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Tuesday Seminar on Topology
Seminar information archive ～05/22｜Next seminar｜Future seminars 05/23～
| Date, time & place | Tuesday 16:00 - 17:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | IKE Yuichi, KONNO Hokuto, SAKASAI Takuya |
2026/06/16
16:00-17:30 Room #hybrid/056 (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
