Dr Ana Peón-Nieto BSc Lic MSc PhD

Dr Ana Peón-Nieto

School of Mathematics
Honorary Senior Research Fellow

Contact details

Email
a.peon-nieto@bham.ac.uk
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Dr Peón-Nieto's work focuses on Higgs bundles. These objects appeared as solutions to differential equations motivated by physics; they are to monopoles what the latter are to instantons. Several approaches allow to tackle Higgs bundles, be it from the differential, symplectic or algebraic geometric point of view. This richness has led to connections with many subjects in mathematics and physics, such as integrable systems, mirror symmetry, geometric structures, gauge theory, S-duality, the geometric Langlands programme,… most of which appear either directly or as a motivation in Dr Peón-Nieto’s research.

As a postdoc, Dr Peón-Nieto was awarded several post-doctoral fellowships, including a Marie Sklodowska-Curie European Individual Fellowship (2020-2022), Juan de la Cierva Incorporación Fellowship (2020-2023) and Beatriu de Pinós-Marie Curie COFUND Fellowship (2019).

Qualifications

  • Acreditación Profesora Ayudante Doctor (Spanish qualification to apply for Lectureships), 2020
  • PhD in Mathematics, Universidad Autónoma de Madrid, 2013
  • Master 2 in Pure Mathematics (equivalent to MPhil), University Paris 7 Denis-Diderot, 2007
  • Licenciatura in Mathematics (equivalent to MSci), Universidad Autónoma de Madrid, 2006
  • Imperial College International Diploma (BSc level qualification awarded to international students), 2005

Biography

Dr Peón-Nieto obtained her PhD from Universidad Autónoma de Madrid in 2013. Her thesis, performed under the supervision of Dr Álvarez-Cónsul and Prof. García-Prada, studies the Hitchin system for Higgs bundles associated to real forms (closely related to geometric structures for real Lie groups).  Prior to that she got a 'Licenciatura' (MSci) in Mathematics from Universidad Autónoma de and a Master II (MPhil) in Pure Mathematics in Paris 7.

Ana's years as a postdoc brought her to Heidelberg (2014-2016), Nice (2017), Geneva (2018-19), Barcelona (2019) and back to Nice (2020). During these years, she evolved towards the study of (Higgs) bundles on non-smooth surfaces, the connections with character varieties, mirror symmetry and more fundamental aspects of moduli spaces of bundles.

Between 2020 and 2023, Dr Peón-Nieto was a Lecturer in the Geometry and Mathematical Physics group of the University of Birmingham.

Research

Research Themes

  • Algebraic and differential geometry
  • Moduli spaces
  • Vector bundles
  • Higgs bundles
  • Hitchin maps
  • Applications to character varieties
  • Integrable systems
  • Mirror symmetry
  • Geometric Langlands

Research Activity

Dr Peón-Nieto's research focuses on moduli spaces, which are manifolds classifying geometric objects in a geometrically faithful way. More specifically, She is interested in moduli spaces of vector bundles and Higgs bundles, both of which can be either constructed in the context of gauge theories (inspired by physics, and of a differential geometric flavor) or via algebraic geometric techniques. This interplay yields a very rich geometry connecting the geometry of these objects with vast programmes in physics (such as mirror symmetry or S-duality) and mathematics (such as integrable systems or the geometric Langlands programme).

Other activities

Ana is an evaluator for the State Research Agency (AEI) of the Spanish Ministry of Science.

Publications

Recent publications

Article

Franco, E, Gothen, PB, Oliveira, AG & Peon-Nieto, A 2024, 'Narasimhan–Ramanan branes and wobbly Higgs bundles', International Journal of Mathematics. https://doi.org/10.1142/S0129167X24410064

Franco, E & Peón-Nieto, A 2023, 'Branes on the singular locus of the Hitchin system via Borel and other parabolic subgroups', Mathematische Nachrichten, vol. 296, no. 5, pp. 1803-1841. https://doi.org/10.1002/mana.202000267

Peon-Nieto, A 2023, 'Equality of the wobbly and shaky loci', International Mathematics Research Notices, pp. 1-21. https://doi.org/10.1093/imrn/rnad254

García-Prada, Ó & Peon-Nieto, A 2021, 'Abelianization of Higgs bundles for quasi-split real groups', Transformation Groups. https://doi.org/10.1007/s00031-021-09658-9

Preprint

Franco, E, Gothen, PB, Oliveira, AG & Peón-Nieto, A 2023 'Narasimhan--Ramanan branes and wobbly Higgs bundles' arXiv. https://doi.org/10.48550/arXiv.2302.02736

View all publications in research portal