A real symplectic manifold is a symplectic manifold endowed with an involution which is anti-symplectic. Given a real symplectic manifold, we may ask: are there any anti-invariant symplectic forms which are cohomologous but not isotopic within anti-invariant forms? In this talk, we will show that such disconnectivity indeed appears for certain real quadric surfaces.

We introduce some classical problems in graph Ramsey Theory. We also discuss new results on a less-classical problem, namely, multicolor Ramsey numbers for some triple system paths of length three. The latter is joint work with Tom Bohman. Come for the tikzpictures, stay for the Ramsey Theory (or vice versa)!

High dimensional non-Gaussian data are increasingly encountered in a wide range of applications. It poses new challenges to traditional statistical tools. In this talk, we will present some recent development on methodologies and theories for the analysis of fat-tailed data as well as some high dimensional estimation and inference problems.

The persistence diagram is an increasingly useful shape descriptor from Topological Data Analysis, but its use alongside typical machine learning techniques requires mathematical finesse. We will describe in this talk a mathematical framework for featurization of said descriptors, and we show how it addresses the problem of approximating continuous functions on compact subsets of the space of persistence diagrams. We will also show how these techniques can be applied to problems in semi-supervised learning where these descriptors are relevant.

I will discuss the Attractor Conjecture for Calabi-Yau
varieties, which was formulated by Moore in the nineties, highlighting
the difference between Calabi-Yau varieties with and without Shimura
moduli. In the Shimura case, I show that the conjecture holds and gives
rise to an explicit parametrization of CM points on certain Shimura
varieties; in the case without Shimura moduli, I'll present
counterexamples to the conjecture using unlikely intersection theory.
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Part of this is joint work with Arnav Tripathy.