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DTSTAMP:20260407T051528Z
UID:5a377c60b1e5d621630958@ist.ac.at
DTSTART:20180108T110000
DTEND:20180108T120000
DESCRIPTION:Speaker: Greta Panova\nhosted by Herbert Edelsbrunner\nAbstract
 : Algebraic Combinatorics studies objects and phenomena originating in alg
 ebra\, representation theory and algebraic geometry via discrete methods a
 nd uses this interplay to solve problems in combinatorics or vice versa. I
 ts applications can reach into farther areas.I will first give a very brie
 f and general overview of the basic objects in Algebraic Combinatorics com
 ing from the representation theory of the symmetric and general linear gro
 ups.These objects and methods can then be applied in Statistical Mechanics
 \, mainly in the study of integrable lattice models. In particular\, we de
 veloped asymptotics of symmetric functions which we used to prove various 
 limit behaviors of lozenge tilings like the GUE-eigenvalues distributions 
 near the boundary and the limit surface of the height function.  [Gorin-Pa
 nova\, Ann. Prob. 2014\, Panova\, Letters Math Phys\, 2015]Another applica
 tion comes in Geometric Complexity Theory\, a program developed by Mulmule
 y and Sohoni for proving computational lower bounds\, and aiming to resolv
 e the algebraic version of the "P vs NP" Millennium Prize problem\, the "e
 asier" "VP vs VNP" problem. GCT's framework goes through the relevant repr
 esentation theory for distinguishing the permanent from the determinant po
 lynomials.  Using combinatorial constructions we can unravel some of the r
 epresentation theoretic mysteries and in particular show that there are no
  "occurrence obstructions" for the distinction necessary to obtain superpo
 lynomial lower bounds\, thereby disproving the main hopeful conjecture in 
 GCT and making the VP vs VNP problem even harder to solve. [Burgisser-Iken
 meyer-Panova\, FOCS 2016]
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
 TA
ORGANIZER:pdelreal@ist.ac.at
SUMMARY:Greta Panova: Algebraic Combinatorics in Statistical Mechanics and 
 Complexity Theory
URL:https://talks-calendar.ista.ac.at/events/1010
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