PhD Seminar — Winter Term 2019
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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
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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
|
