2^{nd} year ~~Master~~ PhD Student in Theory and Algorithms @ UIUC

Advised by Prof. Alexandra Kolla

Email: ccarlsn2 [at] illinois [dot] edu

Office: Siebel 3111

My research interests include spectral graph theory, general graph theory, algorithm design, complexity theory, combinatorics, and matrix theory. I also enjoy thinking about graph coloring problems, matrix signing problems, graph minors, the unique games conjecture, the graceful labeling conjecture, Hadwiger conjecture, the four color theorem, graph isomorphism, etc. Send me your commplexity or graph problems.

I am lucky to be working with Hsien-Chih Chang and Prof. Karthekeyan Chandrasekaran.

I grew up in the Alaskan Bush, went to a public boarding school for high school, and got two bachelor of science degrees (mathematics and computer science) from the University of Alaska Fairbanks. I worked at Microsoft as a software engineer on the Outlook team before returning to school.

**Largest Eigenvalue and Invertibility of Symmetric Matrix Signings.**With Alexandra Kolla, Karthekeyan Chandrasekaran and Hsien-Chih Chang.

*Submitted, 2016*

- Teaching Assistant for CS 473 Spring 2017
- Teaching Assistant for CS 374 Fall 2016
- Teaching Assistant for CS 492 Fall 2015 and CS 493/494 Spring 2016.

Hall's Theorem:

Let $G=(L\cup R,E)$ be a finite bipartite graph with bipartite sets $L$ and $R$. There is a matching that entirely covers $L$ if and only if $$|W| \leq |N_G(W)|$$ for all $W \subseteq L$.

Let $G=(L\cup R,E)$ be a finite bipartite graph with bipartite sets $L$ and $R$. There is a matching that entirely covers $L$ if and only if $$|W| \leq |N_G(W)|$$ for all $W \subseteq L$.