Hello, my name is Adam Marcus. I spent 4 years as a Gibbs Assistant Professor in Applied Mathematics and am now a Visiting Researcher 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.

When I am not at Yale (which is often nowadays), I am the Chief Scientist at Crisply, a machine learning-driven startup based in Boston.

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

Email: FIRSTNAME (dot) LASTNAME (at) yale (dot) edu

Teaching:

For Mokshay's Geometric Probability class, a writeup of my presentation on Grothendieck's Inequality (comments and corrections welcome).

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:

When I am pretending to be a mathematician, my main research interests lie in various areas of combinatorics. In particular, I tend to like things with strange constraints (like restricted orderings and, more recently, dimensionality restrictions).

When I am pretending to be a computer scientist, my interests lie in areas that involve algorithms and computation in high-dimensional vector spaces. In particular, I have a growing interest in a number of topics in machine learning, computational geometry, and optimization.

When I am pretending to be a Frankenstein-like combination of the two, my interests lie in what we (Dan and I) have dubbed "Combinatorial Linear Algebra", a convergence of ideas from the theory of stable polynomials, convex geometry, geometric functional analysis, convex programming, and (of course) linear algebra and combinatorics.

Teaching Interests:

My primary interest here is in the curriculum for general education mathematics courses. There are many practical skills that mathematics can teach someone (problem solving, understanding of probability and statistics, etc) and the current paradigm does not address these.

People I work/worked/will work with:

While at Yale, most of my effort goes to working on problems that share an interest with Daniel Spielman and his former Ph.D. student Nikhil Srivastava (now at Microsoft, Bangalore).

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.

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

Some Talks:

  1. Interlacing Families and Bipartite Ramanujan Graphs PDF
  2. Interlacing Families and Kadison-Singer PDF

Papers:

(in reverse chronological order)
  1. A. Marcus, Real stable polynomials and counting spanning trees, in (perpetual) preparation.

  2. A. Marcus, J. Vekhter, Distances in the rotation system graph, in (perpetual) preparation.

  3. A. W. Marcus, D. A. Spielman,, N. Srivastava, Ramanujan graphs and the solution of the Kadison-Singer problem, to appear (Proc. ICM) arXiv

  4. A. W. Marcus, D. A. Spielman,, N. Srivastava, Interlacing families II: mixed characteristic polynomials and the Kadison-Singer problem, to appear (Ann. of Math.) arXiv

  5. A. W. Marcus, D. A. Spielman, N. Srivatava, Interlacing families I: bipartite Ramanujan graphs of all degrees, to appear (Ann. of Math.) arXiv

  6. M. Madiman, A. W. Marcus, P. Tetali, Entropy and set cardinality inequalities for partition-determined functions, Random Struct. Algorithms 40 (2012), no. 4, 399-424. PDF

  7. 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

  8. 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)

  9. 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

  10. R. Kawai, A. Marcus, Negative Conductance in Two Finite-size Coupled Brownian Motor Models, manuscript (2000). PDF PS BibTeX entry

  11. 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:

Other (still mostly math) links:


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.