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	17
Home institute	Analysis und Geometrie
participating institutes	Institut für Mathematik
Courses type	Vorlesung + Übung in category Teaching
Next date	Monday, 28.04.2025 12:15 - 13:45, Room: (1007/L)
Veranstaltung findet in Präsenz statt / hat Präsenz-Bestandteile	Yes
Hauptunterrichtssprache	englisch
ECTS points	9

Lecturers

• Martin 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.