Past: Winter 2018, Spring 2018, Fall 2018, Winter 2019, Spring 2019
Future: Winter 2020
Friday Oct 4 

4:305:20 Caltech, Linde 310 Svetlana Jitormirskaya (UC Irvine) Fractal properties of the Hofstadter's butterfly and singular continuous spectrum of the critical almost Mathieu operator Harper's operator  the 2D discrete magnetic Laplacian  is the model behind the Hofstadter's butterfly. It reduces to the critical almost Mathieu family, indexed by phase. We discuss the proof of singular continuous spectrum for this family, for all phases, finishing a program with a long history. We also present a result (with I. Krasovsky) that proves one half of the Thouless' one half conjecture from the early 80s: that Hausdorff dimension of the spectrum of Harper's operator is bounded by 1/2 for all irrational fluxes. 

5:306:20 Caltech, Linde 310 Khang Huynh (UCLA) Hodgetheoretic analysis on manifolds with boundary, heatable currents, and Onsager's conjecture in fluid dynamics We use Hodge theory and functional analysis to develop a clean approach to heat flows and Onsager's conjecture on Riemannian manifolds with boundary, where the weak solution lies in the tracecritical Besov space $B_{13}^{3,1}$. We also introduce heatable currents as the natural analogue to tempered distributions and justify their importance in Hodge theory. 

Friday Oct 18 

4:004:50 UCLA, MS 6627 Tarek Elgindi (UCSD) Singularity formation in incompressible fluids We will discuss recent results on singularity formation for solutions to the incompressible Euler equation in various settings. We will discuss in some detail a construction of selfsimilar blowup for C^{1,a} solutions to the 3D Euler equation as well as a proof of stability that yields finiteenergy local selfsimilar blowup. Some of the results are joint with I. Jeong, T. Ghoul, and N. Masmoudi. 

5:005:50 UCLA, MS 6627 Eyvindur Palsson (Virginia Tech) Falconer type theorems and integral operators Finding and understanding patterns in data sets is of significant importance in many applications. One example of a simple pattern is the distance between data points, which can be thought of as a 2point configuration. Two classic questions, the Erdos distinct distance problem, which asks about the least number of distinct distances determined by N points in the plane, and its continuous analog, the Falconer distance problem, explore that simple pattern. Questions similar to the Erdos distinct distance problem and the Falconer distance problem can also be posed for more complicated patterns such as various 3point configurations. In this talk I will explore such generalizations. The key focus will be integral operators, that arise naturally from such point configuration questions. In addition, a novel grouptheoretic viewpoint, which has allowed for much progress recently, will be highlighted. 

Friday Nov 1 

4:305:20 Caltech, Linde 310 Vladimir Markovic (Caltech) TBA 

5:306:20 Caltech, Linde 310 Danielle Hilhorst (U. Paris Sud) TBA 

Friday Nov 15 

4:004:50 UCLA, MS 6627 Florian Richter (Northwestern) TBA 

5:005:50 UCLA, MS 6627 Susan Friedlander (USC) TBA 

Friday Dec 6 

4:305:20 Caltech, Linde 310 Vjekoslav Kovac (U. Zagreb/Georgia Tech) TBA 

5:306:20 Caltech, Linde 310 Vladimir Sverak (U. Minnesota) TBA 

Last update: Sept 29, 2019 