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AGSeminar Summer 2020
 Do 1214 online on Zoom
No  Date  Title / Abstract  Speaker 

1  07.05  Local LefschetzVerdier traces  Benedikt Preis 
2  14.05.  VerdierLurie duality  Marco Volpe 
3  21.05.  Holiday  
4  28.05.  Relative Atiyah duality  Marco Volpe 
5  04.06.  The tangent complex of Ktheory  Benjamin Hennion, University ParisSaclay 
5  11.06.  Holiday  
6  18.06.  Motivic rational homotopy types  Isamu Iwanari, Tohoku University 
7  25.06.  Local structure of algebraic stacks and applications  David Rydh, Royal Institute of Technology (KTH) 
8  02.07.  A cubical model of (∞,1)categories  Christian Sattler, Chalmers University of Technology 
9  09.07.  A cubical model for weak ωcategories  Yuki Maehara, Macquarie University 
10  16.07.  Microlocal sheaf categories and the Jhomomorphism (time change: 14:3016:00)  Xin Jin, Boston College 
11  23.07.  Dimensional reduction for (1)–shifted cotangent stacks  Tasuki Kinjo, University of Tokyo 
12  30.07.  Neeman Duality for stable ∞categories (time change: 13:1514:45)  Paul Bärnreuther 
13  06.08.  Nisnevich Descent for Algebraic Ktheory  Sebastian Wolf 
AGSeminar Winter 2019/20
 Do 1214 MA009
No  Date  Title / Abstract  Speaker 

1  17.10  Left exact infinity categories and injectivity of assembly maps

Ulrich Bunke 
2  24.10  Cartesian modules over representations of small categories
Abstract: We introduce the concept of cartesian module over a pseudofunctor R from a small category to the category of small preadditive categories. Already the case when R is a (strict) functor taking values in the category of commutative rings is sufficient to cover the classical construction of quasicoherent sheaves of modules over a scheme. On the other hand, our general setting allows for a good theory of contravariant additive locally flat functors, providing a geometrically meaningful extension of a classical Representation Theorem of Makkai and Paré. As an application, we relate and extend some previous constructions of the pure derived category of a scheme. 
Simone Virili
(G. Raptis) 
3  31.10  The intrinsic normal cone for Artin stacks
Abstract: We extend the construction of the normal cone of a closed embedding of schemes to any locally of finite type morphism of higher Artin stacks and show that in the DeligneMumford case our construction recovers the relative intrinsic normal cone of Behrend and Fantechi. We characterize our extension as the unique one satisfying a short list of axioms, and use it to construct the deformation to the normal cone. As an application of our methods, we associate to any morphism of Artin stacks equipped with a choice of a global perfect obstruction theory a relative virtual fundamental class in the Chow group of Kresch. 
Dhyan Aranha
and Piotr Pstrągowski (A. Khan) 
4  7.11  Localization theorems in derived rigid analytic geometry
In the seminal joint work of ThomasonTrobaugh, the authors proved an important localization theorem for perfect complexes on schemes. The latter can be thought as an excision statement for dgcategories of perfect complexes on schemes. In this talk, we propose an alternative proof which has the advantage that works in the (derived) rigid analytic setting. More precisely, let k denote a nonarchimedean field of rank 1 valuation and, O_k its ring of integers. Given a (derived) O_kadic scheme X and X^rig its rigidification, we prove that the canonical functor Perf(X) > Perf(X^rig) is a Verdier localization of idempotent complete stable \inftycategories. If time permits, we will also mention some applications of our results. This is a joint work with Mauro Porta and Gabriele Vezzosi. 
Jorge António
(D.C. Cisinski) 
5  14.11  Group actions on moduli spaces
For a complete complex variety X with a C^*action we may subdivide the points of X according to where their C^*orbit converges at infty; the result is a BialynickiBirula decomposition. I will describe a very far reaching functorial generalization of this decomposition and sketch an application to understanding geometry and topology of moduli spaces of projective subschemes. Parts of this is joint work with Lukasz Sienkiewicz. 
Joachim Jelisiejew
(M. Yakerson) 
6  21.11  Regularity of spectral stacks, their algebraic Ktheory, and weight structures
Commutative rings are regular if and only if a homological criterion holds. This criterion can be formulated for connective E_{∞}ring spectra and also for connective spectral stacks. We study this property and show its peculiar behaviour. We do it by putting the whole situation in the context of weight structures and by constructing a weight structure on the category of perfect complexes on spectral stacks that are good quotients of an affine spectral scheme. This also allows us to prove the nilinvariance property of theories like fib(K → TC) and KH for spectral stacks. This is based on a joint work with Adeel Khan, and also on a work in progress joint with Tom Bachmann, Adeel Khan, and Charanya Ravi. 
Vladimir Sosnilo
(A. Khan) 
7  28.11  Generalized bornological coarse spaces  Daniel Heiß 
8  05.12  No seminar  Bavarian Geometry & Topology Meeting (Augsburg) 
9  12.12  Tba  Edoardo Lanari/Andrea Gagna
(HK Nguyen) 
10  19.12  Derived modular functors
Abstract: In my talk, I will present a new approach to a class of nonsemisimple representation categories, more specifically nonsemisimple modular tensor categories, via homotopy theory and lowdimensional topology. This will lead to socalled derived modular functors. It is already wellknown that for a semisimple modular tensor category, the ReshetikhinTuraev construction yields an extended threedimensional topological field theory and hence by restriction a modular functor. By work of LyubachenkoMajid the construction of a modular functor from a modular tensor category remains possible in the nonsemisimple case. We explain that the latter construction is the shadow of a derived modular functor featuring homotopy coherent mapping class group actions on chain complex valued conformal blocks and a version of factorization and selfsewing via homotopy coends. On the torus, we find a derived version of the Verlinde algebra, an algebra over the little disk operad (or more generally a little bundles algebra in the case of equivariant field theories). The concepts will be illustrated for modules over the Drinfeld double of a finite group in finite characteristic. This is joint work with Christoph Schweigert (Hamburg). 
Lukas Woike (U. Bunke) 
11  09.1  Magnetic Laplacians
Abstract: The goal of this talk is to develop some features of the spectral theory of 2D 2periodic magnetic laplacians. The goal of the talk is to explain a simple example in the intersection of mathematical physics, spectral theory and coarse geometry. The main result will be the calculation of the Ktheory classes of spectral projections of this operator as classes in the Ktheory of the group C^{*}algebra using the families index theorem. In this example it is possible to understand certain usually quite abstract constructs in a very explicit manner. 
Ulrich Bunke 
12  16.1.  Dualizability in the higher Morita category
After introducing the (∞,n+k)Morita category of E_{n}algebras (constructed as an (n+k)fold Segal space). I will explain dualizability results therein, in more detail. If time permits, I will go into consequences for (relative) extended topological field theories. 
Claudia Scheimbauer (D.C. Cisinski) 
13  23.1.  Tannaka categories associated to certain triangulated categories
(informal discussion) 
Daniel Schaeppi 
14  30.1.  
15  6.2.  On Codes  Masoud Zargar 