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Tuesday Seminar on Topology
Seminar information archive ～04/30｜Next seminar｜Future seminars 05/01～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2024/02/13
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Paul Norbury (The University of Melbourne)
Measures on the moduli space of curves and super volumes (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Paul Norbury (The University of Melbourne)
Measures on the moduli space of curves and super volumes (ENGLISH)
[ Abstract ]
In this lecture I will define a family of finite measures on the moduli space of smooth curves with marked points. The measures are defined via a construction analogous to that of the Weil-Petersson metric using the extra data of a spin structure. In fact, the measures arise naturally out of the super Weil-Petersson metric defined over the moduli space of super curves. The total measure can be identified with the volume of the moduli space of super curves. It can be calculated in many examples, and conjecturally satisfies a recursion analogous to Mirzakhani's recursion relations between Weil-Petersson volumes of moduli spaces of hyperbolic surfaces. This conjecture has been verified in many cases, including the so-called Neveu-Schwarz case where it coincides with the recursion of Stanford and Witten. The general case produces deformations of the Neveu-Schwarz volume polynomials, satisfying the same Mirzakhani-like recursion relations.
[ Reference URL ]In this lecture I will define a family of finite measures on the moduli space of smooth curves with marked points. The measures are defined via a construction analogous to that of the Weil-Petersson metric using the extra data of a spin structure. In fact, the measures arise naturally out of the super Weil-Petersson metric defined over the moduli space of super curves. The total measure can be identified with the volume of the moduli space of super curves. It can be calculated in many examples, and conjecturally satisfies a recursion analogous to Mirzakhani's recursion relations between Weil-Petersson volumes of moduli spaces of hyperbolic surfaces. This conjecture has been verified in many cases, including the so-called Neveu-Schwarz case where it coincides with the recursion of Stanford and Witten. The general case produces deformations of the Neveu-Schwarz volume polynomials, satisfying the same Mirzakhani-like recursion relations.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
