| Date | SPEAKER | Host |
|---|---|---|
| January 22 | No Seminar
TITLE : ABSTRACT: |
|
| January 29 | Changyou Wang, Purdue University
TITLE : Heat flow of harmonic maps into CAT(0)-metric spaces ABSTRACT: In this talk, we will describe a new approach to construct the existence of a unique suitable weak solution of the heat flow of harmonic maps into CAT(0)-metric space. The target space is the non-smooth version of nonpositively curved smooth manifolds in the sense of Alexandrov. The approach is variational and based on the minimization of a Weighted Energy Dissipation (WED) energy functional, which can be viewed as an elliptic regularization of parabolic problems proposed by De Giorgi back in 1990’s. By introducing a parabolic frequency function in the spirit of Frederick Almgren, we are able to show the existence of a unique global weak solution of the heat flow into a CAT(0) space that is Lipschitz in spatial variable and halfH\”older continuous in time variable. As a byproduct, this provides a new proof of the celebrated Eells-Sampson theorem on heat flow into non-positively curved manifolds. This is a joint work with F. Lin, A. Segatti, and Y. Sire. |
Wang |
| February 5 | Nick Gismondi, Purdue University
TITLE: Integrable Weak Solutions of Stationary Active Scalar Equations ABSTRACT: In this talk, I will discuss the construction of nontrivial integrable weak solutions for certain classes of stationary active scalar equations using a convex integration framework. We focus in particular on stationary active scalar equations with non-odd drift, as well as the stationary surface quasi-geostrophic equation. A central feature of the scheme is measuring the error in a negative-regularity homogeneous Sobolev norm, which enables the use of generic intermittent building blocks and allows us to consider arbitrary dissipation exponents. This talk is based on joint work with Alexandru Radu. |
Wang |
| February 12 | Howen Chuah, Purdue University TITLE : On a Nonlinear Model for Long Range Segregation ABSTRACT : We consider a system of fully nonlinear elliptic equations, depending on a small parameter, that models long-range segregation in population dynamics. The diffusion is governed by the negative nonlinear Pucci operator. We establish the existence of solutions and prove convergence, as the parameter goes to zero, to a free boundary problem. In the limt, high competition forces the species to segregate at a positive distance. Geometric properties of the free boundaries will be discussed, including directions for future research. This talk is based on joint work with Professors Monica Torres and Stefania Patrizi. | Torres |
| February 19 | Raghav Venkatraman, University of Utah
TITLE: ABSTRACT : |
Yip |
| February 26 | Iassc Harris, Purdue University
TITLE: ABSTRACT: | Wang |
| March 5 | Peter Morfe, PSU
TITLE: ABSTRACT: |
Yip |
| March 12 | Mathew George, Purdue University | Wang |
| March 19 | (Spring Break, No Seminar) | |
| March 26 | Monica Torres, Purdue University TITLE: ABSTRACT : |
Wang |
| April 2 | Antonios Zitridis, University of Michigan TITLE: ABSTRACT : |
Han |
| April 9 | Christopher Irving, Georgetown University TITLE: ABSTRACT : |
Torres |
| April 16 | Agnid Banerjee, ASU TITLE: ABSTRACT : | Wang |
| April 23 | Roman Shvydkoy, UIC
TITLE: ABSTRACT : | Novack |
| April 30 | Anuj Kumar, UC Davis
TITLE: ABSTRACT : | Novack |
| May 7 | Junyuan Fang, UTK
TITLE: ABSTRACT : | Wang |