# 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 **Tuesdays at 3pm in LCB 222**. Please contact either me or
Nathan if you are interested in giving a talk or subscribing to our mailing list.

Past AMC: [Spring 2019] | [Fall 2018] | [Summer 2018] | [Spring 2018] | [Fall 2017] | [Spring 2017] | [Fall 2016]

### ➜ Summer 2019

**June 18**

Speaker: Nathan Willis

**Title: **Multivariate Polynomial Interpolation in Newton Forms

**Abstract: **In introductory courses in numerical analysis we all learn that given $n+1$ distinct real nodes there exists a unique interpolating polynomial up to degree $n$. However, in higher dimensions the analogous problem is more intricate. With a multi-index setup we will construct a basis in order to recover an existence and uniqueness theorem in dimensions greater than 1. Time permitting, we will discuss an algorithm to determine the minimal degree polynomial subspace containing an interpolating polynomial to the given data.

**July 2**

Speaker: Yiming Xu

**Title: **An algorithm for approximately solving the maximum cut problem and some related topics

**Abstract: **Given a simple undirected graph, the maximum cut problem is to find a cut of the vertices such that the number of edges between the cut is maximized. This problem is known to be NP-hard. In this talk, we will first introduce a convex relaxation algorithm by Michel Goemans and David Williamson for approximately solving the maximum cut problem. Then we will extend the idea to prove an interesting inequality that measures the quality of the convex relaxation method in general.

**July 9**

Speaker: Rebecca Hardenbrook

**Title: **The Spectral Theorem for Continuous Functions

**Abstract: **At the end of an introductory functional analysis course using Kreyszig, one may be introduced to the spectral theorem for bounded self-adjoint linear operators. These theorem only holds for $p(T)$ when $T$ is a bounded self-adjoint linear operator and $p$ is a polynomial with real coefficients. In this talk we will continue the discussion of spectral theory in section 9.10 of Kreyszig and prove the spectral theorem for general continuous functions.

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