# Lecture

Lecture or course consisting of one or several talks.

## Course on Frobenius Manifolds

Posted in
Date:
Tue, 2017-05-02 10:15 - 12:00
Location:
MPIM Seminar Room

## Brauer Groups in Algebraic Topology III

Posted in
Speaker:
Jacob Lurie
Affiliation:
Harvard
Date:
Fri, 2017-06-23 09:30 - 10:30
Location:
MPIM Lecture Hall

Let $k$ be a field. The collection of (isomorphism classes of) central division algebras over $k$ can be organized into an abelian group $\mathrm{Br}(k)$, called the Brauer group of $k$. In this series of talks, I'll describe some joint work with Mike Hopkins on a variant of the Brauer group which arises in algebraic topology, controlling the classification of certain cohomology theories known as Morava $K$-theories.

## Brauer Groups in Algebraic Topology II

Posted in
Speaker:
Jacob Lurie
Affiliation:
Harvard
Date:
Thu, 2017-06-22 09:30 - 10:30
Location:
MPIM Lecture Hall

Let $k$ be a field. The collection of (isomorphism classes of) central division algebras over $k$ can be organized into an abelian group $\mathrm{Br}(k)$, called the Brauer group of $k$. In this series of talks, I'll describe some joint work with Mike Hopkins on a variant of the Brauer group which arises in algebraic topology, controlling the classification of certain cohomology theories known as Morava $K$-theories.

## Some applications of topology to physics III

Posted in
Speaker:
Dan Freed
Date:
Wed, 2017-06-21 09:30 - 10:30
Location:
MPIM Lecture Hall

An axiom system for special quantum field theories was introduced over 25 years ago by Segal and Atiyah.
It has been much elaborated and developed, particularly in the topological case.  In these three lectures I will
discuss aspects of this mathematical theory and applications to problems in physics.

## Some applications of topology to physics II

Posted in
Speaker:
Dan Freed
Date:
Tue, 2017-06-20 09:30 - 10:30
Location:
MPIM Lecture Hall

An axiom system for special quantum field theories was introduced over 25 years ago by Segal and Atiyah.
It has been much elaborated and developed, particularly in the topological case.  In these three lectures I will
discuss aspects of this mathematical theory and applications to problems in physics.

## Lecture on Anabelian Geometry

Posted in
Date:
Fri, 2015-10-30 10:00 - Fri, 2016-02-26 12:00
Location:
MPIM Lecture Hall

## Characters of representations of Lie (super)algebras and (mock)theta functions

Posted in
Speaker:
V. Kac
Date:
Mon, 2015-03-23 09:00 - 10:15
Location:
MPIM Lecture Hall

Prerequisits:
Understanding of the Weyl character formula, universal enveloping algebra and Verma modules.
Knowledge of some elements of Lie superalgebra theory.
Knowledge of some elements of Jacobi theta functions and modular forms.
Programm:
1. Lie superalgebras
2. Ane Lie (super)algebras: loop and KM constructions
3. Character formula for integrable and admissible representations in the Lie algebra case and Jacobi
theta functions
4. Character formula for tame integrable and admissible modules in the Lie superalgebra case and
mock theta functions

## Modular-invariance in rational conformal field theory: past, present and future

Posted in
Speaker:
G. Mason
Date:
Thu, 2015-03-26 14:00 - 15:00
Location:
MPIM Lecture Hall

This is a tentative outline of my two lectures. No prior knowledge of vertex
rings is assumed, though the foundations will be covered only sketchily due to
time constraints. The main purpose of the lectures is to explain how modularity
enters into VOA theory, and to discuss an approach to the general problem of
modular-invariance in rational CFT based on a theory of vector-valued modular
forms, Fuchsian systems, and the Riemann-Hilbert problem.

## Mock theta functions and representation theory of affine Lie superalgebras and superconformal algebras

Posted in
Speaker:
M. Wakimoto
Date:
Mon, 2015-03-23 15:00 - 16:00
Location:
MPIM Lecture Hall

One of the beautiful properties in representation theory of ane Lie
algebras is the SL2pZq-invariance of the space of characters of integrable modules
discovered by Kac-Peterson in the early 1980's.
However, for ane Lie superalgebras, modular invariance had long been quite un-
clear except for only a few cases. Recently a remarkable breakthrough was brought
by Zwegers, who constructed a modular function from the supercharacter of the
ane slp2|1q-module of level 1 by adding non-holomorphic correction term, which
is called the "modi cation" procedure.

## Rogers-Ramanujan Identities and Moonshine

Posted in
Speaker:
Ken Ono
Date:
Wed, 2015-03-25 13:30 - 14:45
Location:
MPIM Lecture Hall

The Rogers-Ramanujan identities and Monstrous moonshine are among
the deepest results which occur at the interface of number theory and representation
theory. In these lectures the speaker will discuss these identities, and describe recent
work with Duncan, Griffin on Warnaar on their recent generalizations. This will include
a framework of Rogers-Ramanujan identities and singular moduli, and the theory of
umbral Moonshine.

## Rogers-Ramanujan Identities and Moonshine

Posted in
Speaker:
Ken Ono
Date:
Tue, 2015-03-24 13:30 - 14:45
Location:
MPIM Lecture Hall

The Rogers-Ramanujan identities and Monstrous moonshine are among
the deepest results which occur at the interface of number theory and representation
theory. In these lectures the speaker will discuss these identities, and describe recent
work with Duncan, Griffin on Warnaar on their recent generalizations. This will include
a framework of Rogers-Ramanujan identities and singular moduli, and the theory of
umbral Moonshine.

## Rogers-Ramanujan Identities and Moonshine

Posted in
Speaker:
Ken Ono
Date:
Mon, 2015-03-23 13:30 - 14:45
Location:
MPIM Lecture Hall

The Rogers-Ramanujan identities and Monstrous moonshine are among
the deepest results which occur at the interface of number theory and representation
theory. In these lectures the speaker will discuss these identities, and describe recent
work with Duncan, Griffin on Warnaar on their recent generalizations. This will include
a framework of Rogers-Ramanujan identities and singular moduli, and the theory of
umbral Moonshine.

## Kac-Moody superalgebras

Posted in
Speaker:
M. Gorelik
Date:
Fri, 2015-03-27 09:00 - 10:00
Location:
MPIM Lecture Hall

I will review results of C. Hoyt and V. Serganova on the classi cation of Kac-Moody superalgebras.
In the supercase several Cartan matrices may determine the same superalgebra and our de nition
of Kac-Moody superalgebra is based on this fact. Surprisingly, all indecomposable Kac-Moody
superalgebras with isotropic roots are nite-dimensional or ane.

## Kac-Wakimoto character formula for affine Lie superalgebras.

Posted in
Speaker:
M. Gorelik
Date:
Tue, 2015-03-24 15:00 - 16:00
Location:
MPIM Lecture Hall

I will outline a proof of the Kac-Wakimoto character formula for some irreducible highest weight
modules over ane Lie superalgebras. This formula will be used in V. Kac's lectures.

## The arithmetic of Eisenstein cohomology classes

Posted in
Speaker:
Günter Harder
Date:
Tue, 2015-01-27 11:00 - Fri, 2015-07-17 12:30
Location:
MPIM Lecture Hall

## Batalin-Vilkovisky formalism in topological quantum field theory

Posted in
Speaker:
Pavel Mnev
Affiliation:
MPIM
Date:
Fri, 2014-11-28 11:15 - 13:00
Location:
MPIM Lecture Hall

## Lecture on Classical and higher spherical polynomials

Posted in
Speaker:
Don Zagier
Affiliation:
MPI
Date:
Tue, 2014-04-15 16:30 - Tue, 2014-07-15 18:00
Location:
MPIM Lecture Hall

## Minicourse by Marco Maculan

Posted in
Speaker:
Marco Maculan
Date:
Mon, 2014-02-24 10:30 - Tue, 2014-02-25 12:00
Location:
MPIM Seminar Room

Posted in
Speaker:
Jan Swoboda
Affiliation:
MPI
Date:
Wed, 2013-10-16 16:15 - Fri, 2014-02-07 23:00
Location:
MPIM Lecture Hall

## Minicourse on dendroidal topology

Posted in
Speaker:
Ieke Moerdijk
Affiliation:
Nijmegen
Date:
Tue, 2013-10-08 14:30 - Fri, 2013-10-11 12:00
Location:
MPIM Lecture Hall

Dendroidal topology is an extension of simplical topology, geared towards the theory of operads and of infinity-operads. In the first part of the course, we will discuss topological operads and their algebras, and the Boardman-Vogt resolution. Next, we will introduce the category of dendroidal sets, and the corresponding notion of infinity operad. This will naturally include a discussion of the Joyal model structure on simplicial sets and the corresponding notion of infinity category. We will discuss several models for the homotopy theory of dendroidal sets, e.g.

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