Speaker:  Lee Kennard, Syracuse University
Title: Regular matroids and torus representations
Time: 2:30 PM, Monday, November 10, 2025
Place:  Malott 206

Abstract: Recent work with Michael Wiemeler and Burkhard Wilking presents a link between arbitrary finite graphs and torus representations all of whose isotropy groups are connected. The link is via combinatorial objects called regular matroids, which were classified in 1980 by Paul Seymour. We then apply Seymour's deep result to classify and to compute geometric invariants of this class of torus representations. The applications to Riemannian geometry are significant. A highlight of our analysis of these representations is the first proof of Hopf's 1930s Euler Characteristic Positivity Conjecture for metrics invariant under a torus action where the torus rank is independent of the manifold dimension.


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