Computer Science and Discrete Mathematics (CSDM)

A knot is a closed curve embedded in the three-dimensional space, like a rope whose two ends are joined together. As usual in Topology, two knots are equivalent if one can be deformed into the other by continuous moves, where stretching and...

Vapnik's fundamental theorem of statistical learning establishes a computational equivalence between optimization (empirical risk minimization) and learning in the statistical setting. Is the same true for learning in games? We give a precise answer...

The Ramsey number of a graph $G$ is the minimum integer $n$ for which every edge-coloring of the complete graph on $n$ vertices with two colors contains a monochromatic copy of $G$. A graph is $d$-degenerate if all its subgraphs have a vertex of...

We explicitly construct an extractor for two independent sources on $n$ bits, each with min-entropy at least $\log^C n$ for a large enough constant $C$. Our extractor outputs one bit and has error $n^{-\Omega(1)}$. The best previous extractor, by...

We explicitly construct an extractor for two independent sources on $n$ bits, each with min-entropy at least $\log^C n$ for a large enough constant $C$. Our extractor outputs one bit and has error $n^{-\Omega(1)}$. The best previous extractor, by...

Expander walk sampling is an important tool for derandomization. For any bounded function, sampling inputs from a random walk on an expander graph yields a sample average which is quite close to the true mean, and moreover the deviations obtained...

Various motivations recently led Mendel and Naor, Hatami and Kalai to study functions in tail spaces - i.e. function all of whose low level Fourier coefficients vanish. I will discuss the questions and conjectures that they posed and our recent work...

We provide a simple proof of the Rota--Heron--Welsh conjecture for matroids realizable as c-arrangements in the sense of Goresky--MacPherson: we prove that the coefficients of the characteristic polynomial of the associated matroids form log-concave...

We compare methods of computing inverses of matrices over division rings. The most direct way is via Cohn's theory of full matrices, which was improved by Malcolmson, Schofield, and Westreich. But it is simpler to work with finite dimensional...

We prove an $\omega(\log n)$ lower bound on the conondeterministic communication complexity of the Clique vs. Independent Set problem introduced by Yannakakis (STOC 1988, JCSS 1991). As a corollary, this implies superpolynomial lower bounds for the...