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SUMMARY:Jeong-Hoon Ju (University of Copenhagen)
DTSTART:20260629T090000Z
DTEND:20260629T100000Z
DTSTAMP:20260624T181409Z
UID:TropicalmathandML/43
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Tropicalmath
 andML/43/">An introduction to the Asymptotic Spectra of Preordered Semirin
 gs</a>\nby Jeong-Hoon Ju (University of Copenhagen) as part of Tropical ma
 thematics and machine learning\n\n\nAbstract\nIn algebraic complexity theo
 ry\, a flagship problem is to determine the exponent of matrix multiplicat
 ion\, that is\, the infimum of real numbers $\\omega$ such that $n \\times
  n$ matrix multiplication can be computed using $n^{\\omega+o(1)}$ arithme
 tic operations. Motivated by this problem\, Strassen developed the theory 
 of asymptotic spectra\, initially focusing on the preordered semiring of t
 ensors. In this talk\, we give an introduction to the theory of asymptotic
  spectra. We first define preordered semirings and their asymptotic spectr
 a. We then discuss Strassen's duality theorem\, which characterizes the as
 ymptotic preorder on a semiring in terms of elements in its asymptotic spe
 ctrum. Finally\, we discuss the broad applicability of the theory\, its ge
 neralizations\, and related research problems.\n
LOCATION:https://researchseminars.org/talk/TropicalmathandML/43/
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