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DTSTART:20250309T070000
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URL:https://uwaterloo.ca/pure-mathematics/events/joint-pure-math-department
 -colloquium-probability-seminar
SUMMARY:Joint Pure Math Department Colloquium & Probability Seminar
CLASS:PUBLIC
DESCRIPTION:MARK RUDELSON\, UNIVERSITY OF MICHIGAN\n\nWhen a system of real
  quadratic equations has a solution\n\nThe existence and the number of sol
 utions of a system of polynomial\nequations in n variables over an algebra
 ically closed field is a\nclassical topic in algebraic geometry. Much less
  is known about the\nexistence of solutions of a system of polynomial equa
 tions over reals.\nAny such problem can be reduced to a system of quadrati
 c equations by\nintroducing auxiliary variables. Due to the generality of 
 the problem\,\na computationally efficient algorithm for determining wheth
 er a real\nsolution of a system of quadratic equations exists is believed 
 to be\nimpossible. We will discuss a simple and efficient sufficient\ncond
 ition for the existence of a solution. While the problem and the\nconditio
 n are of algebraic nature\, the proof relies on Fourier\nanalysis and conc
 entration of measure.\n\nJoint work with Alexander Barvinok.\n\nMC 5501
DTSTAMP:20260504T134922Z
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