PhD Seminar — Winter Term 2019
This is the the website of the seminar of the PhD students of the
Mathematics Department, research areas Algebra and Number Theory, Analysis and
Differential Geometry and the RTG1670 of the University of Hamburg. If you want to subscribe to the
mailing list please go to the mailing list's
website.
This semester's topic is: Mirror symmetry and the Strominger-Yau-Zaslow conjecture
After last semester's seminar about Electromagnetic Duality, we now turn to the geometry underlying mirror symmetry. The Strominger-Yau-Zaslow conjecture predicts that mirror dual Calabi-Yau manifolds admit dual special Lagrangian torus fibrations. In the seminar we will learn what this means and how one can construct the mirror using the Gross-Siebert program, an algebro-geometric version of the Strominger-Yau-Zaslow conjecture.
The seminar will take place on Thursdays, 12:00 - 13:00 in room 1643 (Geomatikum).
Date |
Speaker |
Title |
Material |
17-10-2019
|
Tim Gabele
|
An invitation to SYZ and GS
|
[1]; Notes
|
24-10-2019
|
Tim Gabele
|
Varieties and manifolds
|
[2]
|
31-10-2019
|
|
Reformation Day; no seminar
|
|
07-11-2019
|
Áron Szabó
|
Kähler and Calabi-Yau manifolds
|
[3], §5
|
14-11-2020
|
|
Conference of academic personnel (KAP); no seminar
|
|
21-11-2019
|
Arpan Saha
|
Moduli of special Lagrangian submanifolds
|
[1], §1; [4],§6.1
|
28-11-2019
|
Manasa Manjunatha
|
Semi-flat mirror symmetry
|
[1], §2; [4],§6.2
|
05-12-2019
|
Vincentas Mulevičius
|
Affine manifolds with singularities and tropical curves
|
[1], §3+4; [5], §1.1-1.4+1.6; [6]
|
12-12-2019
|
David Krusche
|
The problems with the SYZ conjecture and how to get around them
|
[1], §5
|
19-12-2019
|
Duong Dinh
|
Gromov-Hausdorff limits and algebraic degenerations
|
[1], §6
|
26-12-2019
|
|
Christmas holiday; no seminar
|
|
02-01-2020
|
|
Christmas holiday; no seminar
|
|
09-01-2020
|
Vadym Kurylenko
|
Toric varieties and toric degenerations
|
[1], §7, p.27-28
|
16-01-2020
|
Johannes Berger
|
The dual intersection complex
|
[1], §7, p.28(end)-31
|
23-01-2020
|
|
no seminar
|
|
30-01-2020
|
Arpan Saha
|
Concluding talk
|
|
Literature:
We plan to stick rather closely to a paper by Mark Gross:
[1] Mirror symmetry and the Strominger-Yau-Zaslow conjecture
The following references might also be useful in preparing the talks:
- SYZ mirror symmetry for toric Calabi-Yau manifolds, by Kwokwai Chan, Siu-Cheong Lau and Naichung Conan Leung
- Gross fibrations, SYZ mirror symmetry, and open Gromov-Witten invariants for toric Calabi-Yau orbifolds, by Kwokwai Chan, Cheol Hyun Cho, Siu-Cheong Lau, Hsian-Hua Tseng
- Large complex structure limits of K3 surfaces, by Mark Gross and P.M.H. Wilson
- Affine structures and non-archimedean analytic spaces, by Maxim Kontsevich and Yan Soibelman
Additional references for the individual talks are the following:
[2] Algebraic geometry, by Andreas Gathmann
[3] Mirror symmetry, book by several authors
[4] Dirichlet branes and mirror symmetry, book by several authors
[5] Tropical geometry and mirror symmetry, book by Mark Gross
[6] Tropical algebraic geometry, by Andreas Gathmann
Organizers: Tim Gabele and Arpan Saha.
Previous seminars:
Winter term 2014
Summer term 2015
Winter term 2015
Summer term 2016
Winter term 2016
Summer term 2017
Winter term 2017
Summer term 2018
Winter term 2018
Summer term 2019
|