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Upcoming Talks

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Abstracts of upcoming talks at the MPIM. For an overview see also the calendar.

Recent developments in Quantum Topology -- Cancelled --

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We will review the basics of quantum topology such as the colored Jones polynomial of a knot, its standard conjectures relating to asymptotics, arithmeticity and modularity, as well as the recent quantum hyperbolic invariants of Kashaev et al, their state-integrals and their structural properties. The course is aimed to be accessible by graduate students and young researchers.

On the natural stratification of the space of differentiable functions and the space of Morse functions

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Speaker: 
Julian Brueggemann
Affiliation: 
MPIM/Universität Bonn
Date: 
Tue, 30/05/2023 - 16:30 - 18:00
Location: 
MPIM Lecture Hall

Hybrid. Contact: Christian Kaiser (kaiser @ mpim-bonn.mpg.de)

The Stark conjecture over the field of rational numbers: A new approach

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Speaker: 
Robert Sczech
Affiliation: 
Rutgers University
Date: 
Wed, 31/05/2023 - 14:30 - 15:30
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

Contact: Pieter Moree (moree @ mpim-bonn.mpg.de)

 

We present a new proof for the algebraicity of the cyclotomic Stark units. These units are defined in a transcendental way, via the derivative at s=0 of a partial zeta function. The proof links these units to the special values of the Riemann zeta function at positive even integers. The rationality of these special values (modulo a power of pi) implies the algebraicity of the cyclotomic Stark units.

 

The Nielsen realization for non-spin 4-manifolds

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Speaker: 
Mihail Arabadji
Affiliation: 
UMass Amherst/MPIM
Date: 
Thu, 01/06/2023 - 10:30 - 11:30
Location: 
MPIM Lecture Hall

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de)

We are going to show that there are many families of non-spin 4–manifolds for which the smooth Nielsen realization problem fails; that is, there are (finite) subgroups of their mapping class groups that cannot be realized by a group of diffeomorphisms. This extends and complements the recent results for spin 4–manifolds. This is joint work with Inanc Baykur.


 

 


 

4-genus bounds from the 10/8+4 theorem

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Speaker: 
Gordana Matic
Affiliation: 
UGA/MPIM
Date: 
Thu, 01/06/2023 - 12:00 - 13:00
Location: 
MPIM Lecture Hall

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de)

Donald and Vafaee described a way to use Furuta’s 10/8 theorem to obstruct sliceness in the 4-ball and Linh Truong used a refinement, the 10/8 +4 theorem of Hopkins-Lin-Shi and Hu, to strengthen this sliceness obstruction. We will show how to expand on this technique to obtain lower bounds for four-ball genus and present some calculations for satellite knots. This is joint work in progress with Sashka Kjuchukova and Linh Truong.

Margulis Lemma and RCD spaces

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Speaker: 
Sergio Zamora Barrera
Affiliation: 
Penn State University/MPIM
Date: 
Thu, 01/06/2023 - 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Contact: Christian Kaiser (kaiser @ mpim-bonn.mpg.de)

The classic Margulis Lemma states that in a hyperbolic manifold, the subgroup of the fundamental group generated by small loops around a certain point is virtually abelian.
I will present some generalizations of this result, includingrecent work (with Qin Deng, Jaime Santos, and Xinrui Zhao) where we include RCD spaces, a non-smooth analogue of manifolds with a lower bound on the Ricci curvature.

 

 

tba

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Speaker: 
Darrick Lee
Affiliation: 
Oxford
Date: 
Wed, 07/06/2023 - 10:30 - 12:00
Location: 
MPIM Seminar Room

tba

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Speaker: 
Fan Ye
Date: 
Thu, 15/06/2023 - 12:00 - 13:00
Location: 
MPIM Lecture Hall

Contact: Aru Ray (aruray @ mpim-bonn.mpg.de), Steven Sivek (sivek @ mpim-bonn.mpg.de)


 

Conley index theory and condensed sets

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Speaker: 
Yosuke Morita
Affiliation: 
Kyushu University
Date: 
Mon, 19/06/2023 - 09:30 - 10:30
Location: 
MPIM Lecture Hall

The Conley index is a spatial refinement of the Morse index. Informally speaking, it is a ‘space’ that describes the local dynamics around an isolated invariant subset of a topological dynamical system. In this talk, I will explain a new formulation of Conley index theory, which I think is simpler and more flexible than the traditional formulation. One important point is that the Conley index should be defined as a based equivariant condensed set/anima, not as a mere homotopy type of topological spaces.

tba

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Speaker: 
Lucas Mann
Affiliation: 
Universität Münster
Date: 
Mon, 19/06/2023 - 11:00 - 12:00
Location: 
MPIM Lecture Hall
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