In this talk I will present some new results on the structure of
the zero sets of Schrödinger eigenfunctions on compact Riemannian
manifolds. I will first explain how wiggly the zero sets can be by
studying the number of intersections with a fixed...
Chern-Schwartz-MacPherson class is a functorial Chern class defined
for any algebraic variety. I will give a geometric proof of a
positivity conjecture of Aluffi and Mihalcea that Chern classes of
Schubert cells and varieties in Grassmannians are...
During last fifty years a strong machine learning theory has been
developed. This theory includes: 1. The necessary and sufficient
conditions for consistency of learning processes. 2. The bounds on
the rate of convergence which in general cannot be...
We prove that the probability that a curve of the form $y^2 = f(x)$
over $\mathbb Q$ with $\deg f = 2g + 1$ has no rational point other
than the point at infinity tends to 1 as $g$ tends to infinity.
This is joint work with Michael Stoll.
This is joint work with G .Garkusha. Using the machinery of framed
sheaves developed by Voevodsky, a triangulated category of framed
motives is introduced and studied. To any smooth algebraic variety
$X$, the framed motive $M_{fr}(X)$ is associated...
Starting from an example in which the Hitchin correspondence can be
written down explicitly, we look at what might be said relating the
incidence complex of the boundary of the character variety, and the
Hitchin map.
Decoupling inequalities in harmonic analysis permit to bound the
Fourier transform of measures carried by hyper surfaces by certain
square functions defined using the geometry of the hyper surface.
The original motivation has to do with issues in...
At the heart of every local search algorithm is a directed graph on
candidate solutions (states) such that every unsatisfactory state
has at least one outgoing arc. In stochastic local search the hope
is that a random walk will reach a satisfactory...
In this talk, I will present the recent joint work with Yi Zhu on
$A^1$-connectedness for quasi-projective varieties. The theory of
$A^1$-connectedness for quasi-projective varieties is an analogue
of rationally connectedness for projective...
We consider compactifications of the Betti, de Rham and Dolbeault
realizations of the character variety. Starting from an example, we
look at what can be said, mostly conjecturally, about the
relationship between these spaces.
