Higgs Bundles and Character Varieties

A satellite GEAR workshop and Special Session of the
Joint International Meeting of the AMS, EMS and SPM, Porto, June 2015.

Main themes

asymptotics (of Higgs fields),
topology of moduli/character varieties, and
branes (including moduli of G-Higgs bundles for real G).

There will also be space for other approaches to character varieties, as well as other aspects of Higgs bundle theory.

Tuesday, June 9, 2015

A day of introductory overview talks.

Schedule – Room M030

10:00-11:00 Richard Wentworth (Maryland): Higgs bundles at the Fuchsian locus.
11:00-11:30 Coffee
11:30-12:30 Jochen Heinloth (Duisburg-Essen): Introduction to the geometry of moduli of Higgs bundles. Slides.
12:30-14:30 Lunch
14:30-15:30 Ludmil Katzarkov (Vienna): Harmonic maps to buildings and categories.
15:30-16:00 Break (main meeting welcome reception)
16:00-17:00 Sergei Gukov (Caltech): Equivariant integration over moduli space of Higgs bundles from cutting and gluing. Slides.
20:00- Workshop dinner at Madureira's Restaurant (please register by e-mail to pbgothen@fc.up.pt).

Special Session: June 10, 11 and 12, 2015

The official schedule of the special session, including titles and abstracts, can be found here: Schedule of special session 27.

Wednesday June 10, 2015 – 13:00-15:30 – Room M005

13:00-13:20 Vicente Muñoz (Universidad Complutense de Madrid & ICMAT): Geometric techniques for character varieties. Slides.
13:30-13:50 Graeme Wilkin (National University of Singapore): Morse theory for Higgs bundles.
14:00-14:20 Sean Lawton (George Mason University): Homotopy groups of character varieties. Slides.
14:30-14:50 Steven Rayan (Toronto): Hyperpolygons and Hitchin systems. Slides.
15:00 Coffee.

Thursday June 11, 2015 – 9:00-12:00 – Room M005

9:00-9:20 Laura Schaposnik (UIUC): Higgs bundles, spectral data, and applications. Slides.
9:30-9:50 Marina Logares (ICMAT, Madrid): Bohr-Sommerfeld Lagrangians for the moduli space of Higgs bundles. Slides.
10:00-10:20 Alfonso Zamora (Instituto Superior Técnico, Lisbon): GIT characterizations of Harder-Narasimhan filtrations. Slides.
10:20-11:00 Coffee.
11:00-11:20 Ana Peon-Nieto (Heidelberg): Quasi-split real groups and the Hitchin map. Slides.
11:30-11:50 Javier Martínez (Universidad Complutense de Madrid): E-polynomials of SL(2,C)-character varieties. Slides.

Friday June 12, 2015 – 9:00-12:30 – Room M122

9:00-9:20 Brian Collier (UIUC): A mapping class group invariant parameterization of maximal Sp(4,R) representations. Slides.
9:30-9:50 Hartmuth Weiss (Munich): Ends of moduli spaces of Higgs bundles. Slides.
10:00-10:20 Qiongling Li (Rice): Asymptotics of certain families of Higgs bundles. Slides.
10:20-11:00 Coffee.
11:00-11:20 Susana Ferreira (Instituto Politécnico de Leiria): Schottky bundles. Slides.
11:30-11:50 Mario García-Fernández (ICMAT, Madrid): Balanced metrics on twisted Higgs Bundles. Slides.
12:00-12:20 Richard Wentworth (Maryland): Deligne pairings and holomorphic extension of analytic torsion.

Social Programme

Room M113 in the Mathematics Department will be open for participants to use for discussions etc. throughout the workshop.
We will organize a workshop dinner on Tuesday, June 9 at Madureira's Restaurant, which is very near the Mathematics Department. If you wish to participate, please let us know by e-mail to pbgothen@fc.up.pt.

Registration

The talks on Tuesday, June 9 are open to all, but we request that those planning to attend send an e-mail to pbgothen@fc.up.pt stating their intention to do so.

All participants (including speakers) in the special session are required to register for the AMS-EMS-SPM meeting.

Deadline for registration: May 30, 2015.

Practical Information

Wifi access: if your institution participates in the eduroam network we recommend signing up for an account with your university's computing services for (hopefully) trouble free wifi access while you're in Porto.
Here is a google map showing the location of the Mathematics Department, Madureira's Restaurant and a couple of the most popular hotels.
Please see the page of the Joint International Meeting of the AMS, EMS and SPM for further practical information, including accommodation etc.