Hello, my name is Adam Marcus (Adam W. Marcus, not to be confused with the database expert or the director or the Retraction Watch blogger or the cancer researcher).

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 then spent 4 years as a Gibbs Assistant Professor in Applied Mathematics at Yale University under the supervision of Daniel Spielman, followed by 3 years as Chief Scientist at a machine learning-driven startup called Crisply.

I am an Assistant Professor in the Mathematics Department and Program in Applied and Computational Mathematics at Princeton University.

I can typically be found:
Princeton University
Mathematics Department
Fine Hall
Princeton, NJ 08544-1000

Office: Fine 1110
Email: FIRSTNAME (dot) LASTNAME (at) princeton (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 that are constrained in ways that current tools are not equipped to deal with (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 I like to call "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 lies in creating innovative curricula 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 as adequately as it could.

People I work/worked/will work with:

While at Yale, most of my effort went 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, some combinatorial aspects of it) with Steve Sigur.

Support:

My research is supported by a National Science Foundation CAREER grant, Grant No. DMS-1552520.

My time at the Institute for Advanced Study was supported by a Von Neumman Fellowship, National Science Foundation Grant No. DMS-1128155.

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. A more general ``method of interlacing polynomials'' talk PDF
  4. Polynomials and (finite) free probability 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, N. Srivastava, The solution of the Kadison-Singer problem, Current Developments in Mathematics, 2016. arXiv

  4. V. Gorin, A. W. Marcus, Crystallization of random matrix orbits, International Mathematics Research Notices, rny052 (2018). arXiv

  5. A. W. Marcus, A determinantal identity for the permanent of a rank 2 matrix, preprint. PDF

  6. A. W. Marcus, W. Yomjinda, Analysis of rank 1 perturbations in general β ensembles, preprint. PDF

  7. A. W. Marcus, Discrete unitary invariance, arXiv

  8. A. W. Marcus, Polynomial convolutions and (finite) free probability, preprint. PDF

  9. M. Bownik, P. Casazza, A. W. Marcus, D. Speegle, Improved bounds in Weaver and Feichtinger conjectures, Crelles Journal, 2016. arXiv

  10. A. W. Marcus, D. A. Spielman, N. Srivastava, Interlacing families IV: bipartite Ramanujan graphs of all sizes, FOCS (2015). arXiv

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

  12. 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

  13. A. W. Marcus, D. A. Spielman, N. Srivastava, Interlacing families III: improved bounds for restricted invertibility, submitted. arXiv

  14. 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

  15. 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
    (Preliminary version appeared in FOCS 2013)

  16. 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

  17. 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

  18. 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)

  19. 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

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

  21. 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 PRINCETON UNIVERSITY AND PRINCETON UNIVERSITY HAS NOT EDITED OR EXAMINED THE CONTENT. THE AUTHOR OF THIS PAGE IS SOLELY RESPONSIBLE FOR ITS CONTENT.