Ana Rita Pires

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, at Cornell University, at MIT, and at Instituto Superior Tecnico in Portugal.

Research interests:

• I work in symplectic geometry, in particular using hamiltonian actions and moment maps. The work on degenerate symplectic structures -- origami manifolds and b-symplectic or log-symplectic manifolds -- has connections with toric topology, contact geometry, and Poisson geometry. More recently I have become interested in quantitative symplectic geometry by woking on symplectic embedding problems.

Teaching right now:

• In Spring 2020 I will be teaching Fundamentals of Pure Mathematics.

Papers:

• 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; to appear in Mathematics Research Letters.
• 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: 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.