Author Archive: raphy

A major concern in Group Theory is the question of linearity of a given group and, in case the group is linear, the question of determining all its possible Linear Representations. While this question is entirely of algebraic nature, many…
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  Initial developments in the theory of (topological) quantum groups were motivated on one hand by the desire to extend the classical Pontryagin duality for locally compact abelian groups to a wider class of objects and on the other by…
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In convex optimization, quantum information theory and real convex algebraic geometry, many practical and theoretical questions are related to containment problems between convex sets defined by a linear matrix inequality (LMI domains for short). One difficulty when we wish to…
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Since the 1970’s, Physicists and Mathematicians who study random matrices in the standard models of GUE or GOE, are aware of intriguing connections between integrals of such random matrices and enumeration of graphs on surfaces. We establish a new aspect…
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In this talk I will describe the study of certain operator algebras and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of representations. I will try to provide some evidence to show…
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We study the power of the Laplace Beltrami Operator (LBO) in processing and analyzing geometric information. The decomposition of the LBO at one end, and the heat operator at the other end provide us with efficient tools for dealing with…
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A Cohomological field theory (CohFT) is an algebraic structure underlying the properties of the Gromov-Witten invariants and quantum cohomology of projective varieties. I will talk about a CohFT associated to a holomorphic function F with an isolated singularity and a…
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In this talk we discuss the fine scale $L^2$-mass distribution of toral Laplace eigenfunctions with respect to random position. For the 2-dimensional torus, under certain flatness assumptions on the Fourier coefficients of the eigenfunctions and generic restrictions on energy levels,…
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I will discuss a surprising connection between singularity theory and cluster algebras, specifically between (1) the topology of isolated singularities of plane curves and (2) the mutation equivalence of the quivers associated with their morsifications. Joint work with Pavlo Pylyavskyy…
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A common question in mathematics is “Can global questions be answered by local means?”, this is usually referred to as the “local-global principle”. A famous example is the Hasse-Minkowski theorem on quadratic forms. On the other and, it is also…
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