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.