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# RTG2491 Autumn School

"From T-duality via K-theory to representation theory"

September 30 to October 4, 2024

**Registration is closed!**

The aim of the Autumn School is to bring together young researchers with experts in the research areas of T-duality, K-theory, representation theory and their interplay. The school consists of four mini-courses leading towards a broad understanding of the topic from different perspectives.

__SPEAKERS__

Francesca Arici (Leiden)

Marco Gualtieri (Toronto)

Nigel Higson (Penn State)

Konrad Waldorf (Greifswald)

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__REGISTRATION__

**Registration is closed!**

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__POSTER__

Download Poster

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__TENTATIVE PROGRAMME__

The school starts on Monday September 30, at 09:00, with the on-site registration, and ends on Friday, October 4, at 12:30.__Activities:__

You can download the programme here

__The titles of the mini-courses for the upcoming Autumn School are:__

**Francesca Arici**(Leiden)

*Title:*C*-algebras and (K)K-theory in solid-state physics

*Abstract:*This lecture series focuses on Toeplitz algebras and Toeplitz extensions, covering their basic properties and applications in operator algebras. We start by introducing Toeplitz operators and their role in functional analysis. We then look at Toeplitz algebras and their C*-representations. We shall then discuss Toeplitz extensions, including their theoretical framework and their importance in index theory and operator K-theory, including Kasparov's bivariant K-theory. Finally, we discuss recent uses of Toeplitz extension and their index maps in studying solid-state systems, particularly focusing on the bulk-edge correspondence for topological insulators.

Here you can download the Notes for the lecture series of Francesca Arici

**Marco Gualtieri**(Toronto)

*Title:*Groupoids, Gerbes and Generalized Kähler geometry

*Abstract:*Generalized Kahler geometry originated in the study of 2-dimensional sigma models in physics, although the special case of Kahler structures has received far more attention due to its relative simplicity and relation to algebraic geometry. In these lectures, I will explain how several of the strange aspects of Generalized Kahler geometry can now be explained geometrically through the use of U(1) Gerbes, Morita equivalences, T-duality of Courant algebroids, and symplectic stacks. Besides being useful for understanding generalized Kahler structures, these methods should be extended to other forms of generalized geometry arising from other physical theories.

Here you can download the Notes for the lecture series of Marco Gualtieri

**Nigel Higson**(Penn State)

*Title:*C*-algebra K-theory and Tempered Representation Theory

*Abstract:*These lectures will trace some recent developments that have brought together C*-algebra theory and unitary representation theory, particularly for real reductive Lie groups such as the special and general linear groups. I shall start with a short discussion of basic ideas in C*-algebras and K-theory. Then I shall explain how those ideas apply to the (reduced) C*-algebras of real reductive groups. Finally I shall explain how C*-algebra theory and K-theory have led to new perspectives in the tempered representation theory of real reductive Lie groups.

**Konrad Waldorf**(Greifswald)

*Title:*The higher geometry of T-duality

*Abstract:*The aim of these lectures is to present T-duality through the lens of higher geometric structures, highlighting the advantages of this approach. We will begin with an introduction and motivation, touching on the string-theoretic origins of T-duality. Next, we will introduce key higher geometric structures and explore their relations to T-duality. Notably, we will revisit some foundational results by Bunke and Schick, showing how they can be reinterpreted using this framework. Finally, we will demonstrate how this perspective extends to cases previously addressed by Rosenberg and Mathai via non-commutative geometry. If time allows, we will briefly discuss further potential extensions to non-associative T-duality and T-folds.

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## Poster Session

**Anupam Datta**(Bonn)

*Homotopic theoretic ideas in C* algebras*

**Jialong Deng**(Beijing)

*K-theory, almost non-positively curved manifolds and convergences*

**Lennart Döppenschmitt**(Zurich)

*Kähler geometry of brane moduli spaces*

**Gianni Gagliardo**(Edinburgh)

*Principal 3-bundles with Adjusted Connections*

**Maciej Dawid Galazka**(Trento)

*Hilbert scheme of nine points and the variety of commuting matrices*

**Hao Xu**(Göttingen)

*Topological T-duality and Brauer-Picard group*

**Georg Lehner**(Berlin)

*The Rosenberg conjectures*

**Ruben Louis**(Changchun)

*On Nash resolution of (singular) Lie algebroids*

**Stefano Ronchi**(Göttingen)

*Higher Cotangent Groupoids*

**Aldo Witte**(Hamburg)

*T-duality with fixed points*

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__TRAVEL AND ACCOMODATION__

Here you will find information on how to get to and your stay in Göttingen.Arriving in Göttingen

Closest airports: Frankfurt Main International, Hannover

Göttingen is well connected via fast trains to most major cities in Germany. The travel time from Frankfurt is about 2h and from Hannover less than 1h.

Walking from the train station to the Mathematical Institut takes no more than 20 minutes passing through the town centre. Most hotels are in walking distance from the main building, however there is also a chance of using the buses.

Göttingen is well connected via fast trains to most major cities in Germany. The travel time from Frankfurt is about 2h and from Hannover less than 1h.

Walking from the train station to the Mathematical Institut takes no more than 20 minutes passing through the town centre. Most hotels are in walking distance from the main building, however there is also a chance of using the buses.

Hotels

Here is a list of recommended Hotels in Göttingen:

Leine Hotel

Eden Hotel

Hotel Central

G Hotel

Novostar

Hotel Stadt Hannover

Leine Hotel

Eden Hotel

Hotel Central

G Hotel

Novostar

Hotel Stadt Hannover

Map

Here is a map where you can find bus stops, sightseeing points and other information about Göttingen. The link is set to the Autumn School room, you can move freely within the map.

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