Seminars in Geometry/Topology
The usual time for the Geometry and Topology Seminar is TBD.
Get in touch with Clover or Fernando if you would like to be added to the mailing list, give a talk yourself, or have someone in mind that you would like to invite.
Topology Seminar Wednesday 28th May, 11:00-12:00, 656 Simaestuen, Sentralbygg 2
Walker Stern (TU München): A Braided Monoidal Hecke Category
Abstract: Hecke algebras occupy a key position in low-dimensional topology and representation theory, as they govern a broad class of quantum knot invariants. Of particular use, a simulatenous categorification of several Hecke algebras carries a braided monoidal structure induced by a kind of convolution. In this talk,I will present work in progress with Jonte Gödicke, Quoc Ho, and Yang Hu, in which we show that this braided monoidal structure arises naturally as a linearization a far richer structure: lax E_2 algebra in an $(\infty,2)$-category of spans. This lax E_2 algebra can be accessed relatively simply, using the combinatorics of flags and a classification of algebras in spans. Moreover, various linearizations retrieve not only the Hecke algebras, but also the braided monoidal $(\infty,2)$-category of Soergel bimodules recently constructed using obstruction-theoretic techniques.
Angus Rush (University of Hamburg): An (∞,2)-category of lax matrices
Abstract: Recently, a calculus of matrices between lax functors has become a useful calculational tool, for example in the categorified homological algebra program of Dyckerhoff et al. In this talk, I will describe an (∞,2)-category whose composition encodes lax matrix multiplication as defined by Christ–Dyckerhoff–Walde, and describe some applications mimicking the truncated case.
Topology Seminar Monday 10th February, 13:15-14:15, 656 Simaestuen, Sentralbygg 2
Thomas Blom (MPI Bonn): Cofree fibrations and endomorphism objects
Abstract: Cocartesian fibrations are one of the most important tools in higher category. They can be thought of as functors between ∞-categories that admit a notion of "transport" between the fibers, and they feature in Lurie's famous straightening-unstraightening equivalence.
A useful construction that has many applications is to "freely adjoin cocartesian lifts" to a functor. Not so well-known is that there also exists a dual construction: one can "cofreely adjoin cocartesian lifts" to a functor.
I will describe this dual construction and give various applications. In particular, I will show how it allows one to simplify and generalize Lurie's Day convolution construction and his construction of endomorphism objects in ∞-categories.
Fall 2024 - Upcoming Talks
Topology Seminar Thursday 26 September, 13:15-14:15, 822 Møterom, Sentralbygg 2
Tasos Moulinos (Université Paris 13): The synthetic Hilbert additive group
Abstract: The Hilbert additive group scheme arises in algebraic geometry as the "unipotent completion" of the integers over Spec(Z). At the level of functions, it carries a canonical filtration compatible with the group structure. This is intimately related to the HKR filtration on Hochschild homology.
I will briefly review the above story and then discuss ongoing work (joint with Alice Hedenlund) on lifting the Hilbert additive group, together with its filtration on functions, to the setting of spectral algebraic geometry. This crucially uses the yoga of even filtrations, introduced by Hahn-Raksit-Wilson.