The aim of the seminar is to present the theory of Poincaré categories, as well as their L-spectra and Grothendieck-Witt spectra and the relationship. The seminar will follow some sections of the paper series Hermitian K-theory of stable infinity-categories of Calmès-Dotto-Harpaz-Hebestreit-Land-Moi-Nardin-Nikolaus-Steimle, Arxiv: 2009.07223, 2009.0723, 2009.0724.

We will meet on Wednesdays at 4pm during term on MS teams. The talks would be informal, and questions and discussions are encouraged.

Here is an outline of the talks, which will be updated as the seminar progresses. If you would like to volunteer for a talk please get in touch.

Date	Talk	Speaker	Notes
Apr 28	Overview	Emanuele Dotto
May 5	Forms over rings, Witt and Grothendieck-Witt groups	Emanuele Dotto
May 12	Poincaré categories	Emanuele Dotto
May 19	Examples: Poincaré categories of Modules	Emanuele Dotto
May 26	Examples: Poincaré categories of parametrized spectra	Emanuele Dotto
June 2	Examples: Poincaré categories of chain complexes and periodicity	Emanuele Dotto
June 9	Metabolic objects and L-groups	Emanuele Dotto
June 16	L-spectra and bordism invariance	Julie Rasmusen
June 23	Grothendieck-Witt spectra and additivity	David Tintinago Pinzon	at 16:45
June 30	The fundamental Tate square	Emanuele Dotto