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過去の記録 ～03/27｜本日 03/28 | 今後の予定 03/29～
2020年04月07日(火)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) 056号室
５月以降に延期
今野 北斗 氏 (理化学研究所 数理創造プログラム)
Gauge theory and the diffeomorphism and homeomorphism groups of 4-manifolds (JAPANESE)
５月以降に延期
今野 北斗 氏 (理化学研究所 数理創造プログラム)
Gauge theory and the diffeomorphism and homeomorphism groups of 4-manifolds (JAPANESE)
[ 講演概要 ]
I will explain my recent collaboration with several groups that develops gauge theory for families
to extract difference between the diffeomorphism groups and the homeomorphism groups of 4-manifolds.
After Donaldson’s celebrated diagonalization theorem, gauge theory has given strong constraints on the topology of smooth 4-manifolds. Combining such constraints with Freedman’s theory, one may find many non-smoothable topological 4-manifolds.
Recently, a family version of this argument was started by T. Kato, N. Nakamura and myself, and soon later it was developed also by D. Baraglia and his collaborating work with myself. More precisely, considering gauge theory for smooth fiber bundles of 4-manifolds, they obtained some constraints on the topology of smooth 4-manifold bundles. Using such constraints, they detected non-smoothable topological fiber bundles of smooth 4-manifolds. The existence of such bundles implies that there is homotopical difference between the diffeomorphism and homeomorphism groups of the 4-manifolds given as the fibers.
If time permits, I will also mention my collaboration with Baraglia which shows that a K3 surface gives a counterexample to the Nielsen realization problem in dimension 4. This example reveals also that there is difference between the Nielsen realization problems asked in the smooth category and the topological category.
I will explain my recent collaboration with several groups that develops gauge theory for families
to extract difference between the diffeomorphism groups and the homeomorphism groups of 4-manifolds.
After Donaldson’s celebrated diagonalization theorem, gauge theory has given strong constraints on the topology of smooth 4-manifolds. Combining such constraints with Freedman’s theory, one may find many non-smoothable topological 4-manifolds.
Recently, a family version of this argument was started by T. Kato, N. Nakamura and myself, and soon later it was developed also by D. Baraglia and his collaborating work with myself. More precisely, considering gauge theory for smooth fiber bundles of 4-manifolds, they obtained some constraints on the topology of smooth 4-manifold bundles. Using such constraints, they detected non-smoothable topological fiber bundles of smooth 4-manifolds. The existence of such bundles implies that there is homotopical difference between the diffeomorphism and homeomorphism groups of the 4-manifolds given as the fibers.
If time permits, I will also mention my collaboration with Baraglia which shows that a K3 surface gives a counterexample to the Nielsen realization problem in dimension 4. This example reveals also that there is difference between the Nielsen realization problems asked in the smooth category and the topological category.
2020年04月14日(火)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) 056号室
５月以降に延期
Daniel Matei 氏 (IMAR Bucharest)
Homology of right-angled Artin kernels (ENGLISH)
５月以降に延期
Daniel Matei 氏 (IMAR Bucharest)
Homology of right-angled Artin kernels (ENGLISH)
[ 講演概要 ]
The right-angled Artin groups $A(G)$ are the finitely presented groups associated to a finite simplicial graph $G=(V,E)$, which are generated by the vertices $V$ satisfying commutator relations $vw=wv$ for every edge $vw$ in $E$. An Artin kernel $N_h(G)$ is defined by an epimorphism $h$ of $A(G )$ onto the integers. In this talk, we discuss the module structure over the Laurent polynomial ring of the homology groups of $N_h(G)$.
The right-angled Artin groups $A(G)$ are the finitely presented groups associated to a finite simplicial graph $G=(V,E)$, which are generated by the vertices $V$ satisfying commutator relations $vw=wv$ for every edge $vw$ in $E$. An Artin kernel $N_h(G)$ is defined by an epimorphism $h$ of $A(G )$ onto the integers. In this talk, we discuss the module structure over the Laurent polynomial ring of the homology groups of $N_h(G)$.
2020年05月07日(木)
情報数学セミナー
16:50-18:35 数理科学研究科棟(駒場) 126号室
藤原 洋 氏 (株式会社ブロードバンドタワー)
AIと量子計算を主題とする新たな数理科学とは？ (Japanese)
藤原 洋 氏 (株式会社ブロードバンドタワー)
AIと量子計算を主題とする新たな数理科学とは？ (Japanese)
[ 講演概要 ]
（新型コロナウイルス対策として４月は休講にし、
５月７日（木）からセミナーを開始する予定ですが、
詳細は追ってお知らせします。）
（新型コロナウイルス対策として４月は休講にし、
５月７日（木）からセミナーを開始する予定ですが、
詳細は追ってお知らせします。）
