Peter Gothen's Annual Report 2013

Peter Gothen's Annual Report 2013

Year: 

2013

Brief description of the research activities: 

Study of geometric and topological properties of moduli spaces of Higgs bundles.

Projects description: 

- Principal Investigator in the project Topological Invariants via Differential Geometry (PTDC/MAT/
098770/2008; 22/03/2010–21/09/2013). Project funded by the Portuguese Science Foundation (FCT) total approved funding: 100.000€
over three and a half years (2010–2013); number of researchers: 9.

External projects: 

- Member of the Steering Committee of the European Research Council research network ITGP – Interactions of Low-Dimensional Topology and Geometry with Mathematical Physics. http://www.itgp.net

- Member of the Scientific Committee of the European research group Vector Bundles on Algebraic Curves (VBAC).

- Member of the project Algebraic Geometry in Portugal (PTDC/MAT/099275/2008; 25/01/2010-24/01/2013). Project co-ordinated by Prof. Margarida Mendes Lopes (Instituto Superior Técnico, Lisbon) and funded by the Portuguese Science Foundation (FCT).

- Member of the project Portuguese Algebraic Geometry Community (PTDC/MAT-GEO/0675/2012; 26/07/2013-25/07/2015). Project coordinated by Prof. Margarida Mendes Lopes (Instituto Superior Técnico, Lisbon) and funded by the Portuguese Science Foundation (FCT); total funding: 83.000€.

Preprints: 

Higgs bundles for the non-compact dual of the special orthogonal group

Articles in international peer reviewed journals : 

From singularity theory to finiteness of Walrasian equilibria
Higgs bundles and surface group representations in the real symplectic group
The singular fiber of the Hitchin map

Papers accepted for publication in peer reviewed journals: 

Peter Gothen

Communications in international conferences : 

Authors: 

Peter Gothen

Title: 

Higgs bundles and SO∗

Name of the event: 

Workshop on Moduli Spaces and Mathematical Physics

Host institution: 

CIMAT

Start and end date: 

Monday, 28 January, 2013 to Saturday, 2 February, 2013

Location / City: 

Guanajuato

Country: 

Mexico

Authors: 

Peter Gothen

Title: 

Morse theory on the moduli of Higgs bundles

Name of the event: 

Nigel Hitchin LAB Retreat: Topology of moduli spaces of representations

Host institution: 

ICMAT

Start and end date: 

Monday, 11 March, 2013 to Friday, 15 March, 2013

Location / City: 

Miraflores de la Sierra

Country: 

Spain

Talks / Seminars / Courses : 

Title:
Representations of fundamental groups of surfaces: algebra, geometry and algebraic geometry
Name of the event:
22/05/2013
Speakers
Peter Gothen
Country:
Portugal
Location / City:
Vila Real
Website:
University of Trás-os-Montes e Alto Douro
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Title:
Character varieties for real Lie groups and Higgs bundles
Name of the event:
25/11/2013
Speakers
Peter Gothen
Country:
Switzerland
Location / City:
Lausanne
Website:
Ecole Polytechnique Fédérale de Lausanne
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Organization of scientific meetings: 

Role: 

Organizer

Name of the event: 

IST Courses on Algebraic Geometry

start and end date: 

June 25, 2013 to June 28, 2013

Country: 

Portugal

Location / City: 

Porto

Website: 

CMUP

Student Mentoring: 

Hitchin pairs for the indefinite unitary group, 2015, SFRH/BD/51166/2010
Artur de Araújo, Character varieties for surface group representations and compactification of moduli of Higgs bundles, 2016, SFRH/BD/89423/2012
Homotopy groups of moduli of Higgs bundles, 2014, SFRH/BD/51174/2010
Thomas Baier, 2014, SFRH/BPD/81696/2011

Work visits: 

- 29/01/2013-07/02/2013: CIMAT, Guanajuato, Mexico (http://www.cimat.mx). Visiting Prof. Letícia Brambila-Paz.
- 24/06/2013-26/06/2013: Ecole Polytechnique Fédérale de Lausanne. Visiting Prof. Tamás Hausel
- 03/12/2013-04/12/2013: Universitat de Barcelona. Visiting Prof. Ignasi Mundet i Riera.