### Groupe de Travail: Higher Algebra and Geometry

Wednesday 9-10:30 Am. Room 505, Building 15-25, Jussieu

Planning:

Sept 27: 1st Meeting

Oct 4: HH, HC, HN and circle actions: Classical vs fancy Part I (Marco) [ Notes]

Oct 11: Circle Actions and S^1-modules (Mauro) Attention: Akhil Mathew's talk at the 11Am seminar.

Oct 18: GDR topology

Oct 25: HH, HC, HN and circle actions: Classical vs fancy Part II (Marco)

Nov 8: HH, HC, HN and circle actions: Classical vs fancy Part III (Marco) Notes ]

Nov 15: Foundations of Spectra I: Category of Spectra (Jean-Michel) [ Notes]

Nov 22: Foundations of Spectra II: Smash product of spectra (Jean-Michel) [ Notes]

Nov 29: Tate construction (Geoffroy) [ Notes]

Dec 6: Break

Dec 13: Tate orbit Lemma I (Gregory) [6]

Dec 22: Tate orbit Lemma II (Gregory) [6]

Jan 3: Break

Jan 17: Cyclotomic Spectra and computations of TC^-(Fp) and TP(FP) (Matthew) [ Notes]

Jan 24 (Attention: Place: Paris 13, Time: 9AM, Room: B405): Equivariant Homotopy Theory and classical definitions of Cyclotomic Spectra (Denis)

Jan 31: Equivariant Homotopy Theory II: genuine cyclotomic spectra (Denis) Notes]

Feb 7: Scholze-Nikolaus equivalent definitions of Cyclotomic spectra. Comparison Theorem (Christian) [6]

Feb 14: THH as a cyclotomic spectrum (Yonatan)

Feb 21: Construction of THH
as a cyclotomic spectrum I (Yonatan)

Feb 28: Break

March 7: Construction of THH
as a cyclotomic spectrum II (Yonatan)

March 14: (Attention: Place: Paris 13, Time: 9AM, Room: C305)
Special Lecture - The Pullback square (B.I. Dundas)

March 21: Special Lecture II - The Pullback square (B.I. Dundas)

March 28:

- 9AM : Construction of THH
as a cyclotomic spectrum III (Yonatan)

- 10 AM: Bokstedt Computation of THH(Fp) I (Maxime)

April 4: Bokstedt Computation of THH(Fp) II (Maxime) [ Notes]

April 11: Schapira's Conference at IHP

April 18: Break

April 25: Frobenius and Steenrod operations (Gregory)

May 2: More on TC and p-adic computations (Matthew)

June 20 (Closure): (Matthew)

References:

[1] Loday, Cyclic Homology

[2] Weibel, Introduction to Homological Algebra

[3] Toen-Vezzosi Algebres simpliciales S^1-equivariantes et theorie de de Rham.

[4] Hoyois The fixed points of the circle action on Hochschild Homology

[5] J. Lurie Higher Algebra

[6] Scholze-Nikolaus On topological cyclic homology