## Herschel Studies of Extrasolar Kuiper Belt-like Systems

Amaya-Moro Martin

Space Telescope Science Institute

December 2, 2014

Amaya-Moro Martin

Space Telescope Science Institute

December 2, 2014

Mark McLean

Stony Brook University

December 3, 2014

Let $A$ be an affine variety inside a complex $N$ dimensional vector space which either has an isolated singularity at the origin or is smooth at the origin. The intersection of $A$ with a very small sphere turns out to be a contact manifold called the link of $A$. If the first Chern class of our link is torsion (I.e. the singularity is numerically $\mathbb Q$ Gorenstein) then we can assign an invariant of our singularity called the minimal discrepancy. We relate the minimal discrepancy with indices of certain Reeb orbits on our link.

Chao Li

Harvard University

December 4, 2014

We prove a level raising mod $p = 2$ theorem for elliptic curves over $\mathbb Q$, generalizing theorems of Ribet and Diamond-Taylor. As an application, we show that the 2-Selmer rank can be arbitrary in level raising families. We will begin by explaining our motivation from W. Zhang's approach to the $p$-part of the BSD conjecture. Explicit examples will be given to illustrate different phenomena compared to odd $p$. This is joint work with Bao V. Le Hung.

Umesh Vazirani

University of California, Berkeley

December 8, 2014

Bruno Klingler

Université Paris Diderot; Member, School of Mathematics

December 8, 2014

Ball quotients are complex manifolds appearing in many different settings: algebraic geometry, hyperbolic geometry, group theory and number theory. I will describe various results and conjectures on them.

Avi Wigderson

Herbert H. Maass Professor, School of Mathematics

December 9, 2014

While this talk is a continuation of the one I gave on Tue Nov 25, it will be planned as an independent one. I will not assume knowledge from that talk, and will reintroduce that is needed. (That first lecture gave plenty of background material, and anyone interested can watch it on https://video.ias.edu/csdm/2014/1125-AviWigderson).

Pierre-Henri Chaudouard

Université Paris 7; von Neumann Fellow, School of Mathematics

December 9, 2014

The main tool in Ngô's proof of the Langlands-Shelstad fundamental lemma, is a theorem on the support of the relative cohomology of the elliptic part of the Hitchin fibration. For $\mathrm{GL}(n)$ and a divisor of degree $> 2g-2$, the theorem says that the relative cohomology is completely determined by its restriction to any dense open subset of the base of the Hitchin fibration. In this talk, we will explain our extension of that theorem to the whole Hitchin fibration, including the global nilpotent cone (for $\mathrm{GL}(n)$ and a divisor of degree $> 2g-2$).

Tom Abel

Stanford University

December 9, 2014

Bruno Klingler

Université Paris Diderot; Member, School of Mathematics

December 10, 2014

The Andre-Oort conjecture describes the expected distribution of special points on Shimura varieties (typically: the distribution in the moduli space of principally polarized Abelian varieties of points corresponding to Abelian varieties with complex multiplication). From the point of view of Hodge theory, it completely describes the geometric properties of the Hodge locus in some special instances. In these lectures I will try to introduce Shimura varieties, the Andre-Oort conjecture and recent work on it.

Bernd Sturmfels

University of California, Berkeley

December 10, 2014