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 in LCB 222, 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.

Past AMC: [Summer 2018] | [Spring 2018] | [Fall 2017] | [Spring 2017] | [Fall 2016]

➜ Fall 2018

August 30
Speaker: Zach Boyd
Title: Stochastic Block Models are a Discrete Surface Tension
Abstract: The accompanying paper can be found here: [arXiv].

September 6
Speaker: Franco Rota
Title: Lebesgue's integration, integrals of limits and limits of integrals
Abstract: We will introduce and motivate Lebesgue's theory of integration. One of the key results is a theorem of completeness. We will assume it and use it to prove theorems about passing the limit under the integral sign. Then, we will see these theorems in action on a variety of examples.

September 13
Speaker: Adam Brown
Title: Computing stratifications of finite topological space
Abstract: In this talk I will discuss a computational approach to the study of stratified topological spaces. We will see how techniques originating in sheaf theory and the proof of the topological invariance of intersection homology can be used to develop algorithms for computing stratifications of finite topological spaces. Motivated by the applicability of geometric and topological techniques in data science, we will conclude with an overview of current work (joint with Bei Wang) which aims to combine sheaf theory, topological data analysis, and statistics to study finite point sets sampled from stratified topological spaces.

September 20
Speaker: Yiming Xu
Title: Bernstein's inequality and Johnson-Lindenstrauss random projections
Abstract: In this talk I will introduce how to use an old technique in large deviation theory to derive the famous Bernstein’s inequality. Based on that, we will see how the renowned Johnson-Lindenstrauss random projection lemma in data compression comes into display. I will explain how this lemma can also be seen from the perspective of geometric functional analysis as well as the possible extension to a more general setting. [Notes]

October 4 (Cancelled)
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October 18
Speaker: Qing Xia
Title: A Domain Decomposition Approach based on Difference Potentials Method for Chemotaxis Models in 3D
Abstract: In this talk, I will present a domain decomposition approach based on Difference Potentials Method (DPM) for approximating the solution to the classical Patlak-Keller-Segel chemotaxis models in 3D. We employ DPM and uniform Cartesian meshes to handle sub-domains of complex geometric shapes, without loss of accuracy near the irregular boundaries of the sub-domains. As a result of using uniform meshes, fast Poisson solver based on FFT is employed for better efficiency of our numerical algorithms. In addition, our domain decomposition approach is capable of mesh adaptivity and is suitable for parallel computing, which further boosts the efficiency. Numerical results from 3D simulations will be given to demonstrate the significantly improved efficiency and similar accuracy of the domain decomposition approach, in comparison to the single domain approach. This is joint work with Y. Epshteyn.

October 25
Speaker: Hyunjoong Kim
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November 1
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November 15
Speaker: Ryleigh Moore
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November 29
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December 6
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