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QU Lecture - Correlators, topological field theory and categorification

Prof. Dr. Christoph Schweigert, Prof. Tobias Dyckerhoff, Prof. Paul Wedrich

Course

Description

This series of QU lectures consists of three parts given by three lecturers.

Stringnets for CFT correlators (Christoph Schweigert)

We show how recent progress in quantum topology allows for conceptual and simple proofs of the existence of consistent systems of correlators of two-dimensional conformal field theories. We show that all correlators naturally factorize through spaces constructed from defect data. This points to a new general conceptual role for defects in quantum field theories.

Categorified state sums and the topological A-model (Tobias Dyckerhoff)

We begin with an elementary mathematical perspective on state sum constructions for correlators of the most basic kinds of 2D topological field theories. Taking this as a starting point, we will see how a categorified variant of these constructions somewhat surprisingly leads to a description of 2D Fukaya categories (in string theoretic terms, these are categories of branes in the topological A-model introduced by Witten). Time permitting, we will say a few general words about this novel type of categorification and what we would like to do with it.

Categorification in quantum topology (Paul Wedrich)

I will start by giving an introduction to the framework of "categorification" and outline how it is used for the construction and study of topological field theories as a kind of dual to the process of dimensional reduction. After situating some examples that we have met previously, I will present a sequence of increasingly sophisticated categorifications of quantum invariants of knots. As an application, we obtain a new invariant of smooth 4D manifolds from Khovanov's categorification of the Jones polynomial, akin to the string net spaces from the first talk of this series, but with all dimensions doubled.

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The lecture takes place at DESY, building 2a, seminar room 2. It is recommended to wear masks during the lecture and follow distance regulations. You may also follow the lecture via Zoom:
https://uni-hamburg.zoom.us/j/92293543262
(Meeting ID: 922 9354 3262, Passcode: 97540703)

General Data

  • Abbreviation
    qurs-ws22-lecture-correlators
  • Semester
    winter semester 22/23
  • Target Groups
  • Course Type
    lecture
  • Course Language
    English
  • Departments
    MIN Graduate Center > Quantum Universe Research School

Place and Time

Date
  • Place
    Campus Bahrenfeld Gebäude 02a EG, Raum 2
  • Time
    from 13/01/2023 weekly Fridays to 27/01/2023 from 14:30 to 16:00

Recognition Modalities

  • Number of Semester Hours
    0.5
  • Amount of Credit Points
    0.5
  • Creditable as
    • MIN doctoral program: research related for QURS

Registration Modalities

  • Type of Place Allocation
    First come - first served (after the registration has been received)
  • Information about Registration
    –
  • Max. Number of Participants
    –