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.

Mathcamp problem sets:

  1. Problem Set 1
  2. Problem Set 2
  3. Problem Set 3
  4. Slides

I am leading the Spring 2015 Arbeitsgemeinschaft at Oberwolfach.

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

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 Berkeley).

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
  3. My Interview Talk PDF


(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, Interlacing families IV: bipartite Ramanujan graphs of all sizes, submitted (FOCS 2015) arXiv.

  4. A. W. Marcus, D. A. Spielman, N. Srivastava, Finite free convolutions of polynomials, preprint arXiv

  5. A. W. Marcus, D. A. Spielman, N. Srivastava, Ramanujan graphs and the solution of the Kadison-Singer problem, Proc. ICM, Vol III (2014), 375-386. arXiv

  6. A. W. Marcus, D. A. Spielman, N. Srivastava, Interlacing families III: improved bounds for restricted invertibility, in preparation.

  7. A. W. Marcus, D. A. Spielman, N. Srivastava, Interlacing families II: mixed characteristic polynomials and the Kadison-Singer problem, Ann. of Math. 182-1 (2015), 327-350. arXiv

  8. A. W. Marcus, D. A. Spielman, N. Srivastava, Interlacing families I: bipartite Ramanujan graphs of all degrees, Ann. of Math. 182-1 (2015), 307-325. arXiv

  9. 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

  10. 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

  11. 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)

  12. 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

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

  14. 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: