Fachbereich Mathematik 
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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 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 degenerations [1], §7, p.27-28
16-01-2020 Johannes Berger The dual intersection complex [1], §7, p.28(end)-31
23-01-2020 Nicolas Ramirez Diaz The intersection complex [1], §7, p.32-33;
30-01-2020 The discrete Legendre transform and the reconstruction problem [1], §7, p.33-35; [5], §1.5

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:

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


 
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