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DTSTART;TZID=America/Los_Angeles:20251007T121500
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DTSTAMP:20260508T043030
CREATED:20250828T190015Z
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UID:3800-1759839300-1759842600@colleges.claremont.edu
SUMMARY:The integer point transform as a complete invariant (Sinai Robins\, University of São Paulo\, Brazil)
DESCRIPTION:Given any finite set of integer points S\, there is an associated function f_S that encodes S\, which we call its integer point transform.   One can think of this integer point transform f_S algebraically or analytically.  Here we focus on its analytic properties\, showing that it is a complete invariant.   In fact\, we prove that it is only necessary to evaluate f_S at one algebraic point in order to uniquely determine the finite set S\, by employing the Lindemann-Weierstrass theorem.    Similarly\, we prove that it’s only necessary to evaluate the Fourier transform of a rational polytope P (as well as rational cones) at a single algebraic point\, in order to uniquely determine S.   Finally\, by relating the integer point transform to finite Fourier transforms\, we show that a finite number of integer point evaluations of f_S suffice in order to uniquely determine S.  
URL:https://colleges.claremont.edu/ccms/event/antc-talk-sinai-robins-university-of-sao-paulo-brazil/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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