varieties, in this case, conjecturally, Siegel modular forms of weight $3$ and genus $2$ on some paramodular subgroups of $Sp(4,{\bf{Z}})$, and then compute their L-series. Such modular forms may be constructed using Borcherds forms. The ultimate aim is to establish a Langlands correspondence between the two L-series, thereby establishing the modularity/automorphy of such Calabi--Yau threefolds.

This is a joint work with Yifan Yang (National Taiwan University).

Number Theory - Siddhi Pathak (Queen's University)

Tuesday, October 16th, 2018

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.

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.

Probability Seminar - Pei-Lun Tseng (Queen's University)

Thursday, October 11th, 2018

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.

Free Probability and Random Matrices Seminar Webpage:

Curves Seminar - Mike Roth (Queen's University)

Tuesday, October 9th, 2018

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 $P(s) = m$?".

Number Theory - Anup Dixit (Queen's University)

Tuesday, October 9th, 2018

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.

Dynamics, Geometry, & Groups - Francesco Cellarosi (Queen's)

Friday, October 5th, 2018

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.

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