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SUMMARY:Changjie Chen (Université de Montréal)
DTSTART:20250919T150000Z
DTEND:20250919T161500Z
DTSTAMP:20260423T021433Z
UID:CIRGET/144
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CIRGET/144/"
 >Morse theory on moduli spaces</a>\nby Changjie Chen (Université de Montr
 éal) as part of CRM - Séminaire du CIRGET / Géométrie et Topologie\n\n
 Lecture held in PK-5115.\nAbstract: TBA\n\nSarnak conjectured in the 1990s
  that the determinant of the Laplacian is a Morse function on the space of
  unit area Riemannian metrics on a given surface\, and hence induces a Mor
 se function on the moduli space of Riemann surfaces.\n\nIt is known that t
 he systole function\, defined as the length of a shortest closed geodesic 
 with respect to the base metric\, is topologically Morse on the moduli spa
 ce M_{g\,n}. However\, it does not generate a Morse theory.\n\nIn this tal
 k\, I will introduce a family of Morse functions\, defined as weighted exp
 onential averages of all geodesic-length functions\, on the Deligne-Mumfor
 d compactification (M_{g\,n} bar). These functions are compatible with the
  Deligne-Mumford stratification and the Weil-Petersson metric\, and their 
 critical points can be characterized by a combinatorial property.\n\nI wil
 l finally talk about homological consequences of hyperbolic geometry resul
 ts via Morse theory\, including a stability theorem. If time permits\, I w
 ill explain how these Morse functions connect to Sarnak’s conjecture.\n
LOCATION:https://researchseminars.org/talk/CIRGET/144/
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