A (Slightly) Improved Approximation Algorithm for Metric TSP Page 1 A (Slightly) Improved
Approximation Algorithm for Metric TSP Anna R. Karlin karlin@cs.washington.edu …

We study the class of Lorentzian polynomials. The class contains homogeneous stable
polynomials as well as volume polynomials of convex bodies and projective varieties. We …

We design an FPRAS to count the number of bases of any matroid given by an independent
set oracle, and to estimate the partition function of the random cluster model of any matroid …

We show fully polynomial time randomized approximation schemes (FPRAS) for counting
matchings of a given size, or more generally sampling/counting monomer-dimer systems in …

We show that the modified log-Sobolev constant for a natural Markov chain which converges
to an r-homogeneous strongly log-concave distribution is at least 1/r. Applications include an …

We give a self-contained proof of the strongest version of Mason's conjecture, namely that
for any matroid the sequence of the number of independent sets of given sizes is ultra log …

I will tell two interrelated stories illustrating fruitful interactions between combinatorics and
Hodge theory. The first is that of Lorentzian polynomials, based on my joint work with Petter …

We introduce a presentation of the Chow ring of a matroid by a new set of generators, called
“simplicial generators.” These generators are analogous to nef divisors on projective toric …

Logarithmic concavity of Schur and related polynomials Page 1 TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 375, Number 6, June 2022, Pages 4411–4427 …

We prove tight mixing time bounds for natural random walks on bases of matroids,
determinantal distributions, and more generally distributions associated with log-concave …