Published on *Max-Planck-Institut für Mathematik* (https://www.mpim-bonn.mpg.de)

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Ausführliche Liste aller demnächst stattfindenden Vorträge und Seminare. Für eine Übersicht konsultieren Sie bitte auch den Kalender [2].

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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.

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- Vortrag [4]

Speaker:

Tadayuki Watanabe
Zugehörigkeit:

Shimane University
Datum:

Mit, 2019-09-18 09:30 - 10:20 In this talk, I will explain a method to construct families of diffeomorphisms of a 4-manifold by using a 4D analogue of Goussarov-Habiro's theory of graph surgery in 3D. Our graph surgery would produce lots of potentially nontrivial elements of homotopy groups of diffeomorphism groups of 4-manifolds. I will discuss about their applications to 4D analogue of the Smale conjecture and the 4D light bulb theorem for 3-disk.

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Speaker:

JungHwan Park
Zugehörigkeit:

Georgia Institute of Technology (GIT)
Datum:

Mit, 2019-09-18 10:30 - 10:55 We find some restrictions on the intersection forms of smooth definite manifolds bounded by rational homology spheres which are rationally cobordant to lens spaces. As a first consequence, we show that several natural maps to the rational homology cobordism group have infinite rank cokernels. Further, we show that there is no $n$ such that every lens space smoothly embeds in $n$ copies of the complex projective plane. This is joint work with Paolo Aceto and Daniele Celoria.

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Speaker:

Sergei Gukov
Zugehörigkeit:

Caltech
Datum:

Mit, 2019-09-18 11:30 - 12:20 Which 4d TQFTs and 4-manifold invariants detect the Gluck twist? Guided by questions like this, we will look for new invariants of smooth 4-manifolds and knotted surfaces in 4-manifolds.

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Speaker:

Florian Luca
Zugehörigkeit:

Wits University/MPIM/Ostrava
Datum:

Mit, 2019-09-18 14:30 - 15:30 $$\frac{a}{n}=\frac{1}{m_1}+\cdots+\frac{1}{m_k}$$ with positive integers $a,n,m_1,\ldots,m_k$. What is of interest is, given $n$, to count $A^*_k(n)=\{a:(a,n)=1, a/n=1/m_1+\cdots+1/m_k~{\text{for some}}~m_1,\ldots,m_k\}$ as well as $A_k(n)$ which is the same as $A_k^*(n)$ except that without the corporality condition on $a$ and $n$. In my talk, I will survey what is known about this problem for $k=2$ and I will show that $$ x(\log x)^3\ll \sum_{p\le x} A_3^*(p)\ll x(\log x)^5.$$

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Speaker:

Juanita Pinzón-Caicedo
Zugehörigkeit:

North Carolina State University/MPIM
Datum:

Don, 2019-09-19 09:30 - 10:20 A Floer homology is an invariant of a closed, oriented 3-manifold $Y$ that arises as the homology of a chain complex whose generators are either the set of solutions to a differential equation or the intersection points between Lagrangian manifold, and its differential arises as the count of solutions of a differential equation on $Y \times \mathbb{R}$. The Instanton Floer chain complex is generated by flat connections on a principal $SU(2)$-bundle, and the differential counts solutions to the Yang-Mills equation (known as instantons).

- Weiterlesen [12]

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Speaker:

Allison Miller
Zugehörigkeit:

Rice University
Datum:

Don, 2019-09-19 10:30 - 10:55 A knot is slice if it bounds an embedded disc in the 4-ball. There are (at least) two natural generalizations of sliceness: one might weaken either 'disc' to 'small genus surface' or 'the 4-ball' to 'any 4-manifold that is simple in some sense.' In this talk, I'll discuss joint work with Jae Choon Cha and Mark Powell that gives new evidence that these two approaches measure very different things. Our tools include Casson-Gordon style representations of knot groups, L2 signatures of 3-manifolds, and the notion of a minimal generating set for a module.

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Speaker:

Mark Powell
Zugehörigkeit:

Durham University, UK
Datum:

Don, 2019-09-19 11:30 - 12:20 I will explain the definition of the Kervaire-Milnor invariant of an immersed 2-sphere in a 4-manifold, which obstructs the sphere being homotopic to an embedding. I will describe two instances in 4-manifold classification where this invariant appears, one in the sphere embedding theorem and one in stable classification.

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Speaker:

Rob Schneiderman
Zugehörigkeit:

CUNY
Datum:

Don, 2019-09-19 15:00 - 15:50 David Gabai's smooth 4-dimensional "Light Bulb Theorem'' says that in the absence of involutions in the fundamental group of the ambient 4-manifold, homotopy implies isotopy for embedded 2-spheres which have a common geometric dual. In joint work with Peter Teichner we extend his result to orientable 4-manifolds with arbitrary fundamental group by showing that an invariant of Mike Freedman and Frank Quinn gives the complete obstruction to the "homotopy implies isotopy'' question. The invariant takes values in an F2-vector space generated by the involutions in the fundamental group.

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Speaker:

Alex Zupan
Zugehörigkeit:

University of Nebraska Lincoln
Datum:

Don, 2019-09-19 16:30 - 17:20 The Smooth 4-dimensional Poincaré Conjecture (S4PC) asserts that every homotopy 4-sphere is diffeomorphic to the standard 4-sphere $S^4$. We prove a special case of the S4PC: If $X$ is a homotopy 4-sphere that can be built with two 2-handles and two 3-handles, and such that one component of the 2-handle attaching link $L$ is a generalized square knot $T(p,q) \# T(-p,q)$, then $X$ is diffeomorphic to $S^4$. This is joint work with Jeffrey Meier.

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**Links:**

[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/3

[2] https://www.mpim-bonn.mpg.de/calendar

[3] https://www.mpim-bonn.mpg.de/de/node/9454

[4] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39

[5] https://www.mpim-bonn.mpg.de/de/node/9742

[6] https://www.mpim-bonn.mpg.de/de/node/3444

[7] https://www.mpim-bonn.mpg.de/de/node/9096

[8] https://www.mpim-bonn.mpg.de/de/node/9744

[9] https://www.mpim-bonn.mpg.de/de/node/9745

[10] https://www.mpim-bonn.mpg.de/de/node/9718

[11] https://www.mpim-bonn.mpg.de/de/node/246

[12] https://www.mpim-bonn.mpg.de/de/node/9746

[13] https://www.mpim-bonn.mpg.de/de/node/9747

[14] https://www.mpim-bonn.mpg.de/de/node/9749

[15] https://www.mpim-bonn.mpg.de/de/node/9750

[16] https://www.mpim-bonn.mpg.de/de/node/158

[17] https://www.mpim-bonn.mpg.de/de/node/9752

[18] https://www.mpim-bonn.mpg.de/de/print/145?page=1