In this talk, we will discuss so-called ``Tupper's self-referential formula'', given by
$$\displaystyle \frac{1}{2} < \left\lfloor \bmod\left(\left\lfloor\frac{y}{17}\right\rfloor 2^{-17\lfloor x\rfloor-\bmod(\lfloor y\rfloor, 17)},2\right)\right\rfloor$$
Math gets a bad rap. It's too hard, it's not useful, it's not fun... We hope to change your mind! This introductory talk will discuss the goal(s) of the Undergraduate Math Seminar. We will introduce ourselves (the organizers) and talk about the type of research we all do and how we became interested in it. Further, we will tell you of our experiences with research and how you can become involved in the math community. We hope you join us and tell us a bit about yourself as well!
Muckenhoupt Weights are ubiquitous in the field of harmonic analysis. In particular, they are appropriate weights for weighted $L^p$ bounds for many classical harmonic analysis objects (maximal functions, Riesz transforms, etc.) These weights also play a role in the solvability of the $L^p$ Dirichlet problem for the Laplacian in `rough’ sets. In particular, if the harmonic measure is a Muckenhoupt weight (in some sense) then the $L^p$ Dirichlet problem is solvable for some p.
We report on recent progress on some nonlocal Monge--Ampere equations. Our results include the interior Harnack inequality for the fractional linearized Monge--Ampere equation (with Diego Maldonado from Kansas State University) and the regularity for the obstacle problem for the Caffarelli--Charro fractional Monge-Ampere equation (with Yash Jhaveri from Institute of Advanced Study).