André Gama Oliveira's Annual Report
Year:
Brief description of the research activities:
Study of geometric, topological and algebraic structures of moduli spaces of G-Higgs bundles over Riemann surfaces (compact or not), with G being a real reductive Lie group.
More precisely, the following subjects were studied/developed:
- Proof of the equality of the stringy E-polynomials of the moduli spaces of parabolic SL(n,C) and PGL(n,C)-Higgs bundles, when n=2,3 and of any degree and proof of results which allow to conjecture that the same holds for any n. Joint work with P. Gothen (CMUP).
- Conclusion of the proof of the existence of exotic connected components of the moduli space of SO(p,q)-Higgs bundles, and subsequent full count of its connected components. When p>q+1 and p>2, this is the first example of non-split and non-hermitian groups for which these components occur. Joint work in progress with M. Aparicio-Arroyo, S. Bradlow (Illinois), B. Collier (Maryland), O. García-Prada (ICMAT) and P. Gothen (CMUP).
- Description of new families of BBB- and BAA-branes on the moduli space of GL(n,C)-Higgs bundles, and proof that these two families are dual in the sense of mirror symmtery, by providing an explicit Fourier-Mukai transform interchanging both. Joint work in progress with E. Franco (CMUP), P. Gothen (CMUP) and A. Peón (Nice).
Talks / Seminars / Courses :
Communications in international conferences
Seminars
Organization of regular seminars:
Organizer of the regular CMUP's Geometry and Topology seminar.
Outreach activities:
``Formas and (de)formas'' -- seminário de 1 hora, dirigido a estudantes do Ensino Secundário, introduzindo factos básicos de Topologia e incluído na Escola de Verão de Matemática da Faculdade de Ciências da Universidade do Porto -- 05 Setembro 2017
Work visits:
-- Instituto de Ciencias Matematicas (ICMAT), Madrid, Spain, 6-10 November 2017.
-- University of Illinois at Urbana Champaign, USA, 30 April to 7 May 2017.
-- Faculdade de Ciências da Universidade de Lisboa, Portugal, 21-24 February 2017.