Homotopy theory and category theory have the capability to
provide many insights into the structure of quantum field
theory. Using these tools I will explain a comprehensive
framework for characterizing the infrared (IR) phases of a
fermionic QFTs...
We introduce the notion of a Penner-type class of an exact
symplectomorphism on a Liouville domain with an Ak-configuration of
Lagrangian spheres for k⩾2, and prove that such a class has
positive Floer-theoretic entropy. As a corollary, we
construct...
A symplectophagy is a symplectic isotopy satisfying certain
constraints reminiscent of the symplectic camel problem. In this
talk, I will introduce this notion and basic examples, and present
a new phenomenon of symplectic rigidity in the form of...
From their origin sofic groups have had a strong connection to
topological dynamics in that it was shown that sofic groups are
surjunctive - a dynamical notion. Later on, Lewis Bowen
developed an entropy theory for sofic groups. This led to
further...
OpenAI’s recently announced construction of a finite-time
singularity for the Navier–Stokes equations relies crucially on C∞
external forcing. After brief remarks on this development, I will
present two computer-assisted proofs for unforced...
The topology of Lagrangian submanifolds in the standard
symplectic vector space 𝐶𝑛 is a fundamental, yet poorly understood,
problem in symplectic topology. A related question, known as Maslov
class rigidity, concerns constraints on the Maslov...
A cornerstone result in complexity theory is that O(1)-depth
circuits with unbounded fan-in AND/OR gates computing the parity of
an n bit string must have exp(n) size. Two completely different
proofs of this are known, both dating back to the 1980's...
Time-domain surveys are finding tens of thousands (and soon
millions) of transient events. But how do we make new
discoveries of rare and exotic events? And how do we figure out
what causes and powers them? I will discuss several approaches
that...
Even mathematicians make most of their daily decisions without
mathematical help, guided by reasoning and intuition that are
usually reliable. But now and then our intuition will lead us off
the rails. Can we tell when this is liable to happen, and...
