Past Events
Polymers in disordered media are examples of random Gibbs measures on directed paths moving through a random environment. Such disordered systems often exhibit complex landscape behavior rich with multiple valleys which act as metastable states. This generic property manifests in multiple forms…
Despite a lot of progress, the question of whether all the finite groups PSL(n,q) of all n by n matrices with coefficients in F_q and of determinant 1, modulo center, occur as Galois groups of a Galois extension of Q remains open. We study the cohomology of curves with an automorphism with F_p-…
A central theme of arithmetic Ramsey theory is that every finite coloring of the natural numbers should contain monochromatic solutions to certain algebraic equations. While Rado's theorem gives a complete understanding in the linear setting, the nonlinear case remains largely mysterious. A…
Classical del Pezzo surfaces exhibit an unexpected connection with exceptional E‑type root systems, arising from the intersection form on their homology. In 2001, the mathematical physicists Iqbal, Neitzke, and Vafa observed an analogous appearance of E-type root systems in the study…
Let V be a vector space of dimension 2n over the field F_2 with two elements. Assume that we are given a nondegenerate symplectic form on V with values in F_2. Let X be the vector space of complex valued functions on V. Fourier transform is an involution of X. We show that there exists an…
I will review the Picard-Fuchs equation for the Legendre family fixing erros from last time and review the theory of the Gauss-Manin connection.
This lecture will be independent of the following weeks.
The polynomial Szemer\'edi theorem of Bergelson and Leibman gives broad conditions under which polynomial patterns must appear in every positive-density subset of Z^d. When the polynomials do not vanish at zero, the correct replacement condition is conjecturally joint intersectivity, a…