We will describe a recently discovered connection between private information retrieval and secret sharing, and a new secret-sharing scheme for general access structures that breaks a long-conjectured exponential barrier.
Based on joint work with Tianren Liu and Hoeteck Wee.
Hilbert's 12th problem is to provide explicit analytic formulae for elements generating the maximal abelian extension of a given number field. In this talk I will describe an approach to Hilbert’s 12th that involves proving exact p-adic formulae for Gross-Stark units. This builds on prior joint work with Kakde and Ventullo in which we proved Gross’s conjectural leading term formula for Deligne-Ribet p-adic L-functions at s=0. This is joint work with Mahesh Kakde.