Department of Mathematics and Statistics

Wednesday, June 20th, 2018

Time: 2:00-3:20p.m.  Place: Jeffery Hall 422

Speaker: Neha Prabhu (Queen's University)

Title: EXTREMAL PRIMES FOR NON-CM ELLIPTIC CURVES.

Abstract: For an elliptic curve E over the field of rationals, the distribution of the number of points on E modulo a prime p has been well-studied over the last few decades. A relatively recent study is that of extremal primes for a given curve E. These are the primes p of good reduction for which the number of points on E mod p is either maximal or minimal. If E is a curve with CM, an asymptotic for the number of extremal primes was determined by James and Pollack. The talk will discuss the non-CM case and focus on obtaining upper bounds. This is joint work with C. David, A. Gafni, A. Malik and C. Turnage-Butterbaugh

Wednesday, May 23rd, 2018

Time: 3:30-5:00 p.m.  Place: Jeffery Hall 319

Speaker: Benson Au (Berkeley)

Title: Rigid structures in the universal enveloping traffic space

Abstract:  For a tracial $*$-probability space $(\mathcal{A}, \varphi)$, Cébron, Dahlqvist, and Male constructed an enveloping traffic space $(\mathcal{G}(\mathcal{A}), \tau_\varphi)$ that extends the trace $\varphi$. The CDM construction provides a universal object that allows one to appeal to the traffic probability framework in generic situations, prioritizing an understanding of its structure.

We show that $(\mathcal{G}(\mathcal{A}), \tau_\varphi)$ comes equipped with a canonical free product structure, regardless of the choice of $*$-probability space $(\mathcal{A}, \varphi)$. If $(\mathcal{A}, \varphi)$ is itself a free product, then we show how this additional structure lifts into $(\mathcal{G}(\mathcal{A}), \tau_\varphi)$. Here, we find a duality between classical independence and free independence.

We apply our results to study the asymptotics of large (possibly dependent) random matrices, generalizing and providing a unifying framework for results of Bryc, Dembo, and Jiang and of Mingo and Popa. This is joint work with Camille Male.

Free Probability and Random Matrices Seminar Webpage:

Strength in Numbers: A Graduate Workshop in Number Theory and Related Areas

Dates: Friday, May 11th and Saturday, May 12th, 2018

Venue: Jeffery Hall, Queen's University

This is a two-day workshop aimed primarily at graduate students. Participation is open to all. There are five plenary talks by experts and many contributed talks by graduate students on a topic of their choice. Schedules and abstracts of the talks are attached with this email.

A novel feature of this workshop is a presentation by Prof. Erin Maloney, a psychologist specializing in math anxiety and related areas. The invited speakers will also lead a panel discussion regarding professional development on Saturday. Questions can be submitted here - https://docs.google.com/forms/d/e/1FAIpQLSdedZpevw4t8mDHlctq1Nmbmz3hX6v6IC-pyeBmV79jlWLM2g/viewform?usp=sf_link

More information about the workshop can also be found on the website: https://sites.google.com/view/strengthinnumbers2018/home

This workshop is sponsored by the Fields institute, the Number Theory Foundation and the department of Mathematics and Statistics, Queen's.

• General Schedule (PDF, 44 KB)
• Short Talks Schedule (PDF, 88 KB)
• Abstracts for Short Talks (PDF, 185 KB)
• Abstracts for Plenary Talks (PDF, 103 KB)

We hope to see you there!
Sincerely,
The organizing committee
Neha Prabhu, Siddhi Pathak and Vaidehee Thatte

Wednesday, May 2nd, 2018

Time: 4:00-5:30p.m.  Place: Jeffery Hall 422

Speaker: M. Ram Murty (Queen's University)

Title: SPECIAL VALUES OF MODULAR $L$-SERIES.

Abstract: We will discuss the Rankin-Selberg method as well as the analytic continuation of Eisenstein series that allows us to evaluate special values of modular $L$-series at critical point (in the sense of Deligne).

Tuesday, April 10th, 2018

Time: 3:00 p.m.  Place: Jeffery Hall 422

Speaker: Milan Derpich (Universidad Técnica Federico Santa María and Queen's)

Title: Stationarity in the realizations of the causal information rate-distortion function for one-sided stationary sources