PhD Seminar — Winter Term 2019
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Mathematics Department, research areas Algebra and Number Theory, Analysis and
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This semester's topic is: Mirror symmetry and the StromingerYauZaslow conjecture
After last semester's seminar about Electromagnetic Duality, we now turn to the geometry underlying mirror symmetry. The StromingerYauZaslow conjecture predicts that mirror dual CalabiYau 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 GrossSiebert program, an algebrogeometric version of the StromingerYauZaslow conjecture.
The seminar will take place on Thursdays, 12:00  13:00 in room 1643 (Geomatikum).
Date 
Speaker 
Title 
Material 
17102019

Tim Gabele

An invitation to SYZ and GS

[1]; Notes

24102019

Tim Gabele

Varieties and manifolds

[2]

31102019


Reformation Day; no seminar


07112019

Áron Szabó

Kähler and CalabiYau manifolds

[3], §5

14112020


Conference of academic personnel (KAP); no seminar


21112019

Arpan Saha

Moduli of special Lagrangian submanifolds

[1], §1; [4],§6.1

28112019

Manasa Manjunatha

Semiflat mirror symmetry

[1], §2; [4],§6.2

05122019

Vincentas Mulevičius

Affine manifolds with singularities and tropical curves

[1], §3+4; [5], §1.11.4+1.6; [6]

12122019

David Krusche

The problems with the SYZ conjecture and how to get around them

[1], §5

19122019


GromovHausdorff limits and algebraic degenerations

[1], §6

26122019


Christmas holiday; no seminar


02012020


Christmas holiday; no seminar


09012020

Vadym Kurylenko

Toric degenerations

[1], §7, p.2728

16012020

Johannes Berger

The dual intersection complex

[1], §7, p.28(end)31

23012020

Nicolas Ramirez Diaz

The intersection complex

[1], §7, p.3233;

30012020


The discrete Legendre transform and the reconstruction problem

[1], §7, p.3335; [5], §1.5

Literature:
We plan to stick rather closely to a paper by Mark Gross:
[1] Mirror symmetry and the StromingerYauZaslow conjecture
The following references might also be useful in preparing the talks:
 SYZ mirror symmetry for toric CalabiYau manifolds, by Kwokwai Chan, SiuCheong Lau and Naichung Conan Leung
 Gross fibrations, SYZ mirror symmetry, and open GromovWitten invariants for toric CalabiYau orbifolds, by Kwokwai Chan, Cheol Hyun Cho, SiuCheong Lau, HsianHua Tseng
 Large complex structure limits of K3 surfaces, by Mark Gross and P.M.H. Wilson
 Affine structures and nonarchimedean 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
