Upcoming Events
The general goal of Higher Hida theory is to define and understand the ordinary part of integral coherent cohomology of Shimura varieties. In this talk we will focus on the simplest example of a Shimura variety for a non-split reductive group. We describe the results, notably vanishing…
Abstract: Consider a Liouville domain D embedded in a closed symplectic manifold M. To D one can associate two types of Floer theoretic invariants: intrinsic ones like the wrapped Fukaya category which depend on D only, and relative ones which involve both D and M. It is often the case…
In recent years, machine learning has motivated the study of what one might call "nonlinear random matrices." This broad term includes various random matrices whose construction involves the entrywise application of some deterministic nonlinear function, such as ReLU. We study one such…
Abstract: Around 2000, Biran introduced the notion of polarization of a symplectic manifold, and showed that the associated Lagrangian skeleta exhibit remarkable rigidity properties. He proved in particular that their complements may have small Gromov width. In this…
Let S be a finite set of invertible 2-by-2 matrices with algebraic entries. Is there an algorithm to determine a presentation for <S>? We shall pose this question, and suggest a possible avenue to answering it. Note that every finite-volume hyperbolic 3-manifold arises as above. Beyond…
In recent years, researchers have developed a number of fast, randomized algorithms for linear algebra problems. But for widespread deployment of these methods, speed is not enough. To safely incorporate randomized algorithms into general-purpose linear algebra software, we need algorithms which…
Abstract
Determining the structure of the equations of an algebraic curve in its canonical embedding (given by its holomorphic forms) has been a central question in algebraic geometry from the beginning of the subject. In 1984 Mark Green put forward a very elegant conjecture linking the complexity of the…
We give a new proof, along with some generalizations, of a folklore theorem - attributed to Laurent Lafforgue - that a rigid matroid (i.e., a matroid whose base polytope is indecomposable) has only finitely many projective equivalence classes of representations over any given field. A key…