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Peter Gothen completed his PhD in 1996 at University of Warwick and he is currently Associate Professor of Mathematics at the University of Porto. He works in algebraic and differential geometry with a focus on Higgs bundles and their moduli spaces and related geometric questions. He has supervised 6 PhD theses and he has been PI of several research projects. He is vice-chair of the scientific committee of the international research group VBAC (Vector Bundles on Algebraic Curves), on the editorial board of the journal Moduli, and editor-in-chief of the journal Portugaliae Mathematica. He was director of the Centre of Mathematics of the University of Porto in 2011-2012, and he was chairman of the Department of Pure Mathematics of the Faculty of Sciences of the University of Porto in 2006-2007.
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Identification

Personal identification

Full name
Peter Gothen

Citation names

  • Gothen, Peter
  • Gothen, P. B.
  • Gothen, Peter B.

Author identifiers

Ciência ID
641D-B9B6-FE53
ORCID iD
0000-0002-4624-3871
AuthenticusID
R-000-F41
Google Scholar ID
https://scholar.google.com/citations?user=KvXLOukAAAAJ&hl=en&oi=ao
Researcher Id
I-6315-2012
Scopus Author Id
7801588719

Email addresses

  • pbgothen@fc.up.pt (Professional)

Addresses

  • Faculdade de Ciências da Universidade do Porto, Departamento de Matematica, Rua do Campo Alegre, 4169-007, Porto, Porto, Portugal (Professional)

Websites

Knowledge fields

  • Exact Sciences - Mathematics

Languages

Language Speaking Reading Writing Listening Peer-review
Danish (Mother tongue)
Portuguese Proficiency (C2) Proficiency (C2) Proficiency (C2) Proficiency (C2)
English Proficiency (C2) Proficiency (C2) Proficiency (C2) Proficiency (C2)
German Intermediate (B1) Advanced (C1) Elementary (A2) Upper intermediate (B2)
French Elementary (A2) Upper intermediate (B2) Elementary (A2) Elementary (A2)
Education
Degree Classification
2007
Concluded
 Matemática Pura (Título de Agregado)
Universidade do Porto Faculdade de Ciências, Portugal
 N/A
1996/01/12
Concluded
 Mathematics (Doctor of Philosophy)
University of Warwick, United Kingdom
"The Topology of Higgs Bundle Moduli Spaces" (THESIS/DISSERTATION)
 N/A
1993/05/24
Concluded
 Mathematics and Physics (Master)
Aarhus Universitet Science and Technology, Denmark
 N/A
Affiliation

Teaching in Higher Education

Category
Host institution 		Employer
2004/08/23 - Current Associate Professor (University Teacher) Universidade do Porto Faculdade de Ciências, Portugal
2010/01/01 - 2010/06/30 Invited Associate Professor (University Teacher) Aarhus Universitet Institut for Matematik, Denmark
1997/02/17 - 2004/08/22 Assistant Professor (University Teacher) Universidade do Porto Faculdade de Ciências, Portugal
1996/07 - 1997/07 Associate Professor (University Teacher) Universidade Portucalense Infante Dom Henrique, Portugal
1996/04/24 - 1996/07/24 Invited Assistant Professor (University Teacher) Universidade do Porto Faculdade de Ciências, Portugal
1996/02 - 1996/06 Assistant Professor (University Teacher) Universidade Portucalense Infante Dom Henrique, Portugal
1995/10 - 1996/01 Invited Assistant (University Teacher) Universidade Portucalense Infante Dom Henrique, Portugal
1994 - 1995 Tutor (University Teacher) University of Cambridge, United Kingdom
1993 - 1993 Tutor (University Teacher) University of Warwick, United Kingdom
1990 - 1993 Tutor (University Teacher) Aarhus Universitet Institut for Matematik, Denmark
Projects

Contract

Designation Funders
2022/01/17 - Current Mirror symmetry on Higgs bundles moduli spaces
EXPL/MAT-PUR/1162/2021
Researcher
Universidade do Porto Faculdade de Ciências, Portugal
 Fundação para a Ciência e a Tecnologia, I.P.
Concluded
2021 - Current The Hitchin-Ngô Laboratory (ICMAT Madrid)
info
Researcher
Instituto de Ciencias Matemáticas, Spain
 Consejo Superior de Investigaciones Científicas
Ongoing
2012 - 2022 GEAR Network (Geometric Structures and Representation Varieties)
DMS 1107452, 1107263, 1107367
Researcher
University of Illinois at Urbana-Champaign, United States
 National Science Foundation
Concluded
2016/06/01 - 2019/11/30 Geometry of Algebraic Varieties
Provided by PTCRIS: 141450
PTDC/MAT-GEO/2823/2014
Principal investigator
Universidade do Porto Centro de Matemática, Portugal
 Fundação para a Ciência e a Tecnologia, I.P.
Concluded
2013/07 - 2015/07 Portuguese Algebraic Geometry Community
Provided by PTCRIS: 125240
125240
PTDC/MAT-GEO/0675/2012
Researcher
Centro de Análise Matemática Geometria e Sistemas Dinâmicos, Portugal

Universidade do Porto Centro de Matemática, Portugal
Fundação para a Ciência e a Tecnologia, I.P.
Concluded
2009 - 2014 Interactions of low-dimensional Topology and Geometry with mathematical Physics (ITGP) - Steering Committee
07-RNP-105
European Science Foundation, France
 European Science Foundation
Concluded
2010/03 - 2013/09 Topological Invariants via Differential Geometry
Provided by PTCRIS: 98770
98770
PTDC/MAT/098770/2008
Principal investigator
Universidade do Porto Centro de Matemática, Portugal
 Fundação para a Ciência e a Tecnologia, I.P.
Concluded
2010/01 - 2013/07 Algebraic Geometry
99275
Provided by PTCRIS: 99275
PTDC/MAT/099275/2008
Researcher
Centro de Análise Matemática Geometria e Sistemas Dinâmicos, Portugal

Universidade do Porto Centro de Matemática, Portugal
Fundação para a Ciência e a Tecnologia, I.P.
Concluded
2011/01 - 2013/01 Centro de Matemática da Universidade do Porto (CMUP) - Scientific Director
PEst-C/MAT/UI0144/2011
Director
Universidade do Porto Faculdade de Ciências, Portugal
 Fundação para a Ciência e a Tecnologia, I.P.
Concluded
2001 - 2010 5 Bilateral projects Portugal-Spain
Ação Integrada E-24/01
Ação Integrada E-30/03
GRICES/CSIC Fibrados de Higgs e topologia de espaços de moduli
GRICES/CSIC Topologia e teoria de Hodge do espaço de moduli de fibrados de Higgs
Ação Integrada E-38/09
Principal investigator
Fundação para a Ciência e a Tecnologia, I.P., Portugal

Conselho de Reitores das Universidades Portuguesas, Portugal

Consejo Superior de Investigaciones Científicas, Spain

Gobierno de España Ministerio de Ciencia e Innovación, Spain
Fundação para a Ciência e a Tecnologia

Conselho de Reitores das Universidades Portuguesas
Concluded
2007/01 - 2009/04 Moduli Spaces and String Theory
82198
Provided by PTCRIS: 82198
Researcher
Fundação para a Ciência e a Tecnologia, I.P.
2005/07 - 2007/10 Moduli Spaces and String Theory
Provided by PTCRIS: 58549
58549
Researcher
Fundação para a Ciência e a Tecnologia, I.P.
Concluded
Outputs

Publications

Book chapter
  1. Bradlow, S; García Prada, O; Gothen, P; Heinloth, J. "Irreducibility of moduli of semi-stable chains and applications to U(p, q)-Higgs bundles". 2018.
    10.1093/oso/9780198802020.003.0018
Conference paper
  1. Gothen, Peter. "Representations of surface groups in the general linear group". 2004.
Journal article
  1. Franco, Emilio; Gothen, Peter; Peón-Nieto, A.. "Narasimhan--Ramanan branes and wobbly Higgs bundles". International Journal of Mathematics (2024): https://arxiv.org/abs/2302.02736.
    Accepted
  2. G. Barajas; O. García-Prada; P. B. Gothen; I. Mundet i Riera. "Non-connected Lie groups, twisted equivariant bundles and coverings". Geometriae Dedicata 217 2 (2023): https://doi.org/10.1007%2Fs10711-022-00764-w.
    10.1007/s10711-022-00764-w
  3. Peter B. Gothen; António Guedes de Oliveira. "On the classification of the rigid motions of the plane". The College Mathematics Journal (2022): 1-3. https://doi.org/10.1080/07468342.2022.2099718.
    10.1080/07468342.2022.2099718
  4. Peter Gothen; António Guedes de Oliveira. "On Euler's Rotation Theorem". The College Mathematics Journal (2022): https://doi.org/10.1080/07468342.2022.2015214.
    10.1080/07468342.2022.2015214
  5. Peter B. Gothen; Ronald A. Zúñiga-Rojas. "Stratifications on the nilpotent cone of the moduli space of Hitchin pairs". Revista Matemática Complutense (2021): https://doi.org/10.1007/s13163-021-00400-3.
    10.1007/s13163-021-00400-3
  6. Franco, E.; Gothen, P.B.; Oliveira, A.; Peón-Nieto, A.. "Unramified covers and branes on the Hitchin system". Advances in Mathematics 377 (2021): http://www.scopus.com/inward/record.url?eid=2-s2.0-85096602504&partnerID=MN8TOARS.
    10.1016/j.aim.2020.107493
  7. P. B. Gothen; A. Nozad. "Quiver bundles and wall crossing for chains". Geometriae Dedicata (2019): https://doi.org/10.1007/s10711-018-0341-6.
    10.1007/s10711-018-0341-6
  8. Aparicio Arroyo, M; Bradlow, S; Collier, B; Garcia Prada, O; Gothen, PB; Oliveira, A. "SO(p,q)-Higgs bundles and Higher Teichmuller components". INVENTIONES MATHEMATICAE (2019):
    10.1007/s00222-019-00885-2
  9. Gothen, PB; Oliveira, AG. "Topological mirror symmetry for parabolic Higgs bundles". JOURNAL OF GEOMETRY AND PHYSICS (2019):
    10.1016/j.geomphys.2018.08.020
  10. Florentino, C; Gothen, PB; Nozad, A. "Homotopy type of moduli spaces of G-Higgs bundles and reducibility of the nilpotent cone". BULLETIN DES SCIENCES MATHEMATIQUES (2019):
    10.1016/j.bulsci.2018.10.002
  11. Aparicio Arroyo, M; Bradlow, S; Collier, B; Garcia Prada, O; Gothen, P; Oliveira, A. "Exotic components of SO(p, q) surface group representations, and their Higgs bundle avatars". COMPTES RENDUS MATHEMATIQUE (2018):
    10.1016/j.crma.2018.04.024
  12. Gothen, PB; Nozad, A. "Birationality of moduli spaces of twisted U(p, q)-Higgs bundles". REVISTA MATEMATICA COMPLUTENSE (2017): https://www.authenticus.pt/P-00K-P1M.
    10.1007/s13163-016-0207-0
  13. Gothen, PB; Zuniga Rojas, RA. "Stratifications on the moduli space of Higgs bundles". PORTUGALIAE MATHEMATICA (2017):
    10.4171/pm/1996
  14. Peter Gothen. "Hitchin Pairs for non-compact real Lie groups". Travaux Mathématiques - Special issue based on School GEOQUANT at the ICMAT Madrid, Spain, September 2015. 24 (2016): https://arxiv.org/abs/1607.08150.
    Published
  15. Bradlow, SB; Garcia Prada, O; Gothen, PB. "Higgs bundles for the non-compact dual of the special orthogonal group". GEOMETRIAE DEDICATA (2015): https://www.authenticus.pt/P-00A-9V0.
    10.1007/s10711-014-0026-8
  16. García-prada, O.; Gothen, P.B.; Mundet I Riera, I.. "Higgs bundles and surface group representations in the real symplectic group". Journal of Topology 6 1 (2013): 64-118. http://www.scopus.com/inward/record.url?eid=2-s2.0-84874121726&partnerID=MN8TOARS.
    10.1112/jtopol/jts030
  17. Castro, S.B.S.D.; Dakhlia, S.; Gothen, P.B.. "From singularity theory to finiteness of Walrasian equilibria". Mathematical Social Sciences (2013): http://www.scopus.com/inward/record.url?eid=2-s2.0-84877272059&partnerID=MN8TOARS.
    10.1016/j.mathsocsci.2013.03.002
  18. Gothen, P. B.; Oliveira, A. G.. "The Singular Fiber of the Hitchin Map". International Mathematics Research Notices (2012): http://dx.doi.org/10.1093/imrn/rns020.
    10.1093/imrn/rns020
  19. Gothen, P.B.; Oliveira, A.G.. "Rank two quadratic pairs and surface group representations". Geometriae Dedicata 161 1 (2012): 335-375. http://www.scopus.com/inward/record.url?eid=2-s2.0-84869131268&partnerID=MN8TOARS.
    10.1007/s10711-012-9709-1
  20. Bradlow, S.B.; García-Prada, O.; Gothen, P.B.. "Deformations of maximal representations in Sp(4, R)". Quarterly Journal of Mathematics 63 4 (2012): 795-843. http://www.scopus.com/inward/record.url?eid=2-s2.0-84869430266&partnerID=MN8TOARS.
    10.1093/qmath/har010
  21. Biswas, I; Gothen, PB; Logares, M. "On moduli spaces of Hitchin pairs". MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY (2011):
    10.1017/s0305004111000405
  22. Gothen, P.B.. "Higgs bundles and the real symplectic group". AIP Conference Proceedings 1360 (2011): 39-50. http://www.scopus.com/inward/record.url?eid=2-s2.0-80051675333&partnerID=MN8TOARS.
    10.1063/1.3599126
  23. Castro, S.B.S.D.; Dakhlia, S.; Gothen, P.B.. "Direct perturbations of aggregate excess demand". Journal of Mathematical Economics 46 4 (2010): 562-571. http://www.scopus.com/inward/record.url?eid=2-s2.0-77955276317&partnerID=MN8TOARS.
    10.1016/j.jmateco.2010.03.008
  24. Bradlow, S.B.; García-Prada, O.; Gothen, P.B.. "Homotopy groups of moduli spaces of representations". Topology 47 4 (2008): 203-224. http://www.scopus.com/inward/record.url?eid=2-s2.0-40649107685&partnerID=MN8TOARS.
    10.1016/j.top.2007.06.001
  25. Garcia Prada, O; Gothen, PB; Munoz, V. "Betti numbers of the moduli space of rank 3 parabolic Higgs bundles". MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY (2007):
  26. Bradlow, S.B.; García-Prada, O.; Gothen, P.B.. "Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces". Geometriae Dedicata 122 1 (2006): 185-213. http://www.scopus.com/inward/record.url?eid=2-s2.0-34147093196&partnerID=MN8TOARS.
    10.1007/s10711-007-9127-y
  27. Gothen, PB; King, AD. "Homological algebra of twisted quiver bundles". JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES (2005):
    10.1112/s0024610704005962
  28. Bradlow, S.B.; García-Prada, O.; Gothen, P.B.. "Moduli spaces of holomorphic triples over compact Riemann surfaces". Mathematische Annalen 328 1-2 (2004): 299-351. http://www.scopus.com/inward/record.url?eid=2-s2.0-0742288592&partnerID=MN8TOARS.
    10.1007/s00208-003-0484-z
  29. Bradlow, SB; Garcia Prada, O; Gothen, PB. "Surface group representations and U(p, q)-Higgs bundles". JOURNAL OF DIFFERENTIAL GEOMETRY (2003):
    10.4310/jdg/1090426889
  30. Gothen, PB. "Topology of U(2,1) representation spaces". BULLETIN OF THE LONDON MATHEMATICAL SOCIETY (2002):
    10.1112/s0024609301001364
  31. Gothen, PB. "Components of spaces of representations and stable triples". TOPOLOGY (2001):
    10.1016/s0040-9383(99)00086-5
  32. Bradlow, S.B.; García-Prada, O.; Gothen, P.B.. "Representations of the fundamental group of a surface in PU(p,q) and holomorphic triples,Représentations du groupe fondamental d'une surface dans PU(p,q) et triplets holomorphes". Comptes Rendus de l'Academie des Sciences - Series I: Mathematics 333 4 (2001): 347-352. http://www.scopus.com/inward/record.url?eid=2-s2.0-18044403621&partnerID=MN8TOARS.
    10.1016/s0764-4442(01)02069-9
  33. GOTHEN, PETER B.. "THE BETTI NUMBERS OF THE MODULI SPACE OF STABLE RANK 3 HIGGS BUNDLES ON A RIEMANN SURFACE". International Journal of Mathematics 05 06 (1994): 861-875. http://dx.doi.org/10.1142/S0129167X94000449.
    10.1142/s0129167x94000449
Preprint
  1. Gothen, Peter B.; Silva, Pedro Miguel. "The conformal limit and projective structures". 2024. https://doi.org/10.48550/arXiv.2401.07759.
    10.48550/arXiv.2401.07759
  2. Oliveira, André; Gothen, Peter; Bradlow, Steven; Collier, Brian; Garcia-Prada, Oscar. "A general Cayley correspondence and higher Teichmüller spaces". 2021. https://arxiv.org/abs/2101.09377.

Other

Other output
  1. Representations of surface groups and Higgs bundles. 2014. Peter B. Gothen. https://doi.org/10.1017%2Fcbo9781107279544.004.
    10.1017/cbo9781107279544.004
  2. What is a Higgs bundle?. 2007. Bradlow, SB; Garda Prada, O; Gothen, PB.
  3. The topology of Higgs bundle moduli spaces. 1995. Gothen, P.B. http://hdl.handle.net/10068/652926.
Activities

Supervision

Thesis Title
Role 		Degree Subject (Type)
Institution / Organization
2023 - Current Lagrangians in Higgs bundle moduli spaces
Supervisor
 Mathematics (PhD)
Universidade do Porto Faculdade de Ciências, Portugal
2022/09/01 - Current Extensions of Higgs bundles and the nilpotent cone
Supervisor of Gabriel Martinho
 Mathematics (PhD)
Universidade do Porto Faculdade de Ciências, Portugal
2022 - Current Quiver bundles and the moduli space of Higgs bundles
Supervisor of Juan Sebastian Numpaque
 Mathematics (PhD)
Universidade do Porto Faculdade de Ciências, Portugal
2019 - Current Higgs Bundles and Geometric Structures
Supervisor of Pedro Miguel Silva
 Matemática (PhD)
Universidade do Porto Faculdade de Ciências, Portugal
2022 - 2023 Higgs bundles and the Hitchin system
Co-supervisor of Rodrigo Alves dos Santos Pereira
 Mathematics (Master)
Universidade do Porto Faculdade de Ciências, Portugal
2021 - 2022/07/20 Hecke Algebras and Topological Quantum Field Theories
Co-supervisor of Bernardo Leite da Cunha
 Mathematics (Master)
Universidade do Porto Faculdade de Ciências, Portugal
2021 - 2022/07/14 Metrics on Flat Bundles
Co-supervisor of Gabriel Martinho
 Mathematics (Master)
Universidade do Porto Faculdade de Ciências, Portugal
2018 - 2019 Representations on diagrams of categories and applications to parabolic bundles
Supervisor of Rui Rodrigues de Abreu Fernandes Prezado
 Matemática (Master)
Universidade do Porto Faculdade de Ciências, Portugal
2013 - 2017 Representations of Generalized Quivers
Supervisor of Artur Duarte Ferreira de Araújo
 Matemática (PhD)
Universidade do Porto Faculdade de Ciências, Portugal
2012 - 2016 Hitchin Pairs for the Indefinite Unitary Group
Supervisor of Azizeh Nozad
 Matemática (PhD)
Universidade do Porto Faculdade de Ciências, Portugal
2011 - 2015 Homotopy Groups of the Moduli Space of Higgs Bundles
Supervisor of Ronald Alberto Zuñiga Rojas
 Matemática (PhD)
Universidade do Porto Faculdade de Ciências, Portugal
2006 - 2011 Topologia do Espaço Moduli de Fibrados de Higgs Torcidos.
Supervisor of Sandra Margarida Pinho da Cruz Bento
 Matemática (PhD)
Universidade do Porto Faculdade de Ciências, Portugal
2003 - 2008 Higgs Bundles, Quadratic Pairs and the Topology of Moduli Spaces
Supervisor of André Gama Oliveira
 Matemática (PhD)
Universidade do Porto Faculdade de Ciências, Portugal

Committee member

Activity description
Role 		Institution / Organization
2020 - Current Vice-chair of the scientific committee of the international research group Vector Bundles on Algebraic Curves (VBAC) - http://vbac.wikidot.com/.
President / Vice-president
2007 - Current Member of various PhD committees at the Universities Autónoma de Madrid, Coimbra, Complutense de Madrid, Lisboa, Nova de Lisboa, Oxford, Técnica de Lisboa, Trás-os-Montes e Alto Douro
Member
2000 - Current Member of the scientific committee of the international research group Vector Bundles on Algebraic Curves (VBAC).
Member
2000 - Current Member of various selection committees for academic positions at the Universities of Aarhus, Coimbra, Porto and the Polytechnic Institute of Lisbon.
Member
2015 - 2023/01/01 Vice-president of the "Comissão Nacional da Matemática" - the organ under the FCT which coordinates the Portuguese representation in the International Mathematical Union.
President / Vice-president
 Fundação para a Ciência e a Tecnologia, I.P., Portugal
2009 - 2011 Member of the scientific committee for the "Pedro Nunes Lectures" 2009-2011. Lecture series co-organized by the Portuguese Mathematical Society and the Centro Internacional de Matemática (CIM). Lecturers were Luis Caffarelli (2009), Maxim Kontsevich (2010), Jacob Palis (2011) and Sir Michael Atiyah (2011).
Member

Conference scientific committee

Conference name Conference host
2000 - Current Vector Bundles on Algebraic Curves (2000-2004, 2007, 2009, 2010, 2012, 2014-2017, 2019-)
2014 - 2014 National Meeting of the Portuguese Mathematical Society
2008 - 2008 National Meeting of the Portuguese Mathematical Society
1998 - 2000 Oporto Meetings on Geometry, Topology and Physics University of Porto

Journal scientific committee

Journal title (ISSN) Publisher
2022 - Current Portugaliae Mathematica (Editor-in-Chief) ( ISSN 0032-5155) EMS.Press / Sociedade Portuguesa de Matemática
2022 - Current Moduli Foundation Compositio Mathematica / London Mathematical Society / Cambridge University Press

Mentoring / Tutoring

Topic Student name
2007 - Current Mentoring of 7 postdoctoral researchers at CMUP 2007-2019 n/a