Universität Wien
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250131 VO Symplectic Geometry (2023W)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik
ON-SITE

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

There will be a make-up class on Tuesday Dec 5, 9:45am-11:15am, in Seminarraum 7 in OMP. (NB: there is no geometry & topology seminar that day.)

I will be at a conference on Tuesday January 30th. The class will either be cancelled or there will be a guest lecturer: to be confirmed at a later date.

  • Tuesday 03.10. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.10. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 17.10. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 24.10. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 31.10. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 07.11. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 14.11. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 21.11. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 28.11. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 05.12. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 12.12. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 09.01. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 16.01. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 23.01. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 30.01. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This is a masters course in symplectic geometry. It will be taught by lectures (blackboard, no printed notes). It will assume some knowledge of algebraic topology and differential geometry (at the level of an advanced undergraduate course); a little knowledge of algebraic geometry would be useful but is not required.

The course will start with some fundamental notions in symplectic topology: symplectic linear algebra; Hamilton’s equations, cotangent bundles; Lagrangian submanifolds; symplectic submanifolds; Moser’s trick, Darboux and Weinstein neighbourhood theorems; almost complex structures and compatible triples; basic examples and properties of Kaehler manifolds.

Time allowing, and depending on the background and intellectual interests of the audience, the lectures will cover some of the following topics:
-- Surgery constructions: blow ups, symplectic fibre sums.
-- Lefschetz pencils, Gompf's theorem on fundamental groups of symplectic 4-manifolds
-- Weinstein manifolds, Lefschetz fibrations
-- introduction to symplectomorphism groups
-- introduction to Floer theory
-- introduction to homological mirror symmetry
-- further possible topics as determined in consultation with the audience

Assessment and permitted materials

The course will be assessed orally (exposition at the board). Students may use pre-prepared personnal notes, though should demonstrate good independent command of the material.

Update (14.12.2023). The course will be examined by a 30min oral exam, at the board in my office.

Minimum requirements and assessment criteria

The course will be assessed orally (blackboard). The criteria for individual grades will be in line with those applied for other masters courses in pure mathematics.

Update (14.12.2023). I expect any student who is able to solve the exercises / problems which were given during the lectures will be able to pass the course comfortably. Please email me if you would like a standalone copy of these exercises.

Examination topics

The oral assessments will be on a range of pre-assigned topics, the list of which will be drawn up during the semester (and subsequently available upon request).

Update (14.12.2023). The topics lectured up until the Christmas break are examinable. (The January lectures will be more advanced and not for examination.) Please contact me if you require a list of topics.

Reading list

There is no required text. Some suggested reading:

First part of the course:
-- Introduction to symplectic topology (McDuff and Salamon)
-- Lectures on symplectic topology (Cannas da Silva)

For later parts of the course, possibilities include:
-- graduate lecture notes by Auroux and by Sheridan on mirror symmetry
-- Auroux, "Beginner's guide to Fukaya categories"
-- MacDuff-Salamon, "Introduction to J-holomorphic curves"
-- Audin-Damian, "Morse theory and Floer theory"
-- Evans, "Lectures on Lagrangian torus fibrations"

Association in the course directory

MGEV

Last modified: Tu 05.03.2024 13:26