Author Archive: raphy

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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The topological KKMS Theorem is a powerful extension of the Brouwer’s Fixed-Point Theorem, which was proved by Shapley in 1973 in the context of game theory. We prove a colorful and polytopal generalization of the KKMS Theorem, and show that…
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The aim of this talk is to present an elementary approach to Fermat’s last theorem. We translate the condition of (x,y,z) being solution of Fermat’s equation x^n+y^n=z^n to a robust system of p-adic recursion relations (to which we refer as…
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Over the last 15 years, it has been noted that many combinatorial structures, such as real and complex hyperplane arrangements, interval greedoids, matroids, oriented matroids, and others have the structure of a left regular band, a certain kind of finite monoid….
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We give two simple generalizations of commutative rings. They form (co)-complete categories, that contain commutative (semi-) rings (e.g. f0; 1g ⊆ [0; 1] ⊆ [0; 1) with the usual multiplication x + y := maxfx; yg). But they also contains…
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