# Applied Math Collective

Applied Math Collective was initiated by my advisors and Fernando Guevara Vasquez. The aim is to provide an informal platform where the speaker discusses general-interest "SIAM review"-style applied math papers, led by either faculty or graduate student. We meet Thursdays at 4pm, when the Department Colloquium does not have a speaker.Please contact me if you would like to attend or give a talk so that I can add you to the mailing list.

### ➜ Fall 2016 (organised by Todd Reeb)

November 3
Speaker: Bhargav Karamched
Title: Modeling Hard Core Repulsion in Tranport Processes
Abstract: PDE models for transport processes that occur, for example, along microtubules in cells generally involve a linear equation such as the advection-diffusion equation. One limitation of these types of models is that they do not account for the interaction between the particles that are undergoing the motion. I will introduce a modeling framework that accounts for these inter-particle interactions through the totally asymmetric simple exclusion process (TASEP). This process has been studied to death by the statistical physics community. I will talk about several approximation techniques that allow us to formulate the TASEP as a nonlinear PDE and discuss the corresponding steady states. I will then shamelessly discuss how I used the TASEP in a recent paper Paul Bressloff and I published.

October 27
Speaker: Ted Schomay (Scientific Computing and Imaging Institute, University of Utah)
Title: Tensor Decompositions: Multi-linear Generalizations of the Singular Value Decomposition
Abstract: In two-dimensional space, matrix decompositions such as the singular value decomposition rewrite a matrix in terms of canonical basis vectors. These decompositions provide insight into the composition of data in the matrix and have numerous applications including compression, denoising, and signal separation. In higher-dimensional space, generalizations of these decompositions rewrite tensors in terms of canonical basis vectors. Additionally, simulataneous decompositions of two or more tensors can be defined, leading to comparative frameworks. The additional dimensions and different properties of these decompositions allow for exciting new interpretations of the results. In this talk, I will discuss the singular value decomposition and its generalizations to multiple tensors along with application and interpretation.

October 6
Speaker: Heather Brooks
Title: Pattern Formation
Abstract: Ever since Alan Turing's influential 1952 paper on the subject, pattern formation has been a topic of interest to applied mathematics. I will talk about the paper "The Stability and Dynamics of Localized Spot Patterns in the Two-Dimensional Gray-Scott Model" by W. Chen and M. J. Ward. The authors use asymptotic analysis to characterize the instability mechanism of these patterns. Time permitting, I will also discuss the stability of spot patterns on the sphere.

September 22
Speaker: Todd Reeb
Title: Image Denoising
Abstract: The automated processing of images is a key component in many technologies, but images are often too distorted or are missing too many details to be successfully processed. In this talk, I will start by describing the basic problems of image processing and then focus on removing noise from images by local smoothing, frequency domain filters, and a nonlocal method due to Buades, Coll, and Morel. This talk is based on the SIAM-review article "Image Denoising Methods. A New Nonlocal Principle" by A. Buades, B. Coll, and J. M. Morel.

September 15
Speaker: Fernando Guevara Vasquez
Title: Version Control with git
Abstract: Are you tired of keeping track of different versions of your documents/code? Do you want to be able to edit the same documents on different computers and/or with collaborators? A powerful tool called git can help. Bring a laptop for a hands on experience.

September 8
Speaker: Braxton Osting
Title: Mathematics of the Faraday Cage
Abstract: We will discuss the SIAM-review article "Mathematics of the Faraday Cage" by S. J. Chapman, D. P. Hewett, and L. N. Trefethen.