We have an online seminar on "Theoretical studies of topological phases of matter", which is a research subject in the CREST program "Creation of Core Technology based on the Topological Materials Science for Innovative Devices" of Japan Science and Technology Agency. This is supported by the CREST Grant (Number: JPMJCR19T2) held by Yasuyuki Kawahigashi (the University of Tokyo) together with Akira Furusaki (RIKEN) and Masatoshi Sato (Yukawa Institute for Theoretical Physics, Kyoto University). The aim of this seminar is to foster interactions between mathematicians and physicists and promote joint research among the CREST group members. We plan to have one talk every month approximately.

Some talks are public and open to everyone, and others are for our CREST group members only.

- Speaker:
**Yuto Moriwaki**(RIKEN) - Title: Bootstrap hypothesis in two-dimension and the operad structure on moduli spaces
- Date/Time: 16:00-17:30, Friday, June 9, 2023
- Abstract: Conformal field theory is believed to be consistent (well-defined) if it satisfies the bootstrap equation. This claim is called the bootstrap hypothesis and is used, for example, in the numerical calculation of critical exponents for the 3-D Ising model. In this talk, we will formulate the bootstrap hypothesis mathematically in the two-dimensional case and give a proof under certain conditions. The consistency of 2d conformal field theory comes down to the representation theory of chiral conformal field theory (vertex operator algebra), and the important step in the proof is to show that the operad of the moduli spaces of punctured Riemann spheres acts topologically on the representation category of the vertex operator algebra. From this point of view, the bootstrap equation is a generator of a certain groupoid operad, and the consistency follows. This result is inspired by Huang-Kong's full field algebra, but we believe that our approach makes their result more conceptually comprehensible.

The talk will be online with Zoom. The Zoom link will be sent by e-mail to those who have registered on the above form. If you have any inquiry, please contact Kawahigashi (yasuyuki@ms.u-tokyo.ac.jp).