Michael Tait

mtait at math dot ucsd dot edu

Office: APM 6452

I am a fifth year PhD student in the Department of Mathematics at UCSD. I am off the job market; next year I will be an NSF Postdoctoral Fellow at Carnegie Mellon. My advisor is Jacques Verstraëte. My research interests include problems in extremal graph theory, combinatorial number theory, and finite geometry, and I have also worked on questions in (hyper)graph coloring and covering, spectral graph theory, and applications of graph theory in information and coding theory. My M. Sc. advisor was Sebastian Cioaba and my thesis was titled The Alon-Saks-Seymour and Rank-Coloring Conjectures. My Ph. D. thesis is titled Connections between graph theory, additive combinatorics, and finite incidence geometry. For more information, please see my CV and my research statement.

Teaching

During the Spring quarter, I am the TA for Math 121B: Foundations of Teaching and Learning Math II with Dr. Stevens. Our sections are Thursdays at 4 pm in APM B412, and my office hours are Tuesdays 10-11 am and Fridays 2-3 pm. I was the instructor for Math 10B during Summer Session I. Click here for the course web page. Please see my teaching page for previous courses taught and my teaching statement to see who I am as a teacher.

Research

## Published or to appear

More Counterexamples to the Alon-Saks-Seymour and Rank-Coloring Conjectures. Electronic Journal of Combinatorics, 18.1, P26 (2011), with Sebastian Cioaba.Variations on a theme of Graham and Pollak. Discrete Mathematics, Volume 313, Issue 5, 665--676 (2013). Co-authored with Sebastian Cioaba.Sidon sets and graphs without 4-cycles. Journal of Combinatorics, Volume 5, Number 2, 155--165 (2014). Co-authored with Craig Timmons.On Coupon Colorings of Graphs, Discrete Applied Mathematics 193 (2015) 94--101. Co-authored with Bob Chen, Jeong Han Kim, and Jacques Verstraete.Orthogonal polarity graphs and Sidon sets. To appear in Journal of Graph Theory. Co-authored with Craig Timmons.On sets of integers with restrictions on their products, European Journal of Combinatorics 51 (2016) 268--274, with Jacques Verstraete.On the chromatic number of the Erdős-Rényi orthogonal polarity graph. Electronic Journal of Combinatorics, P2.21, 1--19, (2015). With Sam Peng and Craig Timmons.Small dense subgraphs of polarity graphs and the extremal number for the 4-cycle. Australasian Journal of Combinatorics, Volume 63 (1), (2015), 107--114, with Craig Timmons.On the distance spectra of graphs. Linear Algebra and its Applications, Volume 497, (2016), 66--87, with 11 authors.Increasing paths in edge-ordered graphs: the hypercube and random graphs. The Electronic Journal of Combinatorics, 23.2, P2.15, with Jessica De Silva, Theo Molla, Flo Pfender, and Troy Retter.Independent sets in polarity graphs. To appear in SIAM Journal on Discrete Math with Craig Timmons.## Submitted

A Szemerédi-Trotter type theorem, sum-product estimates in finite quasifields, and related results. Submitted with Thang Pham, Craig Timmons, and Le Anh Vinh.Proof of a conjecture of Graham and Lovász concerning unimodality of coefficients of the distance characteristic polynomial of a tree. Submitted with Ghodrat Aalipour, Aida Abiad, Zhanar Berikkyzy, Leslie Hogben, Franklin Kenter, and Jephian Lin.Spectral bounds for the k-independence number of a graph. Submitted with Aida Abiad and Sebastian Cioaba.On a problem of Neumann. Submitted.Characterizing graphs of maximum principal ratio. Submitted with Josh Tobin.Three conjectures in extremal spectral graph theory. With Josh Tobin.## Other

The Alon-Saks-Seymour and Rank-Coloring ConjecturesM. Sc. Thesis, University of Delaware, 2011.Connections between graph theory, additive combinatorics, and finite incidence geometryPh.D. Thesis, UC San Diego, 2016.

## Selected Talks

- Increasing paths in edge-ordered graphs
- Recent results on graphs coming from projective planes
- Sum-product estimates in finite quasifields
- Sets of integers with restrictions on their products
- Coupon colorings of graphs
- Generalizations of the Graham-Pollak Theorem
- The Alon-Saks-Seymour and Rank-Coloring Conjectures (M.Sc. Defense)

## Mathematicians with whom I have had the pleasure to work

Ghodratollah Aalipour, Aida Abiad, Zhanar Berikkyzy, Bob Chen, Sebi Cioaba, Jay Cummings, Jess De Silva, Wei Gao, Kristin Heysse, Leslie Hogben, Franklin Kenter, Jeong Han Kim, Jephian Lin, Theo Molla, Sam Peng, Flo Pfender, Thang Pham, Troy Retter, Craig Timmons, Josh Tobin, Jacques Verstraëte, Le Anh Vinh.

Honorable mentions (no papers [yet!]): Steve Butler, Fan Chung, Paul Horn, Felix Lazebnik, Po-Shen Loh, Humberto Naves, Alex Vardy, Jason Williford, Rob Won.

About Me

Besides mathematics, some things that I like are running, cycling, going to the batting cages, the soggy bottom boys, reading, and Fränk and Andy Schleck. I grew up in Wilmington, DE and attended Concord High School where I participated in basketball, wrestling, cross-country, track and field, and math league. I then ran collegiate track for 4 years and am a University of Delaware record holder in the outdoor 4x800m relay (7:32.89) and the indoor Distance Medley Relay (9:50.12). My NCAA eligibility being up, I am now pursuing my athletic interests on the UCSD Cycling Team. I did some math along the way as well.