Previous Conferences & Workshops

In this talk, I will discuss the geometric expansion of a local twisted trace formula for some special varieties. This generalizes the local (twisted) trace formula for reductive groups proved by Arthur and Waldspurger. By applying the trace formula...

The recent work of Drinfeld and Bhatt-Lurie led to a new geometric approach to p-adic cohomology theories, analogously to what was done earlier in Hodge theory by Simpson. This stacky perspective gives in particular a new approach to p-adic non...

With every bounded prism Bhatt and Scholze associated a cohomology theory of formal p-adic schemes. The prismatic cohomology comes equipped with the Nygaard filtration and the Frobenius endomorphism. The Bhatt-Scholze construction has been advanced...

I will talk about (very much in progress) joint work with Mark Kisin on a Hodge—Newton style inequality for the mod p Breuil—Kisin modules arising from crystalline Galois representations.

The minimal model program for 3-folds has been developed only in characteristics $p \geq 5$. A key difficulty at small primes is that the singularities occurring in the minimal model program need not be Cohen-Macaulay, as they are in characteristic...

Let $f:Y \rightarrow X$ be a finite covering map of complex algebraic varieties. The essential dimension of f is the smallest integer e such that, birationally, f arises as the pullback of a covering $Y^{'} \rightarrow X^{'}$ of dimension e, via a...

A theorem of Borel says that any holomorphic map from a complex algebraic variety to a smooth arithmetic variety is automatically an algebraic map. The key ingredient is to show that any holomorphic map from the (poly) punctured disc to the Baily...

Let $E$ be a finite degree extension of $Qp$. Given a mod p representation of the absolute Galois group of E we construct a sheaf on a punctured absolute Banach-Colmez space that should give the first step in the construction of the mod p local...

Explicit constructions of "random-like" objects play an important role in complexity theory and pseudorandomness. For many important objects such as prime numbers and rigid matrices, it remains elusive to find fast deterministic algorithms for...