In the early 2000’s Ruijsenaars and Felder-Varchenko have
introduced the elliptic gamma function, a remarkable multivariable
meromorphic q-series that comes from mathematical physics. It
satisfies modular functional equations under the group
SL3(Z)...
I will discuss recent progress on approximating the metric
traveling salesperson problem, focusing on a line of work beginning
in 2011 that studies the behavior of the max entropy algorithm.
This algorithm is a randomized variant of the beautiful...
In the search for possible blow-up of the incompressible
Navier-Stokes equations, there has been much recent attention on
the class of axisymmetric solutions with swirl. Several interesting
structures of this system have led to regularity criteria...
An old open question in symplectic topology is whether all
normalized capacities coincide on convex bounded domains in the
standard symplectic vector space. I will discuss this question for
domains which are close to the Euclidean ball and its...
I will present a new theory of motivic cohomology for general
(qcqs) schemes. It is related to non-connective algebraic K-theory
via an Atiyah-Hirzebruch spectral sequence. In particular, it is
non-A1
-invariant in general, but it recovers classical...
Consider the process where a signal propagates downward an
infinite rooted tree. On every edge some independent noise is
applied to the signal. The reconstruction problem asks whether it
is possible to reconstruct the original signal given...
The problem of control of large multi-agent systems, such as
vehicular traffic, poses many challenges both for the development
of mathematical models and their analysis and the application to
real systems. First, we discuss how conservation laws can...
I will give a construction of certain Q-valued deformation
invariants of (in particular) complete non-positively curved
Riemannian manifolds. These are obtained as certain elliptic
Gromov-Witten curve counts. As one immediate application we give
the...
In 1982, S. T. Yau conjectured that there exists at least four
embedded minimal 2-spheres in the 3-sphere with an arbitrary
metric. In this talk, we will show that this conjecture holds true
for bumpy metrics and metrics with positive Ricci...
