Adam's page

Hello, my name is Adam Marcus and I am a Ph.D. student in the ACO program at Georgia Tech. I received my B.A./M.A. in Mathematics from Washington University in St. Louis in 2003. Next year, I will be a Gibbs Assistant Professor in Applied Mathematics at Yale University.

I can be reached at:
School of Mathematics
Georgia Institute of Technology
Atlanta, GA 30332-0160

Office: Skiles 225C (though I am never there)
Email: adam (at) math (dot) gatech (dot) edu

Teaching:

Spring 2006: Math 2602(c) (I was the recitation T.A. under Dan Král' at Georgia Tech).
Summer 2007: Topological Graph Theory (I was a T.A. under sarah-marie belcastro at HCSSiM).
Summer 2007: You Don't Know Jack!! (lead teacher, a mini-course on Information and Coding Theory at HCSSiM).

Research Interests:

My main interests are in Extremal Combinatorics. Specifically, I tend to like Turán-type problems, pattern avoidance, and set intersection properties. And some sort of ordering usually pops up somewhere.

I am also intrigued by the overlaps in various areas in mathematics. In particular, two areas that fascinate me are the interplay between Algebraic Topology, Combinatorics, and LP duality, and the interplay between Information Theory, Regularity, Pseudorandomness, and Spectral Analysis.

My work is supported by a grant from the National Science Foundation Graduate Research Fellowship Program.

People I work/worked/will work with:

At Georgia Tech, my advisor is Prasad Tetali and I also try to work on problems stemming from Robin Thomas and Ernie Croot.

Before coming to Georgia Tech, I spent a year in Budapest working with Gábor Tardos at the Rényi Institute. While there, I took a minor detour to work with Martin Klazar at Charles University in Prague. I also spent Summer 2006 visiting the Theory Group at Microsoft Research to work with Laci Lovász and Fall 2006 visiting Tel Aviv University to work with Noga Alon.

As a side project, I recently worked on a problem known as the Hexagramma Mysticum (specifically, the combinatorial aspects of it) with Steve Sigur.

As another side project, I am helping to write the search algorithms for www.8coupons.com, a new website that specializes in local coupons for small businesses (currently just in New York City).

Papers:

(in reverse chronological order)

M. Klazar, A. Marcus, Extensions of the linear bound in the Füredi-Hajnal conjecture, Adv. in Appl. Math. 38 (2006), no. 2, 258-266. PDF PS BibTeX entry
A. Marcus, G. Tardos, Intersection Reverse Sequences and Geometric Applications, J. Combin. Theory Ser. A 113 (2006), no. 4, 675-691. PDF PS BibTeX entry
(Preliminary version appeared in GD 2004 (J. Pach, ed.), LNCS, no. 3383, 2004, 349-359)
A. Marcus, G. Tardos, Excluded Permutation Matrices and the Stanley-Wilf Conjecture, J. Combin. Theory Ser. A 107 (2004), no. 1, 153-160. PDF PS BibTeX entry
R. Kawai, A. Marcus, Negative Conductance in Two Finite-size Coupled Brownian Motor Models, manuscript (2000). PDF PS BibTeX entry
J. Goodwin, D. Johnston, A. Marcus, Radio Channel Assignments, UMAP Journal 21.3 (Fall 2000), 369-378. Preprint version: PS PDF BibTeX entry **DISCLAIMER**: This paper was written as a contest entry to the MCM 2000 competition, which took place over a span of 4 days (not much time). It is here because it has some mathematical value, but there are some mistakes so please read at your own risk!!

Links related to my research:

Here are links to Mathworld's listing and Wikipedia's listing of the Stanley-Wilf Conjecture, as well as its mentioning in Wikipedia's list of "Recently Solved Problems".
Our solution of the Stanley-Wilf Conjecture is one of the highlights of the book, Combinatorics of Permutations, by Miklós Bóna.
Here are some kind words from Doron Zeilberger regarding one of my papers, as well as his "Loving Rendition" of the proof and a transcript of the talk he gave at Georgia Tech.
My work with Gábor and Martin will be rewarded with the 2008 Dénes Kőnig Prize. at this year's SIAM Conference on Discrete Mathematics.
The results of my work on the Hexagramma Mysticum will appear in the much awaited The Triangle Book, which Steve is coauthoring with John H. Conway. See this page on Steve's site for more information.

Other (still mostly math) links:

Many of my results are due to the work I did in Budapest, where I was supported by The Hungarian-American Fulbright Commission.
Should you need to spend a substantial amount of time there as well, here is a good Hungarian-English and English-Hungarian Translator.
Should you need a reason to spend a substantial amount of time there, I highly recommend the Budapest Semesters in Mathematics program - it is easily the best overseas program for anyone interested in Discrete Math (that I am aware of). If (for some unfortunate reason) you are interested in other areas of mathematics, I have been told that the Budapest Semesters program and the Math in Moscow program are the two best.
While I am shamelessly endorsing math programs, I must recommend the Hampshire College Summer Studies in Mathematics (HCSSiM) for any advanced high-schoolers who love math.
My Erdős number is 3 - many thanks to Russ Lyons, who told me how to make an ő in HTML.
The best way I have found to keep up to date on the most current scientific (not just math) results is through arXiv.

THIS PAGE IS NOT A PUBLICATION OF THE GEORGIA INSTITUTE OF TECHNOLOGY AND THE GEORGIA INSTITUTE OF TECHNOLOGY HAS NOT EDITED OR EXAMINED THE CONTENT. THE AUTHOR(S) OF THE PAGE ARE SOLELY RESPONSIBLE FOR THE CONTENT.