# Past Events

When is a multivariate polynomial nonnegative (over the reals or some other semi algebraic set)? We’ll start with some easy methods to certify positivity, discussing Hilbert’s 17th problem and its positive resolution along the way.

Abstract

I will talk about fluctuations in first passage percolations. I will cover the linear and sublinear variance bounds in Sections 3.1 and 3.2 of “Fifty years of FFP”. This material is also reviewed in the survey “Fluctuations in First Passage Percolation” by Philippe Sosoe: …

I will describe the construction of motivic cohomology classes on hypergeometric families of Calabi-Yau 3-folds using Hadamard convolutions. One can view this as a “higher” version of the Mordell-Weil group for families of elliptic curves, giving rise to sections of “higher” Jacobian…

I will describe the construction of motivic cohomology classes on hypergeometric families of Calabi-Yau 3-folds using Hadamard convolutions. One can view this as a “higher” version of the Mordell-Weil group for families of elliptic curves, giving rise to sections of “higher” Jacobian…

Choose your favourite, compact manifold M. How many rational points, with denominator of bounded size, are near M? We report on joint work with Damaris Schindler and Rajula Srivastava addressing this question. Our new method reveals an intriguing interplay between number theory, harmonic…

I will discuss the problem of solving a system of equations F(x)=0,for x a d-dimensional unit vectors and D a non-linear map from R^d to R^n whose components are independent, rotationally invariant Gaussian processes. We studied this problem under the proportional asymptotics in which n and…

Twist-roll spun knots are a well-studied family of knotted 2-spheres in the 4-sphere. The inputs for determining a twist roll spun knots are an integer number of twists, a number of rolls, and a choice of classical knot in the 3-sphere. I will explain why adding twists, while changing the…