As part of the internal seminar schedule for Stochastic Analysis for this coming term, DPhil students have been invited to present on their works to date. Student talks are 20 minutes, which includes question and answer time. 

Students presenting are:

Adrian Martini, supervisor Alison Ethridge

Fang Rui Lim, supervisor Rama Cont

Thomas Groves, supervisor Dmitry Beylaev

Sarah-Jean Meyer, supervisor Massimiliano Gubinelli

One can think of the stabilisation of an ∞-category as the ∞-category of objects that admit infinite deloopings. For example, the ∞-category of spectra is the stabilisation of the ∞-category of homotopy types. Costabilisation is the opposite notion of stabilisation, where we are interested in objects that allow infinite desuspensions. It is easy to see that the costabilisation of the ∞-category of homotopy types is trivial. Fix a prime number p. In this talk I will show that the costablisation of the ∞-category of T(h)-local spectral Lie algebras is equivalent to the ∞-category of T(h)-local spectra, where T(h) denotes a p-local telescope spectrum of height h. A key ingredient of the proof is to relate spectral Lie algebras to (spectral) Eₙ algebras via Koszul duality.
 

We will kick off the start of the academic year and the Junior Algebra and Representation Theory seminar (JART) with a fun social event in the common room. Come catch up with your fellow students about what happened over the summer, meet the new students and play some board games. We'll go for lunch together afterwards.