Previous Conferences & Workshops

Studying the \’etale cohomology of Shimura varieties with Hecke and Galois actions provides an avenue toward understanding the Langlands correspondence. 
While the structure of the rational cohomology groups is predicted conjectures of Kottwitz and...

A promenade in Serre's paper, plus some related results of mine.

The theory of probabilistically checkable proofs (PCPs) shows how to encode a proof for any theorem into a format where the theorem's correctness can be verified by making only a constant number of queries to the proof. The PCP Theorem [ALMSS] is a...

Recent progress on character bounds for groups of Lie type makes it feasible in many cases to find the asymptotic growth, for fixed q and n tending to infinity, of the number of n-dimensional representations of a Fuchsian group G over the field with...

In the 1940s Mahler initiated the program of determining the bass note spectrum $$\mathrm{Spec}(P):=\left\{\inf_{\underline{x} \in\Lambda \setminus \underline{0}}\left\vert P(\underline{x})\right\vert, \Lambda \subset \mathbb{R}^k \text{ a...

For an embedded stable curve over the real numbers we introduce a hyperplane arrangement in the tangent space of the Hilbert scheme. The connected components of its complement are labeled by embeddings of the graph of the stable curve to a compact...

The Alexandrov-Fenchel inequality---the fundamental log-concavity phenomenon in convex geometry---arose from Minkowski's work in number theory in the late 1800s. It has resurfaced in surprising ways throughout the 20th and 21st centuries in the...

A sequence of nonnegative real numbers $a_1, a_2, \ldots, a_n$, is log-concave if $a_i^2 \geq a_{i-1}a_{i+1}$ for all $i$ ranging from 2 to $n-1$. Examples of log-concave inequalities range from inequalities that are readily provable, such as the...