Location: Room MA B1 524 (Sometimes Zoom)
(For questions about the seminar, please contact the organizers:
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 |
Jean-Claude 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 t-structures
|
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 |
TBA
|
Marco Volpe, University of Toronto (Zoom). |
| 23.04.2024 |
14:00 CET |
CM 517 |
TBA
|
Benjamin Antieau, Northwestern University (Zoom).
|
| 30.04.2024 |
|
|
No seminar.
|
No seminar.
|
| 7.05.2024 |
14:00 CET |
CM 517 |
TBA
|
Paul Arne Oestvaer, University of Milan |
| 14.05.2024 |
14:00 CET |
CM 517 |
TBA |
Vladimir Soslino, University of Regensburg |
| 21.05.2024 |
14:00 CET |
CM 517 |
TBA |
Eric Finster, University of Birmingham |
| 28.05.2024 |
14:00 CET |
CM 517 |
TBA |
Felix Loubaton, MPIM |
|
4.06.2024
|
14:00 CET |
CM 517 |
TBA |
Joost Nuiten, Université de Toulouse |
|
11.06.2024
|
14:00 CET |
CM 517 |
TBA |
Francesca Pratali, Université Paris XIII |
|
18.06.2024
|
14:00 CET |
CM 517 |
TBA |
Thomas Willwacher, ETH |
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 oo-categorical 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.
Jean-Claude Hausmann
Differentiable rigidity for embeddings: Haefliger’s examples
André Haefliger (1929-2023), a former UNIL undergraduate student, became famous in 1960 for constructing smooth embeddings (for example of S^3 into R^6) which are not smoothly isotopic, even though they are topologically isotopic. Such a “differentiable rigidity” (after that for diffeomorphisms discovered by Milnor) indeed astonished the mathematical community. We will present these examples of smooth rigidity and the ideas of Haefliger’s proof, after putting them into perspective.
Rudradip Biswas
Regularity for E1 rings, schemes, and general triangulated categories, with new obstruction results on bounded t-structures
For any essentially small triangulated category S satisfying a finiteness property (in our language, if its opposite category has finite “finitistic dimension”), we show that the existence of a bounded t-structure on S implies that it is invariant under Neeman-completion. This gives a big abstract generalization of Neeman’s own new work on the existence of bounded t-structures on perfect complexes of schemes [2] where he, using very different methods, proved a conjecture due to Antieau, Gepner, and Heller. Neeman had also shown that the derived bounded category of coherent sheaves, under some restrictive conditions on the scheme, only has one bounded t-structure up to “equivalence”. We improve and abstractly generalize this result by showing that under the same general starting conditions mentioned at the start of the paragraph, all bounded t-structures on any intermediate category between the starting category and its completion are equivalent. Perfect complexes can be completed to the derived bounded category of coherent sheaves – so our result, when specialized to schemes, improves the existing Neeman result by removing all the restrictive hypotheses on the scheme.
Applying our treatment to triangulated categories arising in the study of E1 rings, DG algebras, artin algebras, etc, we get many applications and new results. The word “regularity” is used in the title because one can define the singularity category of a general triangulated category in the language of completion (we can then define regularity as corresponding to the vanishing of this singularity category), and our work shows that this singularity category is an obstruction to the existence of bounded t-structures.
Sil Linskens
Higher parametrized semiadditivity
Given a semiadditive category, every object uniquely obtains the structure of a commutative monoid. This simple fact turns out to be crucial in the higher categorical context, where endowing an object with the structure of a commutative monoid can be highly nontrivial endeavour. More recently, the notion of higher semiadditivity has attracted considerable attention, primarily because many categories appearing in chromatic homotopy theory are higher semiadditive. Higher semiadditivity again automatically endows objects with considerable algebraic structure which has been crucial for many recent breakthroughs in chromatic homotopy theory, for example the recent disproof of the telescope conjecture. However to leverage this algebraic structure we require a “generator-and-relations style” description of the operations it entails. This is given by a theorem of Harpaz, which gives a formula for the universal higher semiadditive category on a point. In this talk I will discuss a parametrised analogue of higher semiadditivity, which simultaneously subsumes higher semiadditivity and the Wirthmüller isomorphisms in equivariant homotopy theory. I will then present the analog of the theorem of Harpaz. This is joint work with Bastiaan Cnossen and Tobias Lenz.
