4月26日 (金) 16:00-17:00
Kang Zuo 氏 (Wuhan University)
"p-adic Simpson correspondence, motivic Higgs bundles and Katz convolution"
| Speaker: | Kang Zuo 氏 (Wuhan University) |
| Title: | "p-adic Simpson correspondence, motivic Higgs bundles and Katz convolution" |
| Abstract: | I shall explain our recent work, jointly with Jinbang Yang, on constructing rank-2 motivic local systems on 4-punctures projective line over complex numbers. The proof relies on non-abelian p-adic Hodge theory, p-adic Simpson correspondence for periodic Higgs bundles, Deligne's p to \ell companions, Yu's work on numerical characteristic p Simpson correspondence, Drinfeld's work on Langlands correspondence for rank-2 \ell-adic local systems with cusps and Grothendieck-Messing-Kato deformation theorem for log abelian schemes. It is remarkable that recently Lam-Litt provided a totally different approach to the above results using Katz middle convolution. |
| 開催方法: | ハイブリッド形式 (九州大学伊都キャンパス ウエスト 1号館 5階 C-513 中講義室, およびZoom ミーティングによるオンライン開催) |
| Speaker: | 埴原 紀宏 氏 (九州大学) |
| Title: | Cohen-Macaulay representations in triangulated categories |
| Abstract: | Representation theory of algebras aims at understanding various categories associated with a given ring. Rings we are interested in are, for example, finite dimensional algebras over fields and commutative Cohen-Macaulay rings. In this talk, I would like to talk about representation theory of these rings, especially in triangulated categories such as derived categories, singularity categories, cluster cagtegories, and their differential graded enhancements. We will present some results which connects the representation theories of finite dimensional algebras and commutative rings through these triangulated categories. |
| 開催方法: | ハイブリッド形式 (九州大学伊都キャンパス ウエスト 1号館 5階 C-513 中講義室, およびZoom ミーティングによるオンライン開催) |
| Speaker: | 馬 昭平 氏 (東京工業大学) |
| Title: | "Mixed Hodge structures of locally symmetric varieties" |
| Abstract: | I will talk about the mixed Hodge structures on the cohomology of locally symmetric varieties. In the middle degree, I relate the weight filtration to the Siegel operators for certain modular forms. This has application to a classical problem on the Siegel operators. In the general degrees, I construct a spectral sequence which converges to the edge components in the Hodge triangle, and whose E1 page is expressed by some simple geometric invariants associated to the cusps. This already degenerates at E1 in a certain range. MHS approach also has application to the restriction map to the Borel-Serre boundary. |
| 開催方法: | ハイブリッド形式 (九州大学伊都キャンパス ウエスト 1号館 5階 C-513 中講義室, およびZoom ミーティングによるオンライン開催) |
| Speaker: | Christopher Deninger 氏 (University of Münster) |
| Title: | "Hasse Weil zeta functions as dynamical zeta functions" |
| Abstract: | For any system of diophantine equations or more generally for any separated scheme X of finite type over the integers, there is a zeta function originating from the works of Hasse and Weil. The Riemann zeta funtion is a special case. On the other hand, Ruelle introduced a zeta function for certain dynamical systems where the role of the primes is played by the periodic orbits. In the talk we explain the construction of a dynamical system whose Ruelle zeta function is the Hasse Weil zeta function of X. |
| 開催方法: | ハイブリッド形式 (九州大学伊都キャンパス ウエスト 1号館 4階 D-413 オーディトリアム, およびZoom ミーティングによるオンライン開催) |
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