# Mathematical Sciences Research Institute

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# Workshop

Dynamics on Moduli Spaces April 13, 2015 - April 17, 2015
To apply for Funding you must register by: January 13, 2015 over 4 years ago
Parent Program: Dynamics on Moduli Spaces of Geometric Structures MSRI: Simons Auditorium, Atrium
Organizers Marc Burger (ETH Zürich), LEAD David Dumas (University of Illinois at Chicago), Olivier Guichard (Université de Strasbourg I (Louis Pasteur)), François Labourie (Université Côte d'Azur), Anna Wienhard (Ruprecht-Karls-Universität Heidelberg)
Speaker(s)

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Description
The Research Workshop of the Dynamics on moduli spaces of geometric structures'' will concentrate on some of the following general interrelated themes: (1) Geometric structures on the spaces of geometric structures which extend and generalize classical constructions on Teichmüller spaces, such as the Weil-Petersoon metric, the pressure metric, the Teichmüller metric and its geodesic flow, Fenchel-Nielsen coordinates, Fock-Goncharov Thurson-Penner coordinates, and the symplectic and Poisson  geometries (2) Relations with harmonic maps, Riemann surfaces, complex geometry:  specifically Higgs  bundles, holomorphic differentials (quadratic, cubic, etc.) as parameters  for representations  of the fundamental group, hyperkähler and complex symplectic geometry of  moduli spaces,   lifts of Teichmüller geodesic flows to flat bundles of character varieties (3) Asymptotic properties of higher Teichmüller spaces, including generalized measured geodesic laminations, Culler-Morgan-Shalen asymptotics of character varieties, degenerations of geometric structures and discrete subgroups (4) Actions of mapping class groups and outer automorphism groups,  properness criteria for Anosov representations and their generalizations,  properness criteria for non-discrete representations, chaotic actions of  mapping class groups and the monodromy map from structures to  representations (5) Classification of exotic geometric structures, tameness criteria, generalizations of ending lamination-type invariants to higher rank structures, rigidity and flexibility for thin subgroups, arithmeticity conditions, and geometric transitions Reimbursement Forms: MSRI Per Diem MSRI Travel GEAR Reimbursment Form Bibliography (PDF)
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Funding & Logistics

## Show Funding

To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

## Show Lodging

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link. Click on "Promo/Corporate Code" at the top of the page. When prompted, select the "Promo/Corporate Code" option and enter the code 123MSRI (this code is not case sensitive). Our lowest preferred rate is $139 per night for a Deluxe Queen, based on availability. MSRI has a preferred rate of$174 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount. To book online visit this page. You must select "My dates are: Firm" in order to use the promotional code. Click on "Promo/Corporate Code" at the top of the page. When prompted, select the "Promo/Corporate Code" option and enter the code MSRI (this code is not case sensitive).

MSRI has preferred rates of $130 -$160 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with the Space Sciences Lab, Lawrence Hall of Science or MSRI.” When prompted for your UC Contact/Host, please list Chris Marshall (coord@msri.org).

Additional lodging options may be found on our short term housing page.

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Schedule, Notes/Handouts & Videos
Show Schedule, Notes/Handouts & Videos
Apr 13, 2015
Monday
 09:15 AM - 09:30 AM Welcome 09:30 AM - 10:30 AM Convergence of quasifuchsian hyperbolic 3-manifolds Richard Canary (University of Michigan) 10:30 AM - 11:00 AM Tea 11:00 AM - 12:00 PM The (asymptotic) location of eigenvalues of a representation in the Hitchin component Andrés Sambarino (Université de Paris VII (Denis Diderot) et Université de Paris VI (Pierre et Marie Curie)) 12:00 PM - 02:00 PM Lunch 02:00 PM - 03:00 PM A collar lemma for Hitchin representations Tengren Zhang (University of Michigan) 03:00 PM - 03:30 PM Tea 03:30 PM - 04:30 PM Maximal representations of complex hyperbolic lattices Maria Beatrice Pozzetti (Ruprecht-Karls-Universität Heidelberg)
Apr 14, 2015
Tuesday
 09:30 AM - 10:30 AM The action of a pseudo-Anosov on the Hitchin component Francis Bonahon (University of Southern California) 10:30 AM - 11:00 AM Tea 11:00 AM - 12:00 PM Anosov representations and proper actions Fanny Kassel (Institut des Hautes Études Scientifiques (IHES)) 12:00 PM - 02:00 PM Lunch 02:00 PM - 03:00 PM Coordinates for representation varieties of 3-manifold groups Christian Zickert (University of Maryland) 03:00 PM - 03:30 PM Tea 03:30 PM - 04:30 PM Buildings, spectral networks, and the Riemann-Hilbert correspondence at infinity Pranav Pandit (International Centre for Theoretical Sciences) 04:30 PM - 06:20 PM Reception
Apr 15, 2015
Wednesday
 09:30 AM - 10:30 AM Three proofs from dynamics of rigidity of surface group actions Kathryn Mann (University of California, Berkeley) 10:30 AM - 11:00 AM Tea 11:00 AM - 12:00 PM Entropy of pseudo-Anosovs which fix homology Ian Agol (University of California, Berkeley)
Apr 16, 2015
Thursday
 09:30 AM - 10:30 AM Non archimedean representations of surface groups in PGL(3) and A2-Euclidean buildings Anne Parreau (Université de Grenoble I (Joseph Fourier)) 10:30 AM - 11:00 AM Tea 11:00 AM - 12:00 PM Degeneration of real projective structures on open surfaces Daniele Alessandrini (Ruprecht-Karls-Universität Heidelberg) 12:00 PM - 02:00 PM Lunch 02:00 PM - 03:00 PM Asymptotic Behavior of Certain Families of Higgs bundles in Hitchin Components Qiongling Li (Chern Institute of Mathematics) 03:00 PM - 03:30 PM Tea 03:30 PM - 04:30 PM A transfer principle: from periods to isoperiodic foliations Bertrand Deroin (École Normale Supérieure)
Apr 17, 2015
Friday
 09:30 AM - 10:30 AM Affine sieve and expansion in linear groups Alireza Salehi Golsefidy (University of California, San Diego) 10:30 AM - 11:00 AM Tea 11:00 AM - 12:00 PM Dynamics and geometry of the Weil Petersson metric Ursula Hamenstädt (Rheinische Friedrich-Wilhelms-Universität Bonn) 12:00 PM - 02:00 PM Lunch 02:00 PM - 03:00 PM Counting closed geodesics on a hyperbolic surface Maryam Mirzakhani (Stanford University)