André Gama Oliveira's Annual Report

André Gama Oliveira's Annual Report

Year: 

2017

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

Title:
Topological mirror symmetry for parabolic Higgs bundles
Name of the event:
Workshop / Conference on Character Varieties and String Theory
Speakers
André Gama Oliveira
Talk:
Invited talk
Date:
20.03.2017 to 24.03.2017
Host institution:
Indian Institute of Science
Country:
India
Location / City:
Bangalore
Title:
Topological mirror symmetry, fixed points and branes
Name of the event:
Workshop / Conference on 80th birthday of S. Ramanan
Speakers
André Gama Oliveira
Talk:
Invited talk
Date:
06.11.2017 to 08.11.2017
Host institution:
ICMAT
Country:
Spain
Location / City:
Madrid

Seminars

Title:
Parabolic Higgs bundles and topological mirror symmetry
Speakers
André Gama Oliveira
Date:
21.02.2017
Host institution:
Instituto Superior Técnico
Country:
Portugal
Location / City:
Lisboa
Title:
Higgs bundles and the beauty of unexpected connections in Mathematics
Speakers
André Gama Oliveira
Date:
28.11.2017
Host institution:
Faculdade de Ciências da Universidade do Porto
Country:
Portugal
Location / City:
Porto

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.

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