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Student seminar on higher categories

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Date: 
Fri, 2013-04-26 13:30 - Fri, 2013-07-19 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Classification of Topological 4-manifolds (Semester on 4-manifolds)
Details: 
Program and Abstracts of Student seminar on higher categories

Course Description:

We want to understand the comparison problem in higher category theory, i.e. for structures which have objects, 1-morphisms, 2-morphisms, etc. Higher categories have arisen in many areas of mathematics, as well as in formalisms for quantum field theory. There are many alternative models for higher categories and the goal of this course is to understand some of them and their inter-relationships.

Introduction to Quasicategories

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Speaker: 
Christian Wimmer
Date: 
Fri, 2013-04-26 13:30 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Student seminar on higher categories

  • Basic

Introduction to geometry and physics of knot homologies, IV

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Speaker: 
Sergei Gukov
Date: 
Fri, 2013-04-26 10:30 - 12:00
Location: 
MPIM Lecture Hall
Parent event: 
Lecture Series on 4-manifolds

http://people.mpim-bonn.mpg.de/teichner/Math/4-Manifolds.html

Video: 
video/mp4 icon20130426_gukov4a.mp4
video/mp4 icon20130426_gukov4b.mp4

A new (computer-friendly) approach to Morse--Novikov theory

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Speaker: 
Dan Burghelea
Affiliation: 
The Ohio St. U/MPI
Date: 
Thu, 2013-04-25 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar

Some aspects of exceptional collections on (rational) surfaces

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Speaker: 
Markus Perling
Affiliation: 
z.Z. MPI
Date: 
Thu, 2013-04-25 10:30 - 12:00
Location: 
MPIM Lecture Hall
Parent event: 
Seminar Algebraic Geometry (SAG)

Introduction to geometry and physics of knot homologies, III

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Speaker: 
Sergei Gukov
Date: 
Wed, 2013-04-24 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
Lecture Series on 4-manifolds

http://people.mpim-bonn.mpg.de/teichner/Math/4-Manifolds.html

Video: 
video/mp4 icon20130424_gukov3a.mp4
video/mp4 icon20130424_gukov3b.mp4

Finite Quadratic Modules and Weil Representations over Number Fields

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Speaker: 
Hatice Boylan
Affiliation: 
MPI
Date: 
Wed, 2013-04-24 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

In the study of Hilbert, Jacobi and orthogonal modular forms
of low weight over number fields it is essential to understand the
representations of Hilbert modular groups or of certain two-fold
central extensions. In the case of the field of natural numbers it is
known that the key to the study of all representations of the modular
group $SL(2,Z)$ which are interesting in the mentioned context are
the Weil representations associated to finite quadratic modules. In
analogy to the case of the field of rational numbers we developed a

Descent for $n$-Bundles

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Speaker: 
Jesse Wolfson
Affiliation: 
Northwestern University
Date: 
Wed, 2013-04-24 10:30 - 12:00
Location: 
MPIM Lecture Hall
Parent event: 
Higher Differential Geometry Seminar

 We study principal bundles for strict Lie $n$-groups over simplicial manifolds. Given a Lie group $G$, one can construct a principal $G$-bundle on a manifold $M$ by taking a cover $U$ of $M$, specifying a transition cocycle, and then quotienting $U\times G$ by the equivalence relation generated by the cocycle. We demonstrate the existence of an analogous construction for arbitrary strict Lie $n$-groups. As an application, we show how our construction leads to a simple finite dimensional model of the Lie 2-group String($n$).

The Witten genus and topological modular forms

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Speaker: 
Justin Noel
Affiliation: 
MPI
Date: 
Tue, 2013-04-23 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
Seminar on Algebra, Geometry and Physics

I will give a fairly high level introduction to topological modular forms (Tmf) and their relationship to the Witten genus. Tmf was constructed, in part, as the target of a cohomological lift of Witten genus. The Witten genus assigns a modular form to a string manifold and this assignment is invariant under string bordism. This is analogous to the A-hat genus which assigns to a spin manifold an elliptic operator which, in turn, defines a formal difference of vector spaces. Moreover the A-hat genus is invariant under spin bordism.

Discussion session (Semester on 4-manifolds)

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Date: 
Tue, 2013-04-23 10:30 - 12:00
Location: 
MPIM Lecture Hall
Parent event: 
Discussion session (Semester on 4-manifolds)
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