Vorlesung + Übung: Holomorphic Curves and Quantum Cohomology - Details

General information

Course name	Vorlesung + Übung: Holomorphic Curves and Quantum Cohomology
Course number	MTH-2340
Semester	SS 2025
Current number of participants	18
Home institute	Analysis und Geometrie
participating institutes	Institut für Mathematik
Courses type	Vorlesung + Übung in category Teaching
First date	Thursday, 24.04.2025 08:15 - 09:45
Veranstaltung findet in Präsenz statt / hat Präsenz-Bestandteile	Yes
Hauptunterrichtssprache	englisch
ECTS points	9

Lecturers

• Emilia Konrad
• Prof.Dr. Urs Frauenfelder

Tutors

• Zhen Gao
• Ph.D. Filip Brocic

Rooms and times

(1007/L)

Monday: 12:15 - 13:45, weekly (12x)

Thursday: 15:45 - 17:15, weekly (11x)

(1008/L)

Thursday: 08:15 - 09:45, weekly (10x)

No room preference

Thursday: 08:15 - 09:45, weekly

(2004/L)

Friday: 12:15 - 13:45, weekly (14x)

Fields of study

• Mathematisch-Naturwissenschaftlich-Technische Fakultät > Institut für Mathematik
• Mathematisch-Naturwissenschaftlich-Technische Fakultät > Institut für Mathematik > Master Mathematik

Module assignments

• Mathematik Masterstudiengang Mathematik PO 2013, 19. Version valid from WS 2024/25 > Master Mathematik A: Wahlpflichtbereich Mathematik > MTH-2340 - Holomorphic curves - an introduction to the modern methods of symplectic geometry > Holomorphic curves
• Mathematik Masterstudiengang Mathematik PO 2013, 19. Version valid from WS 2024/25 > Master Mathematik D: Wahlbereich > MTH-2340 - Holomorphic curves - an introduction to the modern methods of symplectic geometry > Holomorphic curves
• Mathematik Masterstudiengang Mathematik PO 2013, 20. Version valid from SS 2025 > Master Mathematik D: Wahlbereich > MTH-2340 - Holomorphic curves - an introduction to the modern methods of symplectic geometry > Holomorphic curves
• Mathematik Masterstudiengang Mathematik PO 2013, 20. Version valid from SS 2025 > Master Mathematik A: Wahlpflichtbereich Mathematik > MTH-2340 - Holomorphic curves - an introduction to the modern methods of symplectic geometry > Holomorphic curves

Comment/Description

What is this course about?

1. Holomorphic curves: First, we will study holomorphic curves (i.e "special" maps from Riemann surfaces to symplectic manifolds) and their moduli spaces. As an application, we will have a look at M. Gromov's original proof of his famous Non-Squeezing Theorem.

2. Gromov-Witten invariants: With our obtained knowledge, we can define invariants connected to Enumerative Geometry by "counting holomorphic curves".

3. Quantum Cohomology: On the cohomology of a symplectic manifold, a "deformed cup product" is constructed using the GW-invariants. From this vantage point, we will explore the famous Mirror Symmetry Conjecture from theoretical physics.

Admission settings

The course is part of admission "Anmeldung gesperrt (global)".

The following rules apply for the admission:

• Admission locked.