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Tuesday Seminar on Topology
Seminar information archive ～06/11｜Next seminar｜Future seminars 06/12～
| Date, time & place | Tuesday 16:00 - 17:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | IKE Yuichi, KONNO Hokuto, SAKASAI Takuya |
Future seminars
2026/06/16
16:00-17:30 Room #hybrid/128 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Yuto Moriwaki (RIKEN iTHEMS)
Conformally flat factorization homology (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Yuto Moriwaki (RIKEN iTHEMS)
Conformally flat factorization homology (JAPANESE)
[ Abstract ]
This talk presents conformally flat factorization homology, introduced as a conformal Riemannian analogue of Lurie's factorization homology. Ordinary factorization homology takes a d-disk algebra as input and produces invariants of d-dimensional manifolds that are independent of the choice of metric. In contrast, conformally flat factorization homology takes as input a conformally flat d-disk algebra, which is an algebra over the operad formed by conformal open embeddings of disks, and constructs, via its left Kan extension, metric-dependent invariants of conformally flat Riemannian manifolds.
This theory provides a framework connecting representations of local conformal transformations with Riemannian geometric invariants, and describes the local structure of d-dimensional conformal field theory. The talk will also discuss concrete examples constructed using Bergman spaces and Grunsky operators in dimension two, and using unitary representations of SO+(d,1) in dimensions three and higher.
This talk is based on arXiv:2602.08729 and arXiv:2603.06491.
[ Reference URL ]This talk presents conformally flat factorization homology, introduced as a conformal Riemannian analogue of Lurie's factorization homology. Ordinary factorization homology takes a d-disk algebra as input and produces invariants of d-dimensional manifolds that are independent of the choice of metric. In contrast, conformally flat factorization homology takes as input a conformally flat d-disk algebra, which is an algebra over the operad formed by conformal open embeddings of disks, and constructs, via its left Kan extension, metric-dependent invariants of conformally flat Riemannian manifolds.
This theory provides a framework connecting representations of local conformal transformations with Riemannian geometric invariants, and describes the local structure of d-dimensional conformal field theory. The talk will also discuss concrete examples constructed using Bergman spaces and Grunsky operators in dimension two, and using unitary representations of SO+(d,1) in dimensions three and higher.
This talk is based on arXiv:2602.08729 and arXiv:2603.06491.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026/06/23
16:00-17:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Andrei Pajitnov (Université de Nantes)
Morse-Novikov theory for links (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Andrei Pajitnov (Université de Nantes)
Morse-Novikov theory for links (ENGLISH)
[ Abstract ]
Let M be a compact manifold with a non-empty boundary N, and x an element of the first cohomology group of M. We assume that the restriction of x to N can be represented by a fibration over a circle. The Morse-Novikov number MN(M,x) is the minimal possible number of critical points of a Morse map f of M to a circle, such that [f]=x, and the restriction of f to N is a fibration over the circle. In this talk we present our results about the Morse-Novikov numbers for the exteriors of links in 3-sphere. This is joint work with L. Chen and H. Endo.
[ Reference URL ]Let M be a compact manifold with a non-empty boundary N, and x an element of the first cohomology group of M. We assume that the restriction of x to N can be represented by a fibration over a circle. The Morse-Novikov number MN(M,x) is the minimal possible number of critical points of a Morse map f of M to a circle, such that [f]=x, and the restriction of f to N is a fibration over the circle. In this talk we present our results about the Morse-Novikov numbers for the exteriors of links in 3-sphere. This is joint work with L. Chen and H. Endo.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
