# Online Seminar: Francis Brown (All Souls College, Oxford University), Invariant differential forms, graph complexes, and Feynman integrals #### calendar\_today Date and Time **June 22, 2021** 10:00AM - 10:00AM EDT #### pin\_drop Location **Zoom** **Location:** Zoom **Time:** Tuesday, 10:00 AM (Eastern US), 15:00 (UK/Eire), 16:00 (Central Europe), 22:00 (China) **Title:** Invariant differential forms, graph complexes, and Feynman integrals **Abstract:** The commutative graph complex, defined by contracting edges in graphs, was introduced by Kontsevich in 1993. Recently, Chan-Galatius-Payne have shown that its cohomology can be identified with a piece of the cohomology of moduli spaces of curves, and Willwacher showed that graph cohomology in degree zero is related to the Grothendieck-Teichmuller Lie algebra. Nevertheless, the cohomology of the graph complex remains mysterious, and little is known explicitly. In this talk I will explain how to use invariant trace forms to construct differential forms on a moduli space of metric graphs. By integrating these forms, one can canonically assign integrals to graphs, which are very closely related to Feynman integrals in perturbative quantum field theory, but have the property that they always converge. A Stokes formula enables us to deduce some information about the cohomology of the graph complex, and leads to new predictions about its structure, and its relation to physics. **Additional Ways to Join** Join by telephone (use any number to dial in) +1 929 436 2866 +1 312 626 6799 +1 669 900 6833 400 669 9381 China Toll-free International numbers available: [https://harvar](https://harvard.zoom.us/u/aclg6kOggb)[d.zoom.us/u/aclg6kOggb](https://harvard.zoom.us/u/aclg6kOggb) One tap mobile: +19294362866,,779283357# US (New York) Join by SIP conference room system Meeting ID: 779 283 357 <779283357@zoomcrc.com> --- Attachments- [ picture\_as\_pdf 2021-06-22\_brown\_seminar.pdf ](/sites/g/files/omnuum6611/files/mathpicture/files/2021-06-22_brown_seminar.pdf) --- Share on:- [ Facebook ](#) - [ Twitter ](#) - [ Linkedin ](#) Save: [ Add to calendar calendar\_today ](https://mathpicture.fas.harvard.edu/node/1590344/event-feed.ics) Copy link link