トポロジー火曜セミナー

過去の記録 ~03/28次回の予定今後の予定 03/29~

開催情報 火曜日 17:00~18:30 数理科学研究科棟(駒場) 056号室
担当者 河澄 響矢, 北山 貴裕, 逆井卓也
セミナーURL http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html

2019年07月09日(火)

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
Florent Schaffhauser 氏 (Université de Strasbourg)
Mod 2 cohomology of moduli stacks of real vector bundles (ENGLISH)
[ 講演概要 ]
The rational cohomology ring of the moduli stack of holomorphic vector bundles of fixed rank and degree over a compact Riemann surface was studied by Atiyah and Bott using tools of differential geometry and algebraic topology: they found generators of that ring and computed its Poincaré series. In joint work with Chiu-Chu Melissa Liu, we study in a similar way the mod 2 cohomology ring of the moduli stack of real vector bundles of fixed topological type over a compact Riemann surface with real structure. The goal of the talk is to explain the principle of that computation, emphasizing the analogies and differences between the real and complex cases, and discuss applications of the method. In particular, we provide explicit generators of mod 2 cohomology rings of moduli stacks of vector bundles over a real algebraic curve.