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...
Consider a closed surface M of genus greater than or equal to 2.
For negatively curved metrics on M and their corresponding geodesic
flow, we can study the topological entropy, the Liouville entropy,
and the mean root curvature. In 2004, Manning...
The notion of singular support has its origin in the theory of
partial differential equations, and was introduced to the world of
constructible sheaves by M. Kashiwara and P. Schapira in the 1970s.
It is a basic invariant (like the support), and...
In 1962, Yudovich established the well-posedness of the
two-dimensional incompressible Euler equations for solutions with
bounded vorticity. However, uniqueness within the broader class of
solutions with L^p vorticity remains a key unresolved...
Although current large language models are complex, the most
basic specifications of the underlying language generation problem
itself are simple to state: given a finite set of training samples
from an unknown language, produce valid new strings...
In this talk, we will explore the relationship between the
geometry and topology of a complexity-one four-manifold and the
combinatorial data that encode it. We will use a
generators-and-relations description for the even part of the
equivariant...
