Non-abelian Hodge theory and higher Teichmüller spaces

Time:Tues., 4:00 pm-5:00 pm, Oct.18,2022

Venue:Zoom Meeting ID: 271 534 5558 Passcode: YMSC

Speaker:Prof. Oscar García-Prada (Instituto de Ciencias Matemáticas)


Non-abelian Hodge theory relates representations of the fundamental group of a compact Riemann surface X into a Lie group G with holomorphic objects on X known as Higgs bundles, introduced by Hitchin more than 35 years ago. Starting with the case in which G is the circle, and the 19th century Abel-Jacobi's theory, we will move to the case of G=SL(2,R) and the relation to Teichmüller theory. We will then explain how, using Higgs bundles, one can construct generalizations of the classical Teichmüller space for certain Lie groups of higher rank.

Oscar García-Prada is a CSIC Research Professor at Instituto de Ciencias Matemáticas in Madrid. He obtained a D.Phil. in Mathematics at the University of Oxford in 1991, under the supervision of Nigel Hitchin and Simon Donaldson,and had postdoctoral appointments at Institut des Hautes Études Scientific (Paris), University of California at Berkeley, and Université de Paris-Sud, before holding positions at Universidad Autónoma de Madrid and École Polytéchnique (Paris). In 2002 he joined the Spanish National Research Council (CSIC). His research interests lie in the interplay of differential and algebraic geometry with differential equations of theoretical physics, more concretely, in the study of moduli spaces and geometric structures. The moduli spaces considered involve objects such as vortices, solutions to general gauge-theoretic equations, Higgs bundles and representations of surface groups and fundamental groups of higher dimensional Kaehler manifolds. He participates regularly in public outreach activities on mathematics and its interactions with physics and music, collaborating with main Spanish newspapers, radio and television.

DATESeptember 29, 2022
Related News
    • 0

      Spaces of norms and Geometric Invariant Theory

      SpeakerSebastien Boucksom is a French mathematician specializing in complex and non-Archimedean geometry. After defending his PhD thesis in 2002 under the supervision of Jean-Pierre Demailly, he became a CNRS Junior Researcher at the Institut de Mathematiques de Jussieu in 2003, then a CNRS Senior Researcher in 2014, first at the Ecole Polytechnique, and then at the Institut de Mathematiques de...

    • 1

      Modern Mathematics Lecture Series | Dynamics on character varieties and Hodge theory

      AbstractLet X_n be the set of tuples of 2x2 matrices (A_1, A_2, ..., A_n) such that the product A_1...A_n is the identity matrix, and considered up to simultaneous conjugation. On each X_n, there is a very classical and explicit action of the so-called braid group B_n. This is an elementary case of the so-called mapping class group action on the character varieties of surface groups, and was st...