Ana Rita Pires

Ana Rita Pires


(she/her/hers)

School of Mathematics
University of Edinburgh
James Clerk Maxwell Building
The King's Buildings
Peter Guthrie Tait Road
Edinburgh EH9 3FD

Email: apires(at)ed.ac.uk

Office: JCMB 5605


I am a Lecturer at the School of Mathematics at the University of Edinburgh and a member of the Geometry and Topology group at the Hodge Institute.
I started at the University of Edinburgh in 2018. Before that, I was at the University of Cambridge and Murray Edwards College, at Fordham University in NYC, at the Institute for Advanced Study in Princeton, at Cornell University in Ithaca, at MIT in Boston, and at Instituto Superior Tecnico in Lisbon, Portugal.
Here is a (possibly outdated) CV.

Research interests:

I work in symplectic geometry: hamiltonian actions, moment maps, toric symplectic manifolds, degenerate symplectic structures (origami manifolds and b-symplectic/log-symplectic manifolds), symplectic embedding problems, etc.

Teaching and such at UofE:

At the University of Edinburgh, I have taught: Combinatorics and Graph Theory, Fundamentals of Pure Mathematics, Advanced Proofs and Problem Solving, Honours Algebra. Most years I supervise a couple of honours projects on a variety of topics. Most years I am an academic cohort lead for Maths students. Also, Outreach Team.

PhD students:

João Camarneiro, started 2024.

Papers:

  • Connectedness in fair division of circle and star cakes between two agents with unequal entitlements, with J. Hanke and A. Heggison (from an honours project!).
  • A classification of infinite staircases for Hirzebruch surfaces, with N. Magill and M. Weiler.
  • Infinite staircases for Hirzebruch surfaces, with M. Bertozzi, T. Holm, E. Maw, D. McDuff, G. Mwakyoma and M. Weiler, chapter in Research Directions in Symplectic and Contact Geometry and Topology, AWMS 27, Springer, 2021.
  • On infinite staircases in toric symplectic four-manifolds, with D. Cristofaro-Gardiner, T. Holm and A. Mandini, to appear in Journal of Differential Geometry.
  • The fundamental group and Betti numbers of toric origami manifolds, with T. Holm, Algebraic and Geometric Topology, 15-4 (2015).
  • Convexity for torus actions on b-symplectic manifolds, with V. Guillemin, E. Miranda and G. Scott; Mathematical Research Letters 24 2 (2017).
  • Toric actions on b-symplectic manifolds, with Victor Guillemin, Eva Miranda and Geoffrey Scott, International Mathematics Research Notices 14 (2015).
  • Topology of toric origami manifolds, with Tara Holm, Mathematics Research Letters, 20 (2013) no.5.
  • Moduli spaces of toric manifolds, with Alvaro Pelayo, Tudor S. Ratiu and Silvia Sabatini, Geometriae Dedicata 169 (1), 2014.
  • Symplectic and Poisson geometry of b-manifolds, with Victor Guillemin and Eva Miranda, Advances in Mathematics 264, 864-896, 2014.
  • Codimension one symplectic foliations and regular Poisson structures, with Victor Guillemin and Eva Miranda, Bulletin of the Brazilian Mathematical Society, New Series 42(4), 2011.
  • Symplectic Origami, with Ana Cannas da Silva and Victor Guillemin, International Mathematics Research Notices, no. 18, pp 4252-4293, 2011.
  • Origami manifolds, Thesis dissertation, MIT, 2010.

    Other publications:

  • Numeros, Cirurgias e Nos de Gravata: 10 anos de Seminario Diagonal no IST, editor, with J.P. Boavida, R.P. Carpentier, L. Cruz-Filipe, P.S. Goncalves, E. Grifo and D. Henriques; IST Press, Lisbon 2012.
  • Seminario Diagonal - Proceedings IST, II, editor, with A. Cannas da Silva, L. Cruz-Filipe, R. Goncalves, J. Pimentel Nunes, T. Reis, P.M. Resende and J. Silva, Lisbon, 2005.

    Unusual:

  • A 6-hour topology workshop for high-school teachers at Math for America;
  • A talk about sphere packing at a bar in Brooklyn for Pint of Science;
  • A college algebra course at a prison in NJ with the Prison Teaching Initiative;
  • A course on Math and Politics at Cornell University;
  • A talk titled "Paper folding geometry: how origami beat Euclid" for the general public or other non-traditional audiences (here in portuguese);
  • Short videos solving Linear Algebra problems for MIT OpenCourseWare;
  • Math "classes" for little kids with Math Circle.

    Etc.:

  • Notes from a long ago talk on Convexity in Symplectic Geometry: The Atiyah-Guillemin-Sternberg Theorem.
  • Some old courses with links that I want to keep: Part III Symplectic Geometry at Cambridge, graduate seminar in Symplectic Geometry at Cornell, Honors Introduction to Analysis I at Cornell, Analysis and Manifolds at MIT.