Location: Room MA B1 524 (Sometimes Zoom)
Program
Date  Time  Place  Title  Speaker 

20.02.2024  14:00 CET  MA B1 524  Computing motivic homotopy types of families of hypersurfaces with polyhedral products  William Hornslien, NTNU 
27.02.2024  14:00 CET  MA B1 524  Lie coalgebraic dual of a group, Milnor invariants, and linking of letters  Dev Sinha, University of Oregon (Zoom). 
05.03.2024  No seminar.  No seminar.  
12.03.2024  No seminar. 
No seminar. 

19.03.2024  14:00 CET  CM 517  Differentiable rigidity for embeddings: Haefliger’s examples  JeanClaude Hausmann, Université de Genève 
26.03.2024  14:00 CET  CM 517 
Regularity for E1 rings, schemes, and general triangulated categories, with new obstruction results on bounded tstructures

Ruradip Biswas, Univrsity of Warwick 
02.04.2024  No seminar.  No seminar.  
09.04.2024  14:00 CET  CM 517  Higher parametrized semiadditivity  Sil Linskens, University of Bonn 
16.04.2024  16:00 CET (Different !)  CM 517 
Traces of dualizable categories and functoriality of the BeckerGottlieb transfers 
Marco Volpe, University of Toronto (Zoom). 
23.04.2024  14:00 CET  CM 517 
Perfection and homotopy type 
Benjamin Antieau, Northwestern University (Zoom). 
30.04.2024 
No seminar. 
No seminar. 

7.05.2024  14:00 CET  CM 517 
Hermitian Kgroups and motives 
Paul Arne Oestvaer, University of Milan 
14.05.2024  14:00 CET  CM 517  A counterexample to the nonconnective theorem of the heart  Vladimir Soslino, University of Regensburg 
21.05.2024  14:00 CET  CM 517  Posets of Modalities in Higher Topoi  Eric Finster, University of Birmingham 
28.05.2024  14:00 CET  CM 517  Grothendieck lax construction  Felix Loubaton, MPIM 
4.06.2024 
14:00 CET  CM 517 
The infinitesimal tangle hypothesis

Joost Nuiten, Université de Toulouse 
11.06.2024 
14:00 CET  CM 517  The root functor  Francesca Pratali, Université Paris XIII 
18.06.2024 
14:00 CET  CM 517  Models for configuration spaces via obstruction theory  Thomas Willwacher, ETH 
25.06.2024 
14:00 CET  CM517  A simple proof of the Mumford conjecture  Dan Petersen, University of Stockholm 
Abstracts:
William Hornslien
Computing motivic homotopy types of families of hypersurfaces with polyhedral products
Polyhedral products are certain natural subspaces of products of CW complexes constructed from the combinatorial information of a simplicial complex. They play an important role in fields such as: toric varieties, homotopy theory, algebraic combinatorics, and robotics. Motivic homotopy theory is a homotopy theory for smooth algebraic varieties. Given a polynomial, it is in general not an easy task to figure out the homotopy type of the associated algebraic hypersurface. In this talk we will study a family of hypersurfaces by modeling them as polyhedral products. To do this, we generalize polyhedral products to an oocategorical setting and prove some general results before applying them to our motivic problem.
Dev Sinha
Lie coalgebraic dual of a group, Milnor invariants, and linking of letters
(joint with Nir Gadish, Aydin Ozbek and Ben Walter) Consider two homomorphisms f, g from a free group to the rational numbers. One can then define a homomorphism {f}g on the commutator subgroup of the free group by {f}g ( [v,w] ) = f(v) g(w) – f(w) g(v). This generalizes to the notion of Lie coalgebraic dual of a group, a framework for all groups which encompasses Magnus expansion and Fox derivatives for free groups. The universal Lie coalgebraic dual of a group pairs with the lower central series Lie algebra, giving a complete set of functionals over the rational numbers for any group and a perfect duality in the finitely generated setting.
JeanClaude Hausmann
Differentiable rigidity for embeddings: Haefliger’s examples
Traces of dualizable categories and functoriality of the BeckerGottlieb transfers
For any fiber bundle with compact smooth manifold fiber X ⟶ Y, Becker and Gottlieb have defined a “wrong way” map S[Y] ⟶ S[X] at the level of homology with coefficients in the sphere spectrum. Later on, these wrong way maps have been defined more generally for continuous functions whose homotopy fibers are finitely dominated, and have been since referred to as the BeckerGottlieb transfers. It has been a long standing open question whether these transfers behave well under composition, i.e. if they can be used to equip homology with a contravariant functoriality.
In this talk, we will approach the transfers from the perspective of sheaf theory. We will recall the notion of a locally contractible geometric morphism, and then define a BeckerGottlieb transfer associated to any proper, locally contractible map between locally contractible and locally compact Hausdorff spaces. We will then use techniques coming from recent work of Efimov on localizing invariants and dualizable stable infinitycategories to construct fully functorial “categorified transfers”. Functoriality of the BeckerGottlieb transfers is then obtained by applying topological Hochschild homology to the categorified transfers.
If time permits, we will also explain how one can use similar methods to extend the DwyerWeissWilliams index theorem for compact topological manifolds fiber bundles to proper locally contractible maps. In particular, this shows that the homotopy fibers of a proper locally contractible map are homotopy equivalent to finite CWcomplexes. Therefore, it is still unclear whether functoriality of the transfers associated to maps with finitely dominated homotopy fibers holds.
This is a joint work with Maxime Ramzi and Sebastian Wolf.
Benjamin Antieau
Perfection and homotopy type
I will discuss the role of perfection in classifying homotopy types by their integral cohomology, building on work of Sullivan, Kriz, Mandell, and Yuan. The main idea involves binomial rings, which in the pcomplete case are deltarings for which the associated Frobenius endomorphism is the identity. This idea has been discovered independently by Horel and by Kubrak—Shuklin—Zakharov.
Let C be a stable infinitycategory equipped with a bounded tstructure with the heart denoted by A. Antieau, Gepner, and Heller conjectured that the map of nonconnective Ktheory spectra K(A) —> K(C) is always an equivalence. Barwick’s theorem of the heart implies that this map is an equivalence on connective covers, and both sides are known to be connective if A is a noetherian abelian category.
To any spectrum M we functorially assign a stable infinitycategory C_M such that the spectrum K(C_M) is equivalent to M.
Using this result and some basic chromatic homotopy theory, we construct a counterexample to the conjecture above.
Eric Finster
Models for configuration spaces via obstruction theory
For M a parallelized nmanifold, the configuration spaces FM_M(r) can be given the structure of a right E_nmodule. Through rational homotopy theory, this then gives rise to a right comodule over the Hopf cooperad H^\bullet(E_n). I will show how to classify all H^\bullet(E_n)comodules of “configuration space type”.
A simple proof of the Mumford conjecture
Andrea Bianchi recently gave a new proof of Mumford’s conjecture on the stable rational cohomology of the moduli space of curves (first proven by Madsen and Weiss). I will explain a streamlined and simplified version of Bianchi’s argument. (Joint with Ronno Das)