# 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 323, 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: [Fall 2017] | [Spring 2017] | [Fall 2016]

### ➜ Spring 2018

January 25
Speaker: Braxton Osting
Title: Extremal Spectral Gaps for Periodic Schrödinger Operator
Abstract: The spectrum of a Schrödinger operator with periodic potential generally consists of bands and gaps. I will discuss the problem of finding a potential that gives maximum length spectral gaps. This is joint work with C.-Y. Kao.

Feburary 8
Speaker: Dong Wang
Title: Recent Advances on the Threshold Dynamics Method
Abstract: The threshold dynamics method developed by Merriman, Bence, and Osher (MBO) is an efficient method for simulating the mean curvature flow. In this talk, I will discuss some recent advances on the threshold dynamics method.

Feburary 15
Speaker: Chee Han Tan
Title: Extremal Problems for Laplacian Eigenvalues
Abstract: Historically, the first spectral optimisation problem is due to Lord Rayleigh in 1877, where he conjectured that the disk should minimise the first Laplace-Dirichlet eigenvalue among all planar domains of equal area. Almost 30 years later G. Faber and E. Krahn proved this result independently and the conjecture holds in higher dimension as well. Much progress has been made over the past few decades due to significant development in variational analysis and optimisation methods. We review existing results for the constrained problem of finding an optimal domain that minimises or maximises the $k$-th eigenvalue of the Laplacian operator with boundary conditions such as Dirichlet, Neumann or Steklov. We will then discuss the proof of the Faber-Krahn inequality for the first Laplace-Dirichlet eigenvalue and the Hersch-Payne-Schiffer inequality for the second Laplace-Steklov eigenvalue, the latter leads to the assertion that the disk maximises the second Laplace-Steklov eigenvalue among plane open sets of given area.

Feburary 22
Speaker: Huy Dinh
Title: To be announced
Abstract:

March 1
Speaker: Nathan Willis
Title: To be announced
Abstract:

March 29
Speaker: Hyunjoong Kim
Title: To be announced
Abstract:

April 5
Speaker: Rebecca Hardenbrook
Title: To be announced
Abstract:

April 29
Speaker: Todd Reeb
Title: To be announced
Abstract: