Past Events
We will discuss the mean curvature flow of $n$-dimensional submanifolds in $\mathbb{R}^{n+k}$ satisfying a pinching condition introduced by Andrews and Baker (2010): $|H| > 0$ and $|A|^2 < c|H|^2$. We will compare what is known about these flows to what is known about flows of…
Computational imaging leverages the co-design of hardware and software to re-define next-generation camera and display systems. In this talk, we discuss recent advances in computational single-photon imaging to enable non-line-of-sight vision and 3D imaging through highly scattering media. We…
Fintushel-Stern and Furuta developed orbifold Yang-Mills gauge theory and proved that infinitely many Brieskorn 3-spheres are linearly independent in the (3-dimensional) homology cobordism group. In this work, by translating their work into the words of filtered instanton Floer homology, we…
Reinforcement learning in a two-player Lewis signaling game is a simple model to study the emergence of communication in cooperative multi-agent systems. When there are a fixed number of states and signals there is a positive probability that a successful communication system does not emerge. If…
A new proof will be given that Seidel's generalized Dehn twist is not symplectically isotopic to the identity. The argument will stay in the language of counting holomorphic spheres in families and family Seiberg-Witten invariants and will not rely on any Floer-theoretic…
Over the summer, I did some climate analysis for the Gates Foundation. In this talk, I'll reflect on my experience looking for math outside of math academia. Also, I'll talk about corn.
Abstract: I will discuss some joint work with Jack Thorne on the symmetric power lifting for modular forms. We prove the existence of all symmetric power lifts for holomorphic Hecke eigenforms. We previously obtained this result with an extra assumption on the ramification of the modular form (…
We use frequency decomposition techniques to give a direct proof of global existence and regularity for the Navier-Stokes equations on two-dimensional Riemannian manifolds without boundary. Our techniques are inspired by an approach of Mattingly and Sinai which was developed in the context…
What is the most singular possible singularity? What can we say about its geometric and algebraic properties? This seemingly naive question has a sensible answer in characteristic p.
The "F-pure threshold," which is an analog of the log canonical threshold, can be used to "measure" how…