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 learningdriven startup called Crisply.
I am an Assistant Professor in the Mathematics Department and Program in Applied and Computational Mathematics at Princeton University.
However, I will be on leave during the 20162017 academic year visiting the Institute for Advanced Study.
I can typically be found:
Princeton University
Mathematics Department
Fine Hall
Princeton, NJ 085441000
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 highdimensional 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 Frankensteinlike 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, the combinatorial aspects of it) with
Steve Sigur.
Support:
My research is supported by a National Science Foundation CAREER grant, Grant No. DMS1552520.
My research at Yale was funded in part by the National Science Foundation under a
Mathematical Sciences Postdoctoral Research Fellowship, Grant No. DMS0902962 and my time at the Institute for Advanced Study was supported by National Science Foundation Grant No. DMS1128155.
Some Talks:

Interlacing families and bipartite Ramanujan graphs PDF

Interlacing families and KadisonSinger PDF

A more general ``method of interlacing polynomials'' talk PDF

Polynomials and (finite) free probability PDF
Papers:
(in reverse chronological order)
 A. Marcus,
Real stable polynomials and counting spanning trees,
in (perpetual) preparation.
 A. Marcus, J. Vekhter,
Distances in the rotation system graph,
in (perpetual) preparation.
 A. W. Marcus,
N. Srivastava,
The solution of the KadisonSinger problem,
Current Developments in Mathematics, 2016. arXiv
 V. Gorin, A. W. Marcus,
Crystallization of random matrix orbits,
International Mathematics Research Notices, rny052 (2018). arXiv
 A. W. Marcus,
A determinantal identity for the permanent of a rank 2 matrix,
preprint. PDF
 A. W. Marcus, W. Yomjinda,
Analysis of rank 1 perturbations in general β ensembles,
preprint. PDF
 A. W. Marcus,
Discrete unitary invariance,
arXiv
 A. W. Marcus,
Polynomial convolutions and (finite) free probability,
preprint. PDF
 M. Bownik,
P. Casazza,
A. W. Marcus,
D. Speegle,
Improved bounds in Weaver and Feichtinger conjectures,
Crelles Journal, 2016.
arXiv
 A. W. Marcus,
D. A. Spielman,
N. Srivastava,
Interlacing families IV: bipartite Ramanujan graphs of all sizes,
FOCS (2015).
arXiv
 A. W. Marcus,
D. A. Spielman,
N. Srivastava,
Finite free convolutions of polynomials,
preprint.
arXiv
 A. W. Marcus,
D. A. Spielman,
N. Srivastava,
Ramanujan graphs and the solution of the KadisonSinger problem,
Proc. ICM, Vol III (2014), 375386.
arXiv
 A. W. Marcus,
D. A. Spielman,
N. Srivastava,
Interlacing families III: improved bounds for restricted invertibility,
submitted. arXiv
 A. W. Marcus,
D. A. Spielman,
N. Srivastava,
Interlacing families II: mixed characteristic polynomials and the KadisonSinger problem,
Ann. of Math. 1821 (2015), 327350.
arXiv
 A. W. Marcus,
D. A. Spielman,
N. Srivastava,
Interlacing families I: bipartite Ramanujan graphs of all degrees,
Ann. of Math. 1821 (2015), 307325.
arXiv
(Preliminary version appeared in FOCS 2013)
 M. Madiman, A. W. Marcus, P. Tetali,
Entropy and set cardinality inequalities for partitiondetermined functions,
Random Struct. Algorithms 40 (2012), no. 4, 399424.
PDF
 M. Klazar, A. Marcus,
Extensions of the linear bound in the FürediHajnal conjecture,
Adv. in Appl. Math. 38 (2006), no. 2, 258266.
PDF
PS
BibTeX entry

A. Marcus, G. Tardos,
Intersection reverse sequences and geometric applications,
J. Combin. Theory Ser. A 113 (2006), no. 4, 675691.
PDF
PS
BibTeX entry
(Preliminary version appeared in
GD 2004 (J. Pach, ed.), LNCS, no. 3383, 2004, 349359)

A. Marcus, G. Tardos,
Excluded permutation matrices and the StanleyWilf conjecture,
J. Combin. Theory Ser. A 107 (2004), no. 1, 153160.
PDF
PS
BibTeX entry

R. Kawai, A. Marcus,
Negative Conductance in Two Finitesize 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), 369378.
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:
 Many of my early results are due to the work I did in Budapest, where I was supported by The HungarianAmerican Fulbright Commission.
 Should you need to spend a substantial amount of time there as well, here is a good
HungarianEnglish and EnglishHungarian 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 both
Hampshire College Summer Studies in Mathematics (HCSSiM)
and Mathily
for any advanced highschoolers who love math.
 My Erdős number is 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.
 I was forced to learn how to use source control and now I am in the habit of forcing others to learn it.
I prefer git simply because that is what I learned first.
You can get started easily with Bitbucket or github.
Here is a nice tutorial written specifically for mathematicians.
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.
