We ask the question, “how does the infinite q-Pochhammer symbol
transform under modular transformations?” and connect the answer to
that question to the Stark conjectures. The infinite q-Pochhammer
symbol transforms by a generalized factor of...
I will discuss infinite-dimensional linear programs producing
bounds on the spectral gap in various settings. This includes new
bounds on the spectral gap of hyperbolic manifolds as well as the
Cohn+Elkies bound on the density of sphere packings...
The albedo of a celestial body is the fraction of incident
starlight reflected by it. The study of the albedos of Solar System
objects is at least a century old, at least in the Western world.
As examples: Bond (1861) speculated on the near-unity...
In this talk, we introduce the analytic de Rham stack for rigid
varieties over Qp
(and more general analytic stacks). This object is an
analytic incarnation of the (algebraic) de Rham stack of Simpson,
and encodes a theory of analytic D-modules...
Planets form from disks of dust and gas surrounding
young stars. As they grow, these new planets inherit their
chemical composition from the surrounding material and then sculpt
it through gravitational interactions to form gaps and other...
I will explain what the question means and how to make it
precise. Then I will give a conjectural answer. This is based on
joint work with Peter Scholze.
The theory of matroids provides a unified abstract treatment of
the concept of dependence in linear algebra and graph theory. In
this talk we explain Bergman fans of matroids, and we investigate
isomorphisms of Bergman fans for different fan...
