THURSDAY SEMINAR: | Mike HopkinsHarvard 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 ZhangHarvard 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 GaitsgoryHarvard 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 WuHarvard 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 SpohnTechnical 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 RohrlichBoston 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 FanHarvard 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. |