RTG 2491 - Fourier Analysis and Spectral Theory

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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.

Autum School Participants 2024


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

T-duality 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:

  • Tuesday, October 1: The poster session will take place at 17:00.
  • Wednesday, October 2: The talks on Wednesday will end at 12:30 and the rest of the day will be free.
  • Thursday, October 3: The conference dinner will take place at 19:30. IMPORTANT: The 3rd of October is a public holiday in Germany (German Unity Day), therefore most shops (except restaurants, bars etc.) are closed during this day.

    • programmeAutumnSchool2024
    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.

    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.

    Here is a list of recommended Hotels in Göttingen:

    Leine Hotel
    Eden Hotel
    Hotel Central
    G Hotel
    Novostar
    Hotel Stadt Hannover

    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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