Winter Term 2020/2021

Prof. Dr. Holger Reich - Prof. Dr. Elmar Vogt - Dr. Gabriel Angelini-Knoll

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• Time and place: Monday,  2pm -- 4pm, online

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Content: Talks by masters and Phd students about ongoing work and selected research topics as well as guest talks.

This winter term our selected research topic will cover the field of
Higher Symmetry
The theory of higher categories provides new perspectives on problems in homotopy theory and homological algebra. Notably, it has been used to resolve several open conjectures in algebraic K-theory. The use of higher categories to study problems in equivariant homotopy theory is relatively new, but it has already led to some important advances such as work of Clausen-Mathew-Naumann-Noel on the Ausoni-Rognes red-shift conjectures, Nikolaus-Scholze and Quigley-Shah on cyclotomic spectra, and work of Calmes et al. on algebraic surgery theory. The goal of this research seminar is to build the necessary foundations in equivariant higher algebra with an eye towards descent in algebraic K-theory, cyclotomic spectra, and algebraic surgery theory.  

Schedule

Date	Title	Speaker
15.09.	THR of group rings	Vincent Boelens
22.09.	TC for group rings of cyclic groups	Vincent Boelens
Thur.01.10. at 2pm sharp	THR, Witt vectors, and norms	Gabriel Angelini-Knoll
	guest talk:
06.10. at 3pm	Finitely F-amenable actions and decomposition complexity of groups	David Rosenthal St. John's Univ.
	two guest talks:
27.10.	Chromatic localisations of algebraic K-theory	Markus Land Univ. of Copenhagen
28.10.	Hermitian K-theory for stable infinity-categories	Markus Land Univ. of Copenhagen
02.11.	preliminary discussion	Gabriel Angelini-Knoll
09.11.	Restriction as base change	Gabriel Angelini-Knoll
	guest talk:
16.11. at 3:30pm	Real cyclotomic spectra	J.D. Quigley (Cornell U.)
23.11.	Family of subgroups and geometric fixed points	Georg Lehner
30.11.	Borel equivariant spectra	Daniel Krupa
07.12.	High cohomology of arithmetic groups	Peter Patzt
14.12.	no talk
2021
04.01.	Parametrized higher categories	Gabriel Angelini-Knoll
11.01.	Lower Algebraic K-theory of finite Groups	Georg Lehner
18.01.	Spectra over finite groupoids	Alexander Müller
25.01.	Spectra over finite groupoids continued	Alexander Müller
01.02.	The map  K0 ZG --> K0 QG  for infinite groups	Georg Lehner
08.02.	cancelled
15.02.	Families and Recollements	Georg Lehner
02.03.	The geometric locus theorem	Vincent Boelens

Literature

• Clausen, D.; Mathew, A.; Naumann, N. and Noel, J.: Descent in algebraic  K -theory and a conjecture of Ausoni–Rognes
• Quigley, J.D. and Shah, J.: On the parametrized Tate construction and two theories of real p-cyclotomic spectra
• Calmès, B. et.al.: Hermitian K-theory for stable ∞-categories III: Grothendieck-Witt groups of rings