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Tuesday Seminar on Topology
Seminar information archive ～12/01｜Next seminar｜Future seminars 12/02～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | HABIRO Kazuo, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
Future seminars
2025/12/02
17:30-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Shinpei Baba (University of Osaka)
Bending Teichmüller spaces and character varieties (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Shinpei Baba (University of Osaka)
Bending Teichmüller spaces and character varieties (JAPANESE)
[ Abstract ]
Let S be a closed oriented surface of genus at least two. The Teichmüller space of S can be regarded as the space of discrete faithful representations from the fundamental group of S into PSL(2, R). Given a simple closed curve on S with positive weight (or more generally, a measured lamination), we can "bend" the repsentation along the curve by an angle equal to the weight, and obtain a representation of the surface group into PSL(2, C). This bending deformation induces a mapping from the Teichmüller space into the space of representations of the surface group into PSL(2, C). We discuss some interesting properties of this mapping.
If time permits, we also discuss a complexification of this mapping.
[ Reference URL ]Let S be a closed oriented surface of genus at least two. The Teichmüller space of S can be regarded as the space of discrete faithful representations from the fundamental group of S into PSL(2, R). Given a simple closed curve on S with positive weight (or more generally, a measured lamination), we can "bend" the repsentation along the curve by an angle equal to the weight, and obtain a representation of the surface group into PSL(2, C). This bending deformation induces a mapping from the Teichmüller space into the space of representations of the surface group into PSL(2, C). We discuss some interesting properties of this mapping.
If time permits, we also discuss a complexification of this mapping.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/12/09
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Yusuke Kuno (Tsuda University)
Emergent version of Drinfeld's associator equations (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Yusuke Kuno (Tsuda University)
Emergent version of Drinfeld's associator equations (JAPANESE)
[ Abstract ]
In 2012, Alekseev and Torossian proved that any solution of Drinfeld's associator equations gives rise to a solution of the Kashiwara-Vergne equations. Both equations arise in natural topological contexts. For the former, these are knots and braids in 3-space, and for the latter there are at least two contexts: one is the w-foams, a certain Reidemeister theory of singular surfaces in 4-space, and the other is the Goldman-Turaev loop operations on oriented 2-manifolds. With the hope of getting a better understanding of the relations among these topological objects, we introduce the concept of emergent braids, a low-degree Vassiliev quotient of braids over a punctured disk. Then we discuss a work in progress on the associated formality equations, the emergent version of Drinfeld's associator equations. This talk is partially based on a joint work with D. Bar-Natan, Z, Dancso, T. Hogan and D. Lin.
[ Reference URL ]In 2012, Alekseev and Torossian proved that any solution of Drinfeld's associator equations gives rise to a solution of the Kashiwara-Vergne equations. Both equations arise in natural topological contexts. For the former, these are knots and braids in 3-space, and for the latter there are at least two contexts: one is the w-foams, a certain Reidemeister theory of singular surfaces in 4-space, and the other is the Goldman-Turaev loop operations on oriented 2-manifolds. With the hope of getting a better understanding of the relations among these topological objects, we introduce the concept of emergent braids, a low-degree Vassiliev quotient of braids over a punctured disk. Then we discuss a work in progress on the associated formality equations, the emergent version of Drinfeld's associator equations. This talk is partially based on a joint work with D. Bar-Natan, Z, Dancso, T. Hogan and D. Lin.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/12/16
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Tomoshige Yukita (Ashikaga University)
Continuity and minimality of growth rates of Coxeter systems (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Tomoshige Yukita (Ashikaga University)
Continuity and minimality of growth rates of Coxeter systems (JAPANESE)
[ Abstract ]
A pair (G, S) consisting of a group G and an ordered finite generating set S is called a marked group. On the set of all marked groups, one can define a distance that measures how similar the neighborhoods of the identity element in their Cayley graphs are. This space is called the space of marked groups. For a marked group, the function that counts the number of elements whose word length with respect to S is k is called the growth function, and the quantity describing its rate of divergence is called the growth rate. In this talk, we will discuss the continuity of the growth rate for marked Coxeter systems, and the problem of determining the minimal growth rate among Coxeter systems that are lattices in the isometry group of hyperbolic space.
[ Reference URL ]A pair (G, S) consisting of a group G and an ordered finite generating set S is called a marked group. On the set of all marked groups, one can define a distance that measures how similar the neighborhoods of the identity element in their Cayley graphs are. This space is called the space of marked groups. For a marked group, the function that counts the number of elements whose word length with respect to S is k is called the growth function, and the quantity describing its rate of divergence is called the growth rate. In this talk, we will discuss the continuity of the growth rate for marked Coxeter systems, and the problem of determining the minimal growth rate among Coxeter systems that are lattices in the isometry group of hyperbolic space.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
