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DTSTART:20250309T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20251204T143000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-taylor
SUMMARY:Algebraic and enumerative combinatorics seminar-Taylor Brysiewicz
CLASS:PUBLIC
DESCRIPTION:TITLE: The degrees of Stiefel Manifolds\n\nSpeaker\n Taylor Br
 ysiewicz\n\nAffiliation\n Western\n\nLocation\n MC 6029\n\nABSTRACT:\n\nTh
 e set of orthonormal bases for k-planes in R^n is cut out by the\nequation
 s X*X^T = I\nwhere X is a k x n matrix of variables and I is k x k identi
 ty. This\nspace\, known as the Stiefel manifold St(k\,n)\, generalizes th
 e\northogonal group and can be realized as the homogeneous space\nO(n)/O
 (n-k). Its algebraic closure\ngives a complex affine variety\, and thus\,
  it has a degree.\n\nI will discuss our derivation of these degrees. Exten
 ding 2017 work\non the degrees of special orthogonal groups\, joint work 
 with\nFulvio Gesmundo gives a combinatorial formula in terms of\nnon-int
 ersecting lattice paths.\nThis result relies on representation theory\, co
 mmutative\nalgebra\, Ehrhart theory\, polyhedral geometry\, and enumerat
 ive\ncombinatorics.\n\nI will conclude with some open problems inspired by
  these objects.\n\nTHERE WILL BE A PRE-SEMINAR PRESENTING RELEVANT BACKGRO
 UND AT THE\nBEGINNING GRADUATE LEVEL STARTING AT 1:30PM.
DTSTAMP:20260402T151055Z
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