In algebraic geometry, the Ceresa cycle provided one of the
first examples of a nullhomologous cycle which is not algebraically
trivial. I will explain how one can obtain a mirror statement about
the Lagrangian Ceresa cycle, a nullhomologous...
For an elliptic curve E defined over Q, the Mordell-Weil group
E(Q) is a finitely generated abelian group. We prove that there are
infinitely many elliptic curves E over Q for which E(Q) has rank 2.
Our elliptic curves will be given by explicit...
The alpha disk model is widely used to describe the accretion
disk structures around supermassive black holes, even though it
cannot explain many observed properties of AGNs. Various
alternative models have been proposed including the ones
where...
Suppose given a class of finite combinatorial structures, such
as graphs or total orders. Nate Harman and I recently introduced a
notion of measure in this context: this is a rule assigning a
number to each structure such that some axioms are...
Fibered 3-manifolds are those constructed via surface
homeomorphisms. Given such a manifold with pseudo-Anosov monodromy,
much is already known about how topological data of the mapping
class determine geometric information about the hyperbolic 3...
In the early 80s Hatcher proved the Smale Conjecture, asserting
that the diffeomorphism group of the three-sphere retracts onto its
isometry group. The corresponding problem for RP^3 was open
nearly 40 years, and resolved only in 2019 by a detailed...
This talk is based on joint work with Yang Li. I will discuss
the problem of counting special Lagrangians in Calabi-Yau 3-folds
and Fueter sections to define new numerical and Floer-theoretic
invariants. The key challenges are the non-compactness...
High dimensional expansion comes in two flavors: spectral, which
relates to random walks; and cosystolic, which relates to
chains of linear maps. The later is a more mysterious notion, which
turns out related to a variety of applications such as...
Persistence modules and their associated barcodes were
intensively studied since the early 2000s with a view towards
applied mathematics. Recently they have also found numerous
applications in pure mathematics. We will discuss a few examples
from...
Deep generative models offer powerful tools for solving
astrophysical inference problems by enabling flexible
representations of prior knowledge and likelihood functions.
In the first part of the talk, I will discuss how generative
models can be...
