Events and Activities

Let X be a (nice) topological space, and suppose that we wish to know if X is homotopy equivalent to a simplicial complex of dimension $\leq n$. An obvious necessary condition is that the cohomology of X (with arbitrary coefficients) must be...

Many societal decisions on which we want collective input — from allocating a public budget to deciding how an automated decision rule should behave — have enormous combinatorial spaces of possible outcomes. The standard approach to eliciting public...

Abstract: 

In 1990, Zagier made a striking conjecture about special values of Dedekind zeta functions. In particular, Zagier's conjecture predicts a direct connection between polylogarithms and the algebraic K-theory of number fields. The classical approach to...

Abstract:  I will discuss two recent papers with Jordan Cotler and Juan Maldacena. I will begin by reviewing the wavefunctional formalism in inflationary cosmology, including its symmetries. I will then introduce a special limit of inflation, which...

It is well-known that a linear differential equation with complex analytic coefficients on a disk admits a full set of solutions convergent on the entire disk, and that the analogous statement does not hold for $p$-adic differential equations. I...

We study bitwise-optimal cryptographic primitives: functions in NC⁰ (where each output bit depends on only a constant number of input bits) that achieve exponential security, together with linear stretch for pseudorandom generators (PRGs) and linear...