Infosheet (January 16th, 2018)

Queen's University - Department of Mathematics and Statistics


Tuesday, January 16

Seminar in Free Probability and Random Matrices

Time: 4:00 p.m.

Place: Jeffery 319

Speaker: Neha Prabu, Queen’s University

Title: Semicircle distribution in number theory

Abstract Attached

Wednesday, January 17

Number Theory Seminar

Time: 1:30 p.m.

Place: Jeffery 319

Speaker: Jung-Jo Lee

Title: The p-adic zeta function and Iwasawa’s main conjectur4e

Abstract Attached

Wednesday, January 17

Curves Seminar

Time: 3:30 p.m.

Place: Jeffery 319

Speaker: Mike Roth

Title: Applications of the connectedness theorem to Secant varieties

Abstract Attached

Friday, January 19

Dynamics Seminar

Time: 10:30 a.m.

Place: Jeffery 422

Speaker: Francesco Cellarosi

Title: The Ten Martini problem

Abstract Attached

Friday, January 19

Department Colloquium

Time: 2:30 p.m.

Place: Jeffery 234

Speaker: Svetlana Jitomirskaya, UC Irvine

Title: Lyapunov exponents, small denominators, arithmetic spectral transitions, and universal hierarchical structure of quasiperiodic eigenfunctions

Abstract Attached

Items for the Info Sheet should reach Anne ( burnsa@queensu.ca) by noon on Monday. The Info Sheet is published every Tuesday.


Tuesday, January 16, 4:00 p.m. Jeffery 319

Seminar in Free Probability and Random Matrices

Speaker: Neha Prabu

Title: Semicircle distribution in number theory

Abstract: In free probability theory, the role of the semicircle distribution is analogous to that of the normal distribution in classical probability theory. However, the semicircle distribution also shows up in number theory: it governs the distribution of eigenvalues of Hecke operators acting on spaces of modular cusp forms. In this talk, I will give a brief introduction to this theory of Hecke operators and sketch the proof of a result which is a central limit type theorem from classical probability theory, that involves the semicircle measure.

Seminar website: http://www.mast.queensu.ca/~mingo/seminar/


Wednesday, January 17, 1:30 p.m. Jeffery 319 - Number Theory Seminar

Speaker: Jung-Jo Lee

Title: The p-adic zeta function and Iwasawa’s main conjecture

Abstract: I would explain the role of the p-adic zeta function in describing the structure of certain Iwasawa module.


Wednesday, January 16, 3:30 p.m. Jeffery 319 - Curves Seminar

Speaker: Mike Roth

Title: Applications of the connectedness theorem to Secant varieties

Abstract: We will begin by recalling what happened the previous semester, and then continue giving applications of the connectedness theorem, this time to the dimensions of secant varieties.


Friday, January 19, 10:30 a.m. Jeffery 422 - Dynamics Seminar

Speaker: Francesco Cellarosi

Title: The Ten Martini problem

Abstract: In honour of our colloquium speaker, I will review the main results that led Artur Avila and Svetlana Jitomirskaya to a proof of the so called “Ten Martini problem” on the topological structure of the spectrum of the almost-Mathieu operator.


Friday, January 19, 2:30 p.m. Jeffery 234 - Department Colloquium

Speaker: Svetlana Jitomirskaya

Title: Lyapunov exponents, small denominators, arithmetic spectral transitions, and universal hierarchical structure of quasiperiodic eigenfunctions

Abstract: A very captivating question in solid state physics is to determine/understand the hierarchical structure of spectral features of operators describing 2D Bloch electrons in perpendicular magnetic fields, as related to the continued fraction expansion of the magnetic flux. In particular, the hierarchical behavior of the eigenfunctions of the almost Mathieu operators, despite significant numerical studies and even a discovery of Bethe Ansatz solutions has remained an important open challenge even at the physics level. I will present a complete solution of this problem in the exponential sense throughout the entire localization regime. Namely, I will describe, with very high precision, the continued fraction driven hierarchy of local maxima, and a universal (also continued fraction expansion dependent) function that determines local behavior of all eigenfunctions around each maximum, thus giving a complete and precise description of the hierarchical structure. In the regime of Diophantine frequencies and phase resonances there is another universal function that governs the behavior around the local maxima, and a reflective-hierarchical structure of those, a phenomena not even described in the physics literature. These results lead also to the proof of sharp arithmetic transitions between pure point and singular continuous spectrum, in both frequency and phase, as conjectured since 1994. The talk is based on papers joint with W. Liu.

Contact Info

Department of Math & Stats
Jeffery Hall, 48 University Ave.
Kingston, ON Canada, K7L 3N6
Phone: (613) 533-2390
Fax: (613) 533-2964
mathstat@mast.queensu.ca
Office Hours: 8:30am-12:00pm & 1:00pm-4:30pm

Search