[Turkmath:5469] Zoom-details::Feza Gursey Center for Physics and Mathematics-Higher Structures Seminars [no.5]: Berkan Uze (Boğaziçi University)

[kazimilhan.ikeda]

Feza Gürsey Center for Physics and Mathematics Higher Structures Seminar 
on 08.03.2022
(We salute all mothers, we salute all the hard working women of labour, 
of Arts and of STEM...)

Speaker: Berkan Üze (Boğaziçi University, Istanbul)

Title: "A Glimpse of Noncommutative Motives"

Date: 08 03 2022, Tuesday at 14:30 Istanbul local time.

Location: Zoom (details below)

Title: "A Glimpse of Noncommutative Motives"
Speaker: Berkan Üze (Boğaziçi University, Istanbul)
Abstract:  The theory of motives was conceived as a universal cohomology 
theory for algebraic varieties. Today it is a vast subject 
systematically developed in many directions spanning algebraic geometry, 
arithmetic geometry, homotopy theory and higher category theory. 
Following ideas of Kontsevich, Tabuada and Robalo independently 
developed a theory of “noncommutative” motives for DG-categories (such  
as enhanced derived categories of schemes) which encompasses the 
classical theory of motives and helps assemble so-called additive 
invariants such as Algebraic K-Theory, Hochschild Homology and 
Topological Cyclic Homology into a motivic formalism in a very precise 
sense of the word. We will review the fundamental concepts at work, 
which will inevitably involve a foray into the formalism of enhanced and 
higher categories.We will then discuss Kontsevich’s notion of a 
noncommutative space and introduce noncommutative motives as “universal 
additive invariants” of noncommutative spaces. We will conclude by 
offering a brief sketch of Robalo’s construction of the noncommutative 
stable homotopy category, which is directly in the spirit of Voevodsky’s 
original construction. This talk contains no original work and is 
intended as an expository recapitulation.

Zoom invitation:
Kazim Ilhan Ikeda is inviting you to a scheduled Zoom meeting.

Topic: Seminar for M.Sc students and beyond (08 March::Berkan Üze)

Time: 08 March 2022 Tuesday at 14:30 Istanbul local time

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