Past Events
Last time, we discussed vanishing criteria for skein lasagna modules and introduced the lasagna s-invariant. Now, we will see how the lasagna s-invariant can be used to distinguish smooth 4-manifolds.
The existence problem for minimal hypersurfaces (or more generally prescribed mean curvature hypersurfaces) in complete noncompact manifolds is fundamental, but little is known. Min-max provides a powerful framework for existence in closed manifolds, but relies critically on compactness. I…
We improve 1987 estimates of Patterson for sums of quartic Gauss sums over primes. Our Type-I and Type-II estimates feature new ideas, including use of the quadratic large sieve over the Gaussian quadratic field, and Suzuki's evaluation of the Fourier-Whittaker coefficients of quartic theta…
A self-interacting random walk is a random process evolving in an environment which depends on its history. In this talk, we will discuss a few examples of these walks including the Lorentz gas, the mirror walk and the cyclic walk in the interchange process. I will present a method to analyze…
Let k be a number field. We provide an asymptotic formula for the number of Galois extensions of k with absolute discriminant bounded by some X, as X tends to infinity. We also provide an asymptotic formula for the closely related count of extensions of k whose normal closure has…
A Cayley graph G is a highly symmetric graph whose vertex set is a finite group Gamma. A rather surprising theorem, due to Payan, shows that, if Gamma is (Z/2Z)^n, then G cannot have chromatic number exactly 3. (In other words, if G is 3-colorable then G is also 2-colorable.) I'll show you…
This will be the first talk in our series on geometric wave equations, the theme for Student Analysis in the second half of fall quarter.
Using tropical geometry, Block-Göttsche defined polynomials with the remarkable property to interpolate between Gromov-Witten counts of complex curves and Welschinger counts of real curves in toric del Pezzo surfaces. I will describe a generalization of Block-Göttsche polynomials to…