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UID:a6bf6919f525484ff7fa59af9816b966
CATEGORIES:Colloquia
CREATED:20240925T093322
SUMMARY: Computational Complexity in Algebraic Combinatorics
LOCATION:Hill 705
DESCRIPTION:Abstract: Algebraic Combinatorics studies objects and quantities originatin
 g in Algebra, Representation Theory and Algebraic Geometry via combinatoria
 l methods, finding formulas and neat interpretations. Some of its feats inc
 lude the hook-length formula for the dimension of an irreducible symmetric 
 group ($S_n$) module, or the Littlewood-Richardson rule to determine multip
 licities of GL irreducibles in tensor products. Yet some natural multiplici
 ties elude us, among them the fundamental Kronecker coefficients for the de
 composition of tensor products of $S_n$ irreducibles, and the plethysm coef
 ficients for compositions of GL modules. Besides enhancing our understandin
 g, answering those questions could also help Geometric Complexity Theory to
 wards establishing lower bounds for the far-reaching goal to show that $P \
 neq NP$.\nWe will discuss how Computational Complexity Theory provides a th
 eoretical framework for understanding what kind of formulas or rules we cou
 ld have. As a proof of concept we show that the square of a symmetric group
  character could not have a combinatorial interpretation.\nBased on joint w
 orks with Christian Ikenmeyer and Igor Pak.\n
X-ALT-DESC;FMTTYPE=text/html:<p><strong>Abstract:</strong> Algebraic Combinatorics studies objects and q
 uantities originating in Algebra, Representation Theory and Algebraic Geome
 try via combinatorial methods, finding formulas and neat interpretations. S
 ome of its feats include the hook-length formula for the dimension of an ir
 reducible symmetric group ($S_n$) module, or the Littlewood-Richardson rule
  to determine multiplicities of GL irreducibles in tensor products. Yet som
 e natural multiplicities elude us, among them the fundamental Kronecker coe
 fficients for the decomposition of tensor products of $S_n$ irreducibles, a
 nd the plethysm coefficients for compositions of GL modules. Besides enhanc
 ing our understanding, answering those questions could also help Geometric 
 Complexity Theory towards establishing lower bounds for the far-reaching go
 al to show that $P <br>eq NP$.</p><p>We will discuss how Computational Comp
 lexity Theory provides a theoretical framework for understanding what kind 
 of formulas or rules we could have. As a proof of concept we show that the 
 square of a symmetric group character could not have a combinatorial interp
 retation.</p><p>Based on joint works with Christian Ikenmeyer and Igor Pak.
 </p>
CONTACT:Greta Panova (USC)
DTSTAMP:20260828T013837
DTSTART;TZID=America/New_York:20241009T153000
DTEND;TZID=America/New_York:20241009T163000
SEQUENCE:0
TRANSP:OPAQUE
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