In theoretical computer science, an increasingly important role
is being played by sparse high-dimensional expanders (HDXs), of
which we know two main constructions: "building" HDXs
[Ballantine'00, ...] and "coset complex" HDXs
[Kaufman--Oppenheim...
Given a Lagrangian L, I will discuss the existence of a
neighborhood W of L with the following property: for any
Hamiltonian diffeomorphism f, if f(L) is contained inside W, then
f(L) intersects L. On the one hand, for any symplectic manifold
of...
Central predictions of arithmetic quantum chaos such as the
Quantum Unique Ergodicity conjecture and the sup-norm problem ask
about the mass distribution of automorphic forms, most classically
in terms of their weight or Laplace eigenvalue (for...
I will show that any Schubert or Richardson variety R in a flag
manifold G/P is equivariantly rigid and convex. Equivariantly rigid
means that R is uniquely determined by its equivariant cohomology
class, and convex means that R contains any torus...
We use the min-max construction to find closed hypersurfaces
which are stationary with respect to anisotropic elliptic
integrands in any closed n-dimensional manifold . These surfaces
are regular outside a closed set of zero n-3 dimension. The...
A result of Jan Nekovář says that the Galois action on p-adic
intersection cohomology of Hilbert modular varieties with
coefficients in automorphic local systems is semisimple. We will
explain a new proof of this result for the non-CM part of
the...
This term’s S. T. Lee Lecture of the School of Historical
Studies, organized by Professor Angelos Chaniotis, is dedicated to
the subject of cultural heritage. The lecture will be delivered by
Professor Hermann Parzinger, President of the Stiftung...
It is well-known that the geodesic flow on ellipsoids of
revolution is integrable. In joint work with Ferreira and Vicente,
we used this fact to obtain a symplectomorphism between the unit
disk bundle of such an ellipsoid without fiber and a toric...
In part 1, I will survey the history of total positivity,
beginning in the 1930's with the introduction of totally positive
matrices, which turn out to have surprising linear-algebraic and
combinatorial properties. I will discuss some modern...
In this talk I will discuss various connections between the
dynamics of integrable Hamiltonian flows, gradient flows, and
combinatorial geometry. A key system is the Toda lattice
which describes the dynamics of interacting particles on the line.
I...
