Planned seminars

Europe/Lisbon Unusual schedule

Cris Negron
, University of Southern California

I will discuss joint work with Agustina Czenky. We introduce a $(3-ε)$-dimensional TQFTs which is generated, in some sense, by the derived category of quantum group representations. This TQFT is valued in the $∞$-category of dg vector spaces, and the value on a genus $g$ surface is a $g$-th iterate of the Hochschild cohomology for the aforementioned category. I will explain how this TQFT arises as a derived variant of the usual Reshetikhin–Turaev theory and, if time allows, I will discuss the possibility of introducing local systems into the theory. Our interest in local systems comes from proposed relationships with 4-dimensional non-topological QFT.

Please note that the normative time for the seminar will be 5 PM in Lisbon until 14 September.

Europe/Lisbon Unusual schedule

Joshua Sussan
, Medgar Evers College, The City University of New York

We construct an action of sl(2) on equivariant Khovanov–Rozansky link homology. We will discuss some topological applications and show how the construction simplifies in characteristic p. This is joint with You Qi, Louis-Hadrien Robert, and Emmanuel Wagner.

Please note that the normative time for the seminar will be 5 PM in Lisbon until 14 September.

Europe/Lisbon

Rhea Palak Bakshi
, University of California, Santa Barbara

To be announced

Europe/Lisbon

Harshit Yadav
, University of Alberta

To be announced

Europe/Lisbon

Aaron Lauda
, University of Southern California

Since the foundational work of Freedman, Kitaev, Larsen, and Wang, it has been understood that 3-dimensional topological quantum field theories (TQFTs), described via modular tensor categories, provide a universal model for fault-tolerant topological quantum computation. These TQFTs, derived from quantum groups at roots of unity, achieve modularity by semisimplifying their representation categories—discarding objects with quantum trace zero. The resulting semisimple categories describe anyons whose braiding enables robust quantum computation.

This talk explores recent advances in low-dimensional topology, focusing on the use of nonsemisimple categories that retain quantum trace zero objects to construct new TQFTs. These nonsemisimple TQFTs surpass their semisimple counterparts, distinguishing topological features inaccessible to the latter. For physical applications, unitarity is essential, ensuring Hom spaces form Hilbert spaces. We present joint work with Nathan Geer, Bertrand Patureau-Mirand, and Joshua Sussan, where nonsemisimple TQFTs are equipped with a Hermitian structure. This framework introduces Hilbert spaces with possibly indefinite metrics, presenting new challenges.

We further discuss collaborative work with Sung Kim, Filippo Iulianelli, and Sussan, demonstrating that nonsemisimple TQFTs enable universal quantum computation at roots of unity where semisimple theories fail. Specifically, we show how Ising anyons within this framework achieve universality through braiding alone. The resulting braiding operations are deeply connected to the Lawrence–Krammer–Bigelow representations, with the Hermitian structure providing a nondegenerate inner product grounded in quantum algebra.

Europe/Lisbon

Julia Plavnik
, Indiana University

To be announced

Europe/Lisbon

Jack Romö
, University of Leeds

To be announced