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UID:a6bf6919f525484ff7fa59af9816b966
CATEGORIES:Colloquia
CREATED:20240925T093322
SUMMARY: Computational Complexity in Algebraic Combinatorics
LOCATION:Hill 705
DESCRIPTION:<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:20260827T103212
DTSTART;TZID=America/New_York:20241009T153000
DTEND;TZID=America/New_York:20241009T163000
SEQUENCE:0
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