Semi-classical approximations in conformal field theory and analytic geometry of moduli spaces
Dr. Claudio Meneses (DFG Principal Investigator, University of Kiel)
Waseda University
January 2022
real-time Zoom lectures* (please see below for registration information)
Two-dimensional conformal field theories are examples of quantum field theories encoding incredibly rich algebraic and geometric structures which have captivated the interest of many mathematicians in the last 40 years. From a geometric perspective, they have been formulated as a branch in moduli theory, and even at the semi-classical level, they have shed new light into an extensive series of classical problems in the theory of complex ODE. The aim of these lectures is to present an overview of examples of this phenomenon in the analytic geometry of moduli spaces of Riemann surfaces and parabolic bundles.
Dr. Claudio Meneses (DFG Principal Investigator, University of Kiel)
Each lecture will include ample time for discussion and questions.
Graduate students and researchers in mathematics, physics, and engineering are welcome.
Details
Short course on
Semi-classical approximations in conformal field theory and analytic geometry of moduli spaces
Date: January 17-27, 2022
Venue: Real-time Zoom lectures*
Languages: English
Lecturer: Dr. Claudio Meneses (DFG Principal Investigator, University of Kiel)
Participants: Open to all students and faculty members
Registration: *Registered students will receive Zoom login information via Waseda Moodle. Visitors/guests are welcome to attend. In order to receive the Zoom login information, please send an e-mail to Martin Guest (martin at waseda.jp) stating your name, university affiliation, and position/student status.
Schedule (all times are Japan time)
Monday, January 17, 17:00-18:30
Tuesday, January 18, 17:00-18:30
Wednesday, January 19, 17:00-18:30
Thursday, January 20, 17:00-18:30
Monday, January 24, 17:00-18:30
Tuesday, January 25, 17:00-18:30
Wednesday, January 26, 17:00-18:30
Thursday, January 27, 17:00-18:30
Topics
Lecture 1: Riemann surfaces and their moduli
Lecture 2: Parabolic vector bundles on a Riemann surface and their moduli
Lecture 3: Analytic geometry of moduli spaces
Lecture 4: The idea of a conformal field theory. A geometric interpretation
Lecture 5: The compact WZNW model and isomonodromy
Lecture 6: The Verlinde formula and relation to 2d quantum Yang-Mills theory
Lecture 7: Liouville theory, Fuchsian uniformization, and the Weil-Petersson metric
Lecture 8: A non-compact WZNW action, Fuchsian systems, and the Narasimhan-Atiyah-Bott metric
*Participants will receive Zoom log in information by e-mail. In order to receive Zoom log in information, please send an e-mail to Prof. Martin Guest (martin at waseda.jp) stating your name, university affiliation, and position/student status.
