This talk will summarize a project I was involved in during the
past 8 years. It started with attempts to understand the PIT
(Polynomial Identity Testing) problem - a central problem involving
randomness and hardness. It has led us to pursue many...
We start by relating a result on the reducibility of
induced representations of a reductive group through local
Langlands correspondence to Artin L-functions. Such a result is of
interest in the study of the arithmetic theory of
intertwining...
We prove results in the direction of showing that for some
affine curves, Baker's method applied to finite étale covers is
insufficient to determine the integral points. This is joint
work with Aaron Landesman.
I will discuss a dictionary between the quantities in the
spectrum of the string theory compactified on the Calabi-Yau and
object in the Calabi-Yau. I will also discuss some properties.
A few months ago, I decide to attempt to formalize one of my own
papers using the Lean4 theorem prover. I will report on this
experiment. (The Lean code can be found there: https://github.com/smorel394/TS1)
A $\mathrm{GL}$-variety $X$ is an (infinite-dimensional) affine
variety with an action of the infinite general linear group
$\mathrm{GL}$ such that the coordinate ring of $X$ is a
polynomial $\mathrm{GL}$-representation and generated by
finitely...
