Algebra / Number Theory / Combinatorics Seminar

A Z-module M in a number field K gives rise to a lattice in the corresponding Euclidean space via Minkowski embedding. Such lattices often carry inherited structure from the number field in question and can be attractive from both, theoretical and applied perspectives. We consider this construction when M is spanned by the set of […]

Given any finite set of integer points S, there is an associated function f_S that encodes S, which we call its integer point transform.   One can think of this integer point transform f_S algebraically or analytically.  Here we focus on its analytic properties, showing that it is a complete invariant.   In fact, we prove that […]

The Riemann–Hilbert correspondence relates algebra to differential equations on complex algebraic varieties. In characteristic p, there is an analogous correspondence due to Emerton–Kisin and later generalized by Bhatt–Lurie, where the […]

It is a fundamental question to find rational solutions to a given system of polynomials, and in modern language this translates into finding rational points in algebraic varieties.  It is […]