We will explain a definition of open Gromov-Witten invariants on
the rational elliptic surfaces and explain the connection of the
invariants with tropical geometry. For certain rational elliptic
surfaces coming from meromorphic Hitchin system, we...
We show that there exist binary locally testable codes (for all
rates) and locally correctable codes (for low rates) with rate and
distance approaching the Gilbert-Varshamov bound (which is the best
rate-distance tradeoff known for general binary...
Gaia is a perfect halo explorer. It makes up for a relatively
shallow depth with an array of features not available to other
surveys/telescopes. These include stable photometry, impeccable
star/galaxy separation and resilience to artefacts, not to...
A celebrated theorem of Duke states that Picard/Galois orbits of
CM points on a complex modular curve equidistribute in the limit
when the absolute value of the discriminant goes to infinity. The
equidistribution of Picard and Galois orbits of...
In the lectures I will formulate a conjecture asserting that
there is a hidden action of certain motivic cohomology groups on
the cohomology of arithmetic groups. One can construct this action,
tensored with $\mathbb C$, using differential forms...
Neural networks have been around for many decades. An important
question is what has led to their recent surge in performance and
popularity. I will start with an introduction to deep neural
networks, covering the terminology and standard approaches...
The definition of the Kauffman bracket skein algebra of an oriented
surface was originally motivated by the Jones polynomial invariant
of knots and links in space, and a representation of the skein
algebra features in Witten's topological quantum...
