Organizers: Minh Bùi and Sarah Strikwerda

Wednesday, April 28, 15:00-16:00
Speaker: Steven Gilmore
Title: Fine regularity of the Burgers-Poisson equation 
Abstract: In this talk, we study the fine regularity of the Burgers-Poisson equation, a nonlinear dispersive balance law derived to model shallow water waves. In 2015, existence and uniqueness results to the Cauchy problem for initial data in L^1(R) were provided. Moreover, it was shown that the admissible weak solution is in BV_loc(R) for all positive time. Following recent advancements in the theory of conservation laws, we show the solutions belong to a subset of BV functions, the space of special functions of bounded variation. In particular, we prove that the derivative of a solution consists of only the absolutely continuous part and the jump part.

Tuesday, April 15, 15:00-16:00
Speaker: Zev Woodstock
Title: Topics in Image Processing
Abstract: I will lead a very informal group discussion on some topics in image processing.We will discuss image recovery problems from saturated, blurred, low-resolution, 
compressed, and/or grayscale images, and how to solve those problems efficiently.

Tuesday, April 7, 15:00-16:00
Speaker: Adam Pickarski
Title: Bounded Variation Estimates of MDS
Abstract: Dimension reduction algorithms are widely used in data science to visualize data. However, the workings of many of the nonlinear are not understood in a clear way. The goal of this talk is to understand properties of solutions of the multi-dimensional scaling algorithm (MDS).

Tuesday, March 30, 15:00-16:00
Speaker: Prerona Dutta
Title: Metric Entropy and Nonlinear Partial Differential Equations

Wednesday, March 17, 14:00-15:00
Speaker: Sarah Strikwerda
Title: Monotone Operator Theory applied to Optimal Control Problems Constrained by Poro-(Visco)-Elastic Models
Abstract: Monotone Operator Theory can be used to show existence and uniqueness to PDE problems in a variety of ways. I will show two different methods used on two PDE systems that have importance in the process of deriving necessary optimality conditions for optimal control problems constrained by a PDE system describing fluid flow through porovisco-elastic media and poro-elastic media. The effectiveness of these methods will be compared to the effectiveness of Roth method for the two systems.

Wednesday, March 10, 14:00-15:00
Title: Problem Session
Abstract: We work through Analysis problems together.

Wednesday, March 3, 14:00-15:00
Title: Teaching Discussion
Abstract: We discuss challenges involved in being an instructor of record for Math courses.

Wednesday, February 24, 14:00-15:00
Speaker: Minh Bùi
Title: Multivariate Monotone Inclusions in Saddle Form
Abstract: We introduce the notion of a saddle operator for highly structured multivariate monotone inclusions involving a mix of set-valued, cocoercive, and Lipschitzian monotone operators, as well as various monotonicity-preserving operations among them. The properties of this saddle operator are discussed, and asynchronous block-iterative algorithms to find its zeros are presented. In turn, this allows us to solve the original system via a novel block-iterative splitting algorithm of great flexibility in terms of processing the constituent operators individually and exploiting their specific attributes. Comparisons with the state-of-the-art in monotone operator splitting will be carried out.

Wednesday, February 17, 14:00-15:00
Speaker: Sarah Strikwerda
Title: Optimal Control in Fluid Flows through Deformable Porous Media
Abstract: We consider an optimal control problem subject to a poro-visco-elastic model with applications to fluid flows through biological tissues. Our goal is to optimize the fluid pressure and solid displacement using distributed or boundary control. We discuss an application of this problem to a tissue in the human eye. Previous literature on well-posedness of the poro-visco-elastic model are reviewed. Results on the existence of an optimal control and the associated necessary optimality conditions are presented for the linear case.

Wednesday, February 10, 14:00-15:00
Title: Problem Session
Abstract: We work through Analysis problems together.

Wednesday, February 3, 14:00-15:00
Title: Problem Session
Abstract: We work through Analysis problems together.

Wednesday, January 27, 14:00-15:00
Title: Thesis Discussion
Abstract: We share tips and questions about compiling our PhD theses.