Infosheet (February 6th, 2018) |
Queen's University - Department of Mathematics and Statistics |
Tuesday, February 6 |
Seminar in Free Probability and Random Matrices Time: 3:30 p.m. Place: Jeffery 319 |
Speaker: Jamie Mingo Title: The Infinitesimal Law of the GOE Abstract Attached |
Wednesday, February 7 |
Number Theory Seminar Time: 2:15 p.m. Place: Jeffery 319 |
Speaker: Jung-Jo Lee Title: Iwasawa’s main conjecture and Euler systems Abstract Attached |
Wednesday, February 7 |
Curves Seminar Time: 3:30 p.m. Place: Jeffery 319 |
Speaker: Daniel Erman, Wisconsin – Madison Title: Big polynomial rings and Stillman’s conjecture Abstract Attached |
Thursday, February 8 |
Math Club Time: 5:30 p.m. Place: Jeffery 118 |
Speaker: Greg Smith Title: The Empty Set |
Friday, February 9 |
Graduate Seminar Time: 11:30 a.m. Place: Jeffery 118 |
Speaker: Daniel Adu Owusu Title: Introduction to Optimal transportation Abstract Attached |
Friday, February 9 |
Department Colloquium Time: 3:30 p.m. Place: Jeffery 234 |
Speaker: Daniel Le, University of Toronto Title: The geometry of Galois representations 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, February 6, 3:30 p.m. Jeffery 319
Seminar in Free Probability and Random Matrices
Speaker: Jamie Mingo
Title: The Infinitesimal Law of the GOE
Abstract: If X_N is the N x N Gaussian Orthogonal Ensemble (GOE) of random matrices, we can expand E(tr(X_N^n)) as a polynomial in 1/N, often called a genus expansion. Following the celebrated formula of Harer and Zagier for the GUE, Ledoux (2009) found a five term recurrence for the coefficients of E(tr(X_N^n)). We show that the coefficient of 1/N counts the number of non-crossing annular pairings of a certain type.
Our method is quite elementary. A similar formula holds for the Wishart ensemble. This identification is related to the theory of infinitesimal freeness of Belinschi and Shlyakhtenko.
Wednesday, February 7, 2:15 p.m. Jeffery 319 - Number Theory Seminar
Speaker: Jung-Jo Lee
Title: Iwasawa’s main conjecture and Euler systems
Abstract: The purpose of this talk is to explain the idea how an Euler system can be used to prove Iwasawa's main conjecture.
Wednesday, February 7, 3:30 p.m. Jeffery 319 - Curves Seminar
Speaker: Daniel Erman
Title: Big polynomial rings and Stillman’s conjecture
Abstract: Ananyan–Hochster's recent proof of Stillman's conjecture is based on a key principle: if f_1,.., f_r are sufficiently general forms in a polynomial ring, then as the number of variables tends to infinity, they will behave increasingly like independent variables. We show that this principle becomes a theorem if ones passes to a limit of polynomial rings, using either the inverse limit or the ultraproduct. This yields the surprising fact that these limiting rings are themselves polynomial rings (in uncountably many variables).
It also yields two new proofs of Stillman's conjecture. This is joint work with Steven Sam and Andrew Snowden.
Friday, February 9, 11:30 a.m. Jeffery 118 - Graduate Seminar
Speaker: Daniel Adu Owusu
Title: Introduction to Optimal transportation
Abstract: I will motivate the problem and introduce the original Monge's problem and analysis it. I will convince you that it is a very difficult problem and the solution does not exist using simple example(s) and hence a tractable formulation will be needed to tackle the optimal transportation problem. This leads to the Kantorovich problem. I will convince you it is a relaxed version of the Monge's problem and with this new formulation will prove that solution(s) to the optimal transportation problem exists. We will then look at the duality of the Kantorovich problem if time permits. Hope you enjoy this talk.
Friday, February 9, 3:30 p.m. Jeffery 234 - Department Colloquium
Speaker: Daniel Le
Title: The geometry of Galois representations
Abstract: The arithmetic of number fields can be profitably studied through the representation theory of their absolute Galois groups. These representations exhibit a number of elegant and surprising phenomena, most famously the quadratic reciprocity law. Many of these phenomena are explained by the modularity conjecture of Langlands that all Galois representations come from modular forms. Startling progress towards this conjecture began with Taylor and Wiles's study of Galois deformation spaces. We give a construction of local models for some Galois deformation spaces coming from geometric representation theory, and describe some applications to modularity conjectures and congruences between modular forms. Much of what we discuss is joint work with Bao Le Hung, Brandon Levin, and Stefano Morra.