Speaker: Leonid Rybnikov, Harvard CMSA/National Research University Higher School of Economics Title: Quantum magnet chains and Kashiwara crystals Abstract: Solutions of the algebraic Bethe ansatz for quantum magnet chains are, generally, multivalued functions of the parameters of the integrable system. I will explain how to compute some monodromies of solutions of Bethe ansatz for the Gaudin magnet […]
Speaker: David Zuckerman, Harvard CMSA/University of Texas at Austin Title: Explicit Ramsey Graphs and Two Source Extractors Abstract: Ramsey showed that any graph on N nodes contains a clique or independent set of size (log N)/2. Erdos showed that there exist graphs on N nodes with no clique or independent set of size 2 log N, […]
Member Seminar Speaker: Shuaijie Qian (Harvard CMSA) Title: Some non-concave dynamic optimization problems in finance Abstract: Non-concave dynamic optimization problems appear in many areas of finance and economics. Most of existing literature solves these problems using the concavification principle, and derives equivalent, concave optimization problems whose value functions are still concave. In this talk, I will present […]
Probability Seminar Speaker: Hugo Falconet (Courant Institute, NYU) Title: Liouville quantum gravity from random matrix dynamics Abstract: The Liouville quantum gravity measure is a properly renormalized exponential of the 2d GFF. In this talk, I will explain how it appears as a limit of natural random matrix dynamics: if (U_t) is a Brownian motion on the unitary […]
Member Seminar Speaker: Mauricio Romo Title: Quantum trace and length conjecture for hyperbolic knot Abstract: I will define the quantum trace map for an ideally triangulated hyperbolic knot complement on S^3. This map assigns an operator to each element L of the Kauffman Skein module of knot complement. Motivated by an interpretation of this operator in the context of […]
Probability Seminar Speaker: Ainesh Bakshi (MIT) Title: Outlier-Robust Algorithms for Clustering Non-Spherical Mixtures Abstract: In this talk, we describe the first polynomial time algorithm for robustly clustering a mixture of statistically-separated, high-dimensional Gaussians. Prior to our work this question was open even in the special case of 2 components in the mixture. Our main conceptual contribution […]
Member Seminar Speaker: Damian van de Heisteeg Title: Light states in the interior of CY moduli spaces Abstract: In string theory one finds that states become massless as one approaches boundaries in Calabi-Yau moduli spaces. In this talk we look in the opposite direction, that is, we search for points where the mass gap for these light […]
Probability Seminar Location: Room 109, Harvard Science Center, 1 Oxford Street, Cambridge MA 02138 Speaker: Dan Mikulincer (MIT) Title: Lipschitz properties of transport maps under a log-Lipschitz condition Abstract: Consider the problem of realizing a target probability measure as a push forward, by a transport map, of a given source measure. Typically one thinks about […]
Member Seminar Speaker: Alejandro Poveda Title: Compactness and Anticompactness Principles in Set Theory Abstract: Several fundamental properties in Topology, Algebra or Logic are expressed in terms of Compactness Principles.For instance, a natural algebraic question is the following: Suppose that G is an Abelian group whose all small subgroups are free - Is the group G free? […]
Probability Seminar Note location change: Science Center Room 300H Speaker: Lior Alon (MIT) Title: Fourier quasicrystals and stable polynomials Abstract: The Poisson summation formula says that the countable sum of exp(int), over all integers n, vanishes as long as t is not an integer multiple of 2 pi. Can we find a non-periodic discrete set A, such […]
Probability Seminar Speaker: Roland Bauerschmidt (Cambridge) Title: Bakry-Emery theory and renormalisation Abstract: I will discuss an approach to log-Sobolev inequalities that combines the Bakry-Emery theory with renormalisation and present several applications. These include log-Sobolev inequalities with polynomial dependence for critical Ising models on Z^d when d>4 and singular SPDEs with uniform dependence of the log-Sobolev […]
Probability Seminar Speaker: Zhigang Yao (Harvard CMSA/National University of Singapore) Title: Manifold Fitting: An Invitation to Statistics Abstract: This manifold fitting problem can go back to H. Whitney’s work in the early 1930s (Whitney (1992)), and finally has been answered in recent years by C. Fefferman’s works (Fefferman, 2006, 2005). The solution to the Whitney extension problem […]