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==Abstracts==
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'''Ko Aoki:''' Some recent progress on algebraic versus topological K-theory
 +
 +
For nice topological algebras, we have both algebraic K-theory and topological K-theory.
 +
Although algebraic K-theory is typically uncontrollable, it is believed to share nice properties with topological K-theory in certain situations.
 +
In my talk, I will highlight why these parallels are interesting and how Clausen–Scholze's condensed mathematics is useful to study them.
 +
In addition, I will discuss (partial) solutions to conjectures of Rosenberg.
 +
I will keep the talk accessible by avoiding technical details and not assuming any prior knowledge of algebraic K-theory or condensed mathematics.
 +
 +
 +
'''Alice Hedenlund:''' Twisted Floer Homotopy Types From Seiberg-Witten Floer Data
 +
 +
In the 90s, Cohen- Jones, and Segal asked the question of whether various types of Floer homology theories could be upgraded to the homotopy level by constructing stable homotopy types encoding Floer data. They also sketched how one could construct these Floer homotopy types as (pro)spectra in the situation that the infinite-dimensional manifold involved is “trivially polarized”. It has since been realized that the correct home for Floer homotopy types, in the polarized situation, is twisted spectra. This is a generalization of parametrized spectra that one can roughly think of as sections of bundles of categories whose fibre is the category of spectra.
 +
 +
The aim of this talk is to give an introduction of Floer homotopy theory and twisted spectra. I will also outline the construction of a circle equivariant twisted spectrum from Seiberg-Witten Floer data associated to a 3-manifold equipped with a complex spin structure. As there are many moving parts to this (Atiyah-Singer index theory, finite-dimensional approximation, Conley index theory etc.), I will try to keep the talk on a conceptual level that will hopefully be accessible to a large audience. This is joint work in progress with S. Behrens and T. Kragh.
 +
 +
 +
'''Filip Misev:''' On the unknotting number and the genus
 +
 +
While these two classical knot invariants, the unknotting number and the Seifert genus, are both easy to define, the former is incomparably harder to compute than the latter. They are incomparable in their values, too: there exist knots of small unknotting number and large genus and there are knots for which the unknotting number is larger than their genus.
 +
For many knots, however, their values actually coincide. This includes all positive braid knots, which in turn contain all algebraic knots, that is, connected links of plane curve singularities. It was conjectured by Stoimenow that equality between unknotting number and genus holds for the larger set of fibred positive knots.
 +
I would like to discuss the problem of determining the unknotting number for these knots, on one hand by example of some old and new unknotting algorithms, and on the other hand by presenting an infinite family of knots that seem to challenge Stoimenow's conjecture.
 +
Joint work with M. Kegel, L. Lewark, N. Manikandan, L. Mousseau, and M. Silvero.
  
 
==Conference Dinner==
 
==Conference Dinner==

Revision as of 11:20, 31 March 2024


12th Bavarian Geometry & Topology Meeting

Date and Location

The Bavarian Geometry & Topology Meeting XII will take place on 08-09 April 2024 at the University of Regensburg.

All talks will take place in room M311 on the 3rd floor of the Mathematics building of the University of Regensburg. (Attention: not the department "Mathematik und Informatik" of the OTH Regensburg).

Talks

Speakers:

  • Ko Aoki (MPIM Bonn)
  • Francesco Cattafi (Würzburg)
  • Bernhard Hanke (Augsburg)
  • Alice Hedenlund (Uppsala)
  • Filip Misev (Regensburg)
  • Luca Pol (Regensburg)
  • Claudia Scheimbauer (TUM München)

Short Presentations:

  • Divya Ghanshani (Regensburg)
  • Thorsten Hertl (Freiburg)
  • Andreas Huber (Augsburg)
  • Rosa Marchesini (Göttingen)

Schedule

Monday 08 April Tuesday 09 April
10:00 - 11:00 Francesco Cattafi
11:00 - 11:30 Coffee break & Registration Coffee break
11:30 - 12:30 Luca Pol Ko Aoki
12:30 - 14:00 Lunch Lunch
14:00 - 15:00 Bernhard Hanke Filip Misev
15:00 - 15:30 Coffee break Coffee break
15:30 - 16:30 Alice Hedenlund Claudia Scheimbauer
16:30 - 16:45 Break
16:45 - 17:45 Contributed talks
19:00 - End Conference dinner at

"Weltenburger am Dom"

Abstracts

Ko Aoki: Some recent progress on algebraic versus topological K-theory

For nice topological algebras, we have both algebraic K-theory and topological K-theory. Although algebraic K-theory is typically uncontrollable, it is believed to share nice properties with topological K-theory in certain situations. In my talk, I will highlight why these parallels are interesting and how Clausen–Scholze's condensed mathematics is useful to study them. In addition, I will discuss (partial) solutions to conjectures of Rosenberg. I will keep the talk accessible by avoiding technical details and not assuming any prior knowledge of algebraic K-theory or condensed mathematics.


Alice Hedenlund: Twisted Floer Homotopy Types From Seiberg-Witten Floer Data

In the 90s, Cohen- Jones, and Segal asked the question of whether various types of Floer homology theories could be upgraded to the homotopy level by constructing stable homotopy types encoding Floer data. They also sketched how one could construct these Floer homotopy types as (pro)spectra in the situation that the infinite-dimensional manifold involved is “trivially polarized”. It has since been realized that the correct home for Floer homotopy types, in the polarized situation, is twisted spectra. This is a generalization of parametrized spectra that one can roughly think of as sections of bundles of categories whose fibre is the category of spectra.

The aim of this talk is to give an introduction of Floer homotopy theory and twisted spectra. I will also outline the construction of a circle equivariant twisted spectrum from Seiberg-Witten Floer data associated to a 3-manifold equipped with a complex spin structure. As there are many moving parts to this (Atiyah-Singer index theory, finite-dimensional approximation, Conley index theory etc.), I will try to keep the talk on a conceptual level that will hopefully be accessible to a large audience. This is joint work in progress with S. Behrens and T. Kragh.


Filip Misev: On the unknotting number and the genus

While these two classical knot invariants, the unknotting number and the Seifert genus, are both easy to define, the former is incomparably harder to compute than the latter. They are incomparable in their values, too: there exist knots of small unknotting number and large genus and there are knots for which the unknotting number is larger than their genus. For many knots, however, their values actually coincide. This includes all positive braid knots, which in turn contain all algebraic knots, that is, connected links of plane curve singularities. It was conjectured by Stoimenow that equality between unknotting number and genus holds for the larger set of fibred positive knots. I would like to discuss the problem of determining the unknotting number for these knots, on one hand by example of some old and new unknotting algorithms, and on the other hand by presenting an infinite family of knots that seem to challenge Stoimenow's conjecture. Joint work with M. Kegel, L. Lewark, N. Manikandan, L. Mousseau, and M. Silvero.

Conference Dinner

The conference dinner will take place on Monday 19:00 at the restaurant Weltenburger am Dom.

Registration & Financial Support

Please register by filling out this form.

We ask participants to organize an accommodation by themselves. The deadline to apply for financial support has passed.

Practical Information

DIRECTIONS: One can reach the University of Regensburg by following the instructions here and see here for maps of the campus.

INTERNET: Access to eduroam and BayernWLAN is available throughout the Mathematics Building.

ACCOMMODATION: Here is a list of hotels in the area:

Previous iterations of the BGTM

  • 4th BGTM (Augsburg)
  • 3rd BGTM (Regensburg)
  • 2nd BGTM (Augsburg)
  • 1st BGTM (Regensburg)

Conference Poster

Topology meeting3.png

You can download the conference poster here.

Organizers

Retrieved from "https://sfb-higher-invariants.app.uni-regensburg.de/index.php?title=Bavarian_Geometry_and_Topology_Meeting_XII&oldid=2135"
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