Recently Added

A PSPACE construction of a hitting set for the closure of small algebraic circuits

Amir Shpilka
Tel Aviv University
December 12, 2017

We study the complexity of constructing a hitting set for the class of polynomials that can be infinitesimally approximated by polynomials that are computed by polynomial sized algebraic circuits, over the real or complex numbers. Specifically, we show that there is a PSPACE algorithm that given nsr in unary outputs a set of inputs from of size poly(nsr), with poly(nsr) bit complexity, that hits all $n$-variate polynomials of degree $r$ that are the limit of size $s$ algebraic circuits.

Recent developments in knot contact homology

Lenny Ng
Duke University
December 11, 2017
Knot contact homology is a knot invariant derived from counting holomorphic curves with boundary on the Legendrian conormal to a knot. I will discuss some new developments around the subject, including an enhancement that completely determines the knot (joint work with Tobias Ekholm and Vivek Shende) and recent progress in the circle of ideas connecting knot contact homology, recurrence relations for colored HOMFLY polynomials, and topological strings (joint work in progress with Tobias Ekholm).