Video Lectures

In my talk I will report on recent work with Hansjörg Geiges about a strong connection between the topology of a contact manifold and the existence of contractible periodic Reeb orbits. Namely, if the contact manifold appears as non-trivial contact...

Let $X$ be a smooth canonically polarised surface defined over an algebraically closed field of characteristic 2. In this talk I will present some results about the geometry of $X$ in the case when the automorphism scheme $\mathrm{Aut}(X)$ of $X$...

KSBA (Kollár-Shepherd-Barron-Alexeev) stable pairs are higher dimensional generalizations of (weighted) stable pointed curves. I will present a joint work in progress with Sándor Kovács on proving the projectivity of this moduli space, by showing...

We compare methods of computing inverses of matrices over division rings. The most direct way is via Cohn's theory of full matrices, which was improved by Malcolmson, Schofield, and Westreich. But it is simpler to work with finite dimensional...

A classical problem in the theory of automorphic forms is to count the number of Laplace eigenfunctions on the quotient of the upper half plane by a lattice $L$. For $L$ a congruence subgroup in $\mathrm{SL}(2,\mathbb Z)$ the Weyl law was proven by...

We prove an $\omega(\log n)$ lower bound on the conondeterministic communication complexity of the Clique vs. Independent Set problem introduced by Yannakakis (STOC 1988, JCSS 1991). As a corollary, this implies superpolynomial lower bounds for the...

To begin we will recall Banyaga's Hofer-like metric on the group of symplectic diffeomorphisms, and explain its conjugation invariance up to a factor. From there we will prove the positivity of the symplectic displacement energy of open subsets in...

Eigencurve was introduced by Coleman and Mazur to parametrize modular forms varying $p$-adically. It is a rigid analytic curve such that each point corresponds to an overconvegent eigenform. In this talk, we discuss a conjecture on the geometry of...

I will first discuss a relation between the cohomology groups (with rational coefficients) of the compactified Jacobian and those of the Hilbert schemes of a projective irreducible curve $C$ with planar singularities, which extends the classical...

We study the restriction map to the closed fiber for the Chow group of zero-cycles over a complete discrete valuation ring. It turns out that, for proper families of varieties and for certain finite coefficients, the restriction map is an...