Previous Conferences & Workshops

In this talk, I will present the recent joint work with Yi Zhu on $A^1$-connectedness for quasi-projective varieties. The theory of $A^1$-connectedness for quasi-projective varieties is an analogue of rationally connectedness for projective...

We give an explicit example for a Boolean function $f : \{0,1\}^n \to \{0,1\}$, such that every Boolean formula of size at most $n^{2.999}$, with gates AND, OR and NOT, computes $f$ correctly on at most $1/2 + \epsilon$ fraction of the inputs, where...

In this talk I'll first go over some problems and related results in spectral geometry. Then I'll explain how one can apply Quantum Ergodicity and Bochner's theorem to prove that the number of nodal domains of quantum ergodic sequence of even...

We consider compactifications of the Betti, de Rham and Dolbeault realizations of the character variety. Starting from an example, we look at what can be said, mostly conjecturally, about the relationship between these spaces.

We prove that for any $\epsilon > 0$ it is NP-hard to approximate the non-commutative Grothendieck problem to within a factor $1/2 + \epsilon$, which matches the approximation ratio of the algorithm of Naor, Regev, and Vidick (STOC'13). Our proof...

We study symplectic invariants of the open symplectic manifolds $X$ obtained by plumbing cotangent bundles of spheres according to a plumbing tree. We prove that certain models for the Fukaya category $\mathcal F(X)$ of closed exact Lagrangians in...

We will discuss some recent constructions of "exotic" Lagrangian tori in simple symplectic manifolds such as $\mathbb{CP}^2$ (work of Renato Vianna) and $\mathbb R^6$ that are not Hamiltonian isotopic to previously known examples, inspired by wall...

Kisin module is very useful to study crystalline representations. In this talk, we extend the theory of Kisin modules and crystalline representations to allow more general coefficient fields and lifts of Frobenius. In particular, we construct a...