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Higgs bundles in mathematics and physics summer school

10-14 of September 2018
Hamburg

Higgs bundles were introduced by Nigel Hitchin in 1987 while studying the dimensional reduction of the self-duality equations from four to two dimensions. Higgs bundles on Riemann surfaces and their moduli spaces have a rich mathematical structure. They are important for a number of research areas such as gauge theory, Kähler and hyperkähler geometry, integrable systems as well as mirror symmetry and Langlands duality.

This 5-day summer school is addressed to students and researchers in differential geometry, algebraic geometry, theoretical physics and related areas. There will be a number of introductory mini courses covering different aspects of Higgs bundles.

The school poster is available here.

The school programme will be available here.

List of speakers, titles and abstracts:

Laura Fredrickson


Oscar García-Prada

Higgs bundles and higher Teichmueller spaces


Tamás Hausel

Topological mirror symmetry for Hitchin systems

1. Definitions: Higgs bundles and their moduli spaces for GL, SL and PGL
2. Hitchin system, and dual SYZ fibrations
3. Cohomology and (stringy) Hodge numbers, topological mirror symmetry
4. Toy example of topological mirror symmetry
5. (stringy) Cohomology of Higgs moduli spaces, computation for SL_2 PGL_2
6. Sketch of proof for SL_n vs PGL_n by p-adic integration
7. Mirror symmetry with branes by equivariant Verlinde formulae

Nigel Hitchin

Gregory Moore

Theories of class S and their associated Hitchin systems
Reading Material:
1. talks 46 and 47. (71 is a colloquium-level introduction.)
2. Tachikawa's review

Richard Wentworth


Registration and financial support:

Please fill out this form to register. The registration fee is 30 euros, payable on arrival. There will be a social dinner on Wednesday evening. Please indicate on the registration form if you would like to attend the dinner. The dinner will cost an additional 20 euros.

For a limited number of participants we can offer a contribution up to 400 euros to their expenses. You can apply for financial support on the registration form. If you are a student applying for a financial contribution, please arrange for a short letter of support from your advisor to be sent to higgs2018.math [at] lists [dot] uni-hamburg [dot] de.

The deadline for registration is 1 August 2018.
The deadline for applying for financial support is 30 June 2018.

Poster Session:

A poster session will take place on Tuesday afternoon. Participants of the school are welcome to submit their applications for the poster session. Title and abstract of the poster should be sent to higgs2018.math [at] lists [dot] uni-hamburg [dot] de by July 8th, 2018. The applicants will then be notified of the acceptance of their posters.

Venue:

The summer school will take place in the Department of Mathematics, Bundesstr. 55, of the University of Hamburg. Here is a map. The closest metro station is "Schlump" on the red line U2 and the yellow line U3. The train station "Sternschanze" (train lines S11, S21 and S31) is also in walking distance. Here is the website for public transport in Hamburg.

Accommodations:

Participants of the summer school are kindly asked to arrange their accommodation on their own. Here is a list of some hotels.

Introductory course in Hamburg:

During the week preceding the summer school there will be an introductory block course of 14 hours on Higgs bundles. This course is aimed for graduate students and researchers in Hamburg as a preparation for the summer school but is open for other participants of the summer school as well. The homepage of the course is here. This course does not require registration, however please send an email to murad.alim_at_uni-hamburg.de if you plan to attend so we can have an estimate of the number of participants.


Organizers:

Murad Alim, Vicente Cortés, Sebastian Heller, Jörg Teschner

If you have any questions or special needs, please feel free to contact the organizers at higgs2018.math [at] lists [dot] uni-hamburg [dot] de.

Sponsored by:
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Verein zur Ausrichtung von Tagungen am Fachbereich Mathematik der Universität Hamburg (VATFBMUHH) e.V.



 
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