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Random determinants, the elastic manifold, and landscape complexity beyond invariance

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Member Seminar Speaker: Ben McKenna Title: Random determinants, the elastic manifold, and landscape complexity beyond invariance Abstract: The Kac-Rice formula allows one to study the complexity of high-dimensional Gaussian random functions (meaning asymptotic counts of critical points) via the determinants of large random matrices. We present new results on determinant asymptotics for non-invariant random matrices, and […]

Kahler geometry in twisted materials

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Member Seminar Speaker: Jie Wang Title: Kahler geometry in twisted materials Abstract: Flatbands are versatile platform for realizing exotic quantum phases due to the enhanced interactions. The canonical example is Landau level where fractional quantum Hall physics exists. Although interaction is strong, the fractional quantum Hall effect is relatively well understood thanks to its model wavefunction, […]

Principal flow, sub-manifold and boundary

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

Member Seminar  Speaker: Zhigang Yao Title: Principal flow, sub-manifold and boundary Abstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects, taking values in spaces which […]

Quantum magnet chains and Kashiwara crystals

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

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 […]

Explicit Ramsey Graphs and Two Source Extractors

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

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, […]

Some non-concave dynamic optimization problems in finance

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

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 […]

Quantum trace and length conjecture for hyperbolic knot

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

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 […]

Light states in the interior of CY moduli spaces

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

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 […]

Compactness and Anticompactness Principles in Set Theory

CMSA Room G10 CMSA, 20 Garden Street, Cambridge, MA, United States

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? […]