Adam's page

Hello, my name is Adam Marcus and I am a Gibbs Assistant Professor in Applied Mathematics at Yale University. I received my B.A./M.A. in Mathematics from Washington University in St. Louis in 2003 and my Ph.D. in Algorithms, Combinatorics, and Optimization under the supervision of Prasad Tetali from Georgia Tech in 2008.

I can be reached at:
Yale University
Mathematics Department
PO Box 208283
New Haven, CT 06520-8283

Office: AKW 207a
Email: FIRSTNAME (dot) LASTNAME (at) yale (dot) edu

Teaching:

Fall 2009: AMTH 110 Intro to Quantitative Reasoning.

Spring 2009: AMTH 950b Topics in Discrete Mathematics: The Probabilistic Method

For Gil's Combinatorics class, a Walkthrough of Szemerédi Regularity Lemma (comments and corrections welcome).

Fall 2008: AMTH 110 Intro to Quantitative Reasoning.

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 research is funded in part by the National Science Foundation under a Mathematical Sciences Postdoctoral Research Fellowship, Grant No. DMS-0902962.

People I work/worked/will work with:

Here at Yale, most of my effort goes to working on problems that share an interest with Daniel Spielman and his Ph.D. student Nikhil Srivastava.

At Georgia Tech, most of my time was spent working with my advisor, Prasad Tetali

Before 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 had the pleasure of working 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 website that offers coupons for small local businesses (currently just in New York City).

Papers:

(in reverse chronological order)

A. Marcus, Real stable polynomials and counting spanning trees, in preparation.

A. Marcus, J. Vekhter, Distances in the rotation system graph, in preparation.

M. Madiman, A. Marcus, P. Tetali, Entropy and set cardinality inequalities for partition-determined functions, submitted. PDF

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: PDF PS 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 Tardos and Martin Klazar was honored by SIAM with the 2008 Dénes Kőnig Prize.

My work with Joshua Vekhter was honored by the AMS with the 2009 Karl Menger Award.

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.

The Triangle Book was mentioned in the October 10, 2008 episode of NUMB3RS, you can watch it here (it happens within the first 2 minutes).

Other (still mostly math) links:

Many of my early 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 now 2 - 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 YALE UNIVERSITY OR THE NSF AND NEITHER YALE UNIVERSITY NOR THE NSF HAS EDITED OR EXAMINED THE CONTENT. THE AUTHOR OF THE PAGE IS SOLELY RESPONSIBLE FOR THE CONTENT.