Previous Conferences & Workshops

p-adic heights have been a rich source of explicit functions vanishing on rational points on a curve. In this talk, we will outline a new construction of canonical p-adic heights on abelian varieties from p-adic adelic metrics, using p-adic Arakelov...

Any non-negative univariate polynomial over the reals can be written as a sum of squares.  This gives a simple-to-verify certificate of non-negativity of the polynomial. Rooted in Hilbert's 17th problem, there's now more than a century's work that...

In distributed certification, our goal is to certify that a network has a certain desired property, e.g., the network is connected, or the internal states of its nodes encode a valid spanning tree of the network. To this end, a prover generates...

Abstract: I'll give an exposition of the theory of "multiplicative polynomial laws," introduced by Roby, and how (following a suggestion of Scholze) they can be applied to the theory of commutative (flat) group schemes. This talk will feature more...

Abstract: The key principle in Grothendieck's algebraic geometry is that every commutative ring be considered as the ring of functions on some geometric object. Clausen and Scholze have introduced a categorification of algebraic and analytic...

In 2001, Conrey, Farmer, Keating, Rubinstein, and Snaith developed a "recipe" utilizing heuristic arguments to predict the asymptotics of moments of various families of L-functions. This heuristic was later extended by Andrade and Keating to include...

Abstract: For a reductive group $G$, its $B_{d}R^{+}$-affine Grassmannian is defined as the étale (equivalently, v-) sheafification of the presheaf quotient $LG/L^{+}G$ of the $B_{d}R$-loop group $LG$ by the $B_{d}R^{+}$-loop subgroup $L^{+}G$. We...

Abstract: Let p be a prime number. Emerton introduced the p-adically completed cohomology, which admits a representation of some p-adic group and can be thought of as some spaces of p-adic automorphic forms. In this talk, I want to explain that for...