6 EC
Semester 1, period 1, 2
5324TFMS6Y
| Owner | Master Mathematics |
| Coordinator | prof. dr. S. Shadrin |
| Part of | Master Mathematics, year 1Master Mathematical Physics, year 1 |
We'll discuss the structure of the moduli spaces of curves from different points of view. We'll see how the information about the topology of moduli spaces emerges in different ways as a system of the universal properties of different families of topological field theories. In particular, we'll give an introduction to the Gromov-Witten theory, Batalin-Vilkovisky algebras, integrable hierarchies of hydrodynamic type, and Givental's formalism.
Study materials will be advised after each lecture.
Understanding of the interplay of the algebraic structures behind the topology of the moduli spaces of curves and topological field theories. The goal is to achieve the level that allows to read and understand recent research papers on these subjects.
Lectures: general introduction to all necessary diverse concepts.
Self-study: these are homeworks and extra reading that are necessary to make the theory more clear and precise.
Presentation/symposium: at the end of the course every student will get a recent research paper to prepare a presentation for the other students. The goal is to learn to read recent research articles on the topics of the course
|
Activity |
Number of hours |
|
Lectures |
14 |
|
Presentations |
4 |
|
Zelfstudie |
150 |
|
Total |
168 |
The programme does not have requirements concerning attendance (OER-B).
Additional requirements for this course:
Additional requirements for this course:
No additional requirements.
| Item and weight | Details |
|
Final grade | |
|
20% Homeworks | |
|
80% Presentation | Must be ≥ 5 |
The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.uva.nl/plagiarism
| Weeknummer | Onderwerpen | Studiestof |
| 1 | Genus 0 and genus 1 moduli | |
| 2 | Topology on the space of curves, nodal curves | |
| 3 | Dual graphs, stratification, natural maps | |
| 4 | CohFT and TFT, Keel's theorem | |
| 5 | Universal curve, genus 0 examples | |
| 6 | Psi-classes | |
| 7 | Topological recursion, WDVV and string equations | |
| 8 | ||
| 9 | Tautological ring, kappa classes | |
| 10 | Topological recursion relations for correlators | |
| 11 | Dependant variables of integrable systems | |
| 12 | Examples of CohFT's and their enumerative meaning | |
| 13 | Poisson geometry and hydrodynamics | |
| 14 | Miura transformation and higher genera | |
| 15 | BV algebras, BCOV theory, Gromov-Witten theory | |
| 16 |
The schedule for this course is published on DataNose.
The required background for this course: an overall good understanding of algebra, geometry, and topology.