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DTSTART:20250309T070000
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DTSTART;TZID=America/Toronto:20250919T153000
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URL:https://uwaterloo.ca/pure-mathematics/events/geometry-and-topology-semi
 nar-37
SUMMARY:Geometry and Topology Seminar
CLASS:PUBLIC
DESCRIPTION:LORENZO SARNATARO\, UNIVERSITY OF TORONTO\n\n_Index\, Intersect
 ions\, and Multiplicity of Min-Max Geodesics_\n\nThe p-widths of a closed 
 Riemannian surface are geometric invariants\nassociated with the length fu
 nctional. In a recent work\, Chodosh and\nMantoulidis showed that these in
 variants are realised as the weighted\nlengths of unions of closed immerse
 d geodesics (possibly\, with\nmultiplicity). I will discuss joint work wit
 h Jared Marx-Kuo and\nDouglas Stryker\, where we prove upper bounds for th
 e Morse index and\nnumber of intersections of min-max geodesics achieving 
 the p-width of\na closed surface. A key tool in our analysis is a proof th
 at for a\ngeneric set of metrics\, the tangent cone at any vertex of any f
 inite\nunion of closed immersed geodesics consists of exactly two lines. W
 e\nalso construct examples to demonstrate that multiplicity one does not\n
 hold generically in this setting. Specifically\, we construct an open\nset
  of metrics on S^2 for which the p-width is only achieved by p\ncopies of 
 a single closed geodesic.\n\nMC 5417
DTSTAMP:20260502T041615Z
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