Recently, a number of formulas reminiscent of Weyl's law have
been discovered in the context of symplectic geometry. Various
three-manifold invariants, defined by building on ideas originating
in Morse theory, have been at the heart of these...
The algebraic structure of various groups of homeomorphisms and
diffeomorphisms was studied extensively in the 1960s and 1970s,
when it was shown that these groups are (mostly) simple. A notable
open case concerned the group of area-preserving...
A surprising property of the cohomology of locally symmetric
spaces is that Hecke operators can act on multiple cohomological
degrees with the same eigenvalues. In a series of papers, Venkatesh
and his collaborators proposed an arithmetic reason for...
After ten years of gravitational-wave observations with the
LIGO–Virgo–KAGRA interferometers, over 200 signals from merging
black hole binaries have been detected, bringing us closer to
understanding how these systems form. Addressing this
question...
Differential Galois groups are algebraic groups that describe
symmetries of some systems of differential equations. The solutions
considered can live in any differential field and thus a natural
framework to consider such symmetries is the setting...
In this talk, I will completely describe the decomposition of an
oscillator representation under the tensor embedding of a product
of a symplectic and orthogonal group in the case of finite fields
via a correspondence proposed by Roger Howe...
Harmonic analysis studies functions on the real line by
expanding them as sums of frequencies (exponentials) and analyzing
how each term contributes to the whole. In many applications—such
as speech recognition—only the low frequencies matter.
The Hopf-Tsuji-Sullivan theorem states that the geodesic flow on
(an infinite) Riemann surface is ergodic iff the Poincare series is
divergent iff the Brownian motion is recurrent. Infinite Riemann
surfaces can be built by gluing infinitely many...
Complex lines are a class of pseudoholomorphic curves which
generalize rational curves. Applications of complex lines to
symplectic geometry have been proposed, but they remain poorly
understood. In this talk, I will describe a framework for...
