Department of Mathematics FAS Harvard University One Oxford Street Cambridge MA 02138 USA Tel: (617) 495-2171 Fax: (617) 495-5132
To post a seminar which takes place at the Mathematics department, please email seminars@math.harvard.edu with date, time, room, title and possibly with an abstract.
THURSDAY SEMINAR: Mike Hopkins
Harvard University
Unstable chromatic localizations
on Thursday, September 21, 2017, at 4:00 - 6:00 PM in Science Center 507

GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR: Boyu Zhang
Harvard University
Derived category of sheaves and the six functors
on Friday, September 22, 2017, at 3:30 - 4:30 PM in Science Center 507
In this talk we will define the derived category of sheaves, and introduce the six functors between such categories. We will then discuss the properties of sheaves on manifolds and state the Poincare-Verdier duality theorem.

LEARNING SEMINAR ON THE FARGUE-FONTAINE CURVE: Dennis Gaitsgory
Harvard University
The relative Fargues-Fontaine curve and ``untilts", continued
on Monday, September 25, 2017, at 4:00 - 5:30 PM in Science Center 507

MATHEMATICAL PHYSICS SEMINAR : Jinsong Wu
Harvard University
The Brascamp-Lieb Inequalities for Planar Algebras
on Tuesday, September 26, 2017, at 4:00 PM in Jefferson 356
The Brascamp-Lieb inequalities for a Euclidean space generalized many important inequalities such as Hölder’s inequality, Young’s inequality, the Loomis-Whitney inequality. They have Gaussian functions as their extremizers under certain conditions. The bi-shift of bi-projections for planar algebras introduced by C. Jiang, Z. Liu, and J. Wu have many properties analogous to the Gaussian functions for Euclidean spaces. In this talk, we introduce the Brascamp-Lieb inequalities for planar algebras.

RANDOM MATRIX AND PROBABILITY THEORY SEMINAR: Herbert Spohn
Technical University Munich & Columbia
Hydrodynamics of integrable classical and quantum systems
on Wednesday, September 27, 2017, at 3:00 - 4:00 PM in CMSA Building, 20 Garden Street, Room G10
In the cold atoms community there is great interest in developing Euler-type hydrodynamics for one-dimensional integrable quantum systems, in particular with application to domain wall initial states. I provide some mathematical physics background and also compare with integrable classical systems.

NUMBER THEORY SEMINAR: David Rohrlich
Boston University
Counting Artin representatives
on Wednesday, September 27, 2017, at 3:15 pm in Science Center 507
Recently there has been a resurgence of interest in asymptotic counting problems in number theory, or ``arithmetic statistics,'' growing out of the extraordinary advances made by Bhargava and his students and collaborators in counting discriminants of quartic and quintic number fields, Selmer ranks of elliptic curves over the rationals, and many other quantities of number-theoretic interest. In this talk we consider a few problems in the arithmetic statistics of Artin representations. A classic result in this domain is Siegel's formula for averages of class numbers of binary quadratic forms, which implies that for $x\to \infty$, \[ \vartheta ^{\mathrm{di}}(x)\sim \dfrac{\pi}{36\zeta(3)^2} x^{3/2}, \] where $\vartheta ^{\mathrm{di}}(x)$ is the number of isomorphism classes of dihedral Artin representations of $\Q$ of conductor $\leqslant x$. We shall describe some variants of this formula and then pose the following question: Are most Artin representations abelian? Results of Ambrose, Pomerance, and Zelinsky suggest that this may not be an easy question to answer.

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR: Yu-Wei Fan
Harvard University
Weil-Petersson geometry on the space of Bridgeland stability conditions
on Wednesday, September 27, 2017, at 12:00 - 1:00 PM in CMSA Building, 20 Garden Street, Room G10
Inspired by mirror symmetry, we define Weil-Petersson geometry on the space of Bridgeland stability conditions on a Calabi-Yau category. The goal is to further understand the stringy Kahler moduli space of Calabi-Yau manifolds. This is a joint work with A. Kanazawa and S.-T. Yau.

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