# Online: Seminar, Paul Fendley (Oxford University), Integrability and Braided Tensor Categories #### calendar\_today Date and Time **July 14, 2020** 10:00AM - 10:00AM EDT #### pin\_drop Location **Zoom** ![Paul Fendley](/sites/g/files/omnuum6611/files/styles/hwp_1_1__360x360_scale/public/mathpicture/files/paul_fendley.png?itok=TMe4W8O1) **Location:** Zoom [https://harvard.zoom.us/j/779283357 ](https://harvard.zoom.us/j/779283357%C2%A0) **Time:** Tuesday, July 14, 2020, 10:00 AM (Eastern US), 16:00 (Central Europe), 22:00 (China) **Title:** Integrability and Braided Tensor Categories **Abstract:** Many integrable critical classical statistical mechanical models and the corresponding quantum spin chains possess a fractional-spin conserved current. Such currents have been constructed by utilizing quantum-group algebras, fermionic and parafermionic operators, and ideas from "discrete holomorphicity". I define them generally and naturally using a braided tensor category, a topological structure familiar from the study of knot invariants, anyons and conformal field theory. I derive simple constraints on the Boltzmann weights necessary and sufficient for such a current to exist, generalizing those found using quantum-group algebras. I find many solutions, in both geometric and local models. In all cases, the resulting weights are those of an integrable lattice model, giving a linear construction for "Baxterizing", i.e. building a solution of the Yang-Baxter equation out of topological data. **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 +1 253 215 8782 +1 301 715 8592 +1 346 248 7799 +41 43 210 70 42 +41 43 210 71 08 +41 22 591 00 05 +41 22 591 01 56 +41 31 528 09 88 +31 20 794 6520 +31 20 794 7345 +31 20 241 0288 +31 20 794 0854 +31 20 794 6519 +65 3165 1065 +65 3158 7288 +33 1 7095 0350 +33 7 5678 4048 +33 1 7037 2246 +33 1 7037 9729 +33 1 7095 0103 +49 30 5679 5800 +49 695 050 2596 +49 69 7104 9922 +45 32 72 80 11 +45 89 88 37 88 +45 32 70 12 06 +45 32 71 31 57 +45 32 72 80 10 400 669 9381 China Toll-free 400 616 8835 China Toll-free 0 800 561 252 Switzerland Toll-free 0 800 002 622 Switzerland Toll-free 0 800 220 0040 Netherlands Toll-free 0 800 022 1954 Netherlands Toll-free 800 852 6054 Singapore Toll-free 800 101 3814 Singapore Toll-free 0 805 082 588 France Toll-free 0 800 940 415 France Toll-free 0 800 1800 150 Germany Toll-free 0 800 000 6954 Germany Toll-free 80 82 02 88 Denmark Toll-free 80 71 12 51 Denmark 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 Flyer ](/sites/g/files/omnuum6611/files/mathpicture/files/fendley_seminar_july_14_2020.pdf) --- Share on:- [ Facebook ](#) - [ Twitter ](#) - [ Linkedin ](#) Save: [ Add to calendar calendar\_today ](https://mathpicture.fas.harvard.edu/node/1517010/event-feed.ics) Copy link link