Some 25 years ago, as announced at a previous version of this
seminar, Vaughan and the speaker obtained asymptotic upper and
lower bounds for the number of non-trivial integral points on the
Segre cubic $$x_1^3+...+x_6^3=x_1+...+x_6=0$$ with naive...
Modern machine learning often optimizes a nonconvex objective
using simple algorithm such as gradient descent. One way of
explaining the success of such simple algorithms is by analyzing
the optimization landscape and show that all local minima
are...
Scaling problems, such as operator scaling and tensor scaling,
have recently found several applications in diverse areas of math
and CS. They have been used to give efficient algorithms for
non-commutative rational identity testing, compute the...
The well-posedness of the incompressible Euler equations in
borderline spaces has attracted much attention in recent years. To
understand the behavior of solutions in these spaces, the
logarithmically regularized Euler equations were introduced.
In...
Symplectic capacities are measurements of symplectic size. They
are often defined as the lengths of certain periodic trajectories
of dynamical systems, and so they connect symplectic embedding
problems with dynamics. I will explain joint work...
The problem of learning arithmetic circuits is the following:
given a polynomial as a black box that is promised to have a small
arithmetic circuit computing it, can we find this arithmetic
circuit? This problem is hard in the worst case and so...
