The Langlands and Fontaine–Mazur conjectures in number theory
describe when an automorphic representation f arises geometrically,
meaning that there is a smooth projective variety X, or more
generally a Chow motive M in the cohomology of X, such...
Kazhdan–Lusztig (KL) polynomials for Coxeter groups were
introduced in the 1970s, providing deep relationships among
representation theory, geometry, and combinatorics. In 2016, Elias,
Proudfoot, and Wakefield defined analogous polynomials in
the...
Computing volumes of moduli spaces has significance in many
fields. For instance, Witten's conjecture regarding intersection
numbers on the Deligne–Mumford moduli space of stable Riemann
surfaces has a fascinating connection to the Weil–Petersson...
In the course of constructing the Langlands correspondence for
GL(2) over a function field, Drinfeld discovered a surprising fact
about the interaction between étale fundamental groups and products
of schemes in characteristic p. We state this...
