José Manuel Cidade Mourão
Keywords: Mathematical physics, quantum gravity, theories of
rigorous quantum theory, symplectic geometry, algebraic geometry,
analysis, difeomorphism invariant theories
Member of the
Center for Mathematical Analysis, Geometry, and Dynamical Systems,
at the Mathematics Department of
From October 25 to November 24, 2015, I visited the Mathematics Department of Geneva University.
From July 1, 2014 to February 15, 2015 I was guest professor
at the Institute for Quantum Gravity of the
Friedrich-Alexander Universität Erlangen-Nürnberg, Germany.
From September 1994 to July 1996 I was visiting Assistant Professor at the Physics Department
of the University of Algarve.
From September 1993 to July 1994 I was on sabatical leave at the Center for Gravitational Physics
and Geometry of the Penn State University.
I am interested in different aspects of the interaction between
Quantum Field Theory and Modern Geometry.
One thing that fascinates me is the role of Feynman Path Integral
in Modern Mathematics. Some reflections about PI in the proceedings of the
XII Fall Workshop on Geometry and Physics, Coimbra University, 2003.
Presently I am, with
João Pimentel Nunes and other
collaborators, investigating evolution in complex time
both in quantum physics and in geometry.
Here are some notes (see also below) of a minicurse at the
International School on Geometry, Grupoids and Quantization, University of Hong Kong, 2013.
Slides and Notes for some recent courses and talks
- April 2018:
Non-uniqueness of quantization, (no-)reality conditions,
complex time evolution and generalized coherent state
- December 2016:
Complexified Hamiltonian Symplectomorphisms
and Solutions of the Homogeneous Complex
Hong Kong Geometry Colloquium
- December 2015:
Quantum Mechanics versus Complex Geometry:
Lectures at the Physics Department of the
Beijing Normal University.
- Fall 2015: Imaginary time in Kähler geometry,
quantization and tropical amoebas: Notes for the
(overview of the course) and
at the Mathematics Department
of Geneva University.
- Fall 2014: Quantum Mechanics and Kähler Geometry, Lectures 1-3 (notes), Lectures 4, 5 (notes).
Lectures at the Institute for Quantum Gravity,
Friedrich-Alexander Universität Erlangen-Nürnberg.
- February 3, 2014: Imaginary time flow in geometric quantization and in Kähler geometry, degeneration to real polarizations and tropicalization,
Seminar at the Mathematics Department, University of Illinois at Urbana-Champaign.
- January 31, 2014: Imaginary time flow in geometric quantization and in Kähler geometry degeneration to real polarizations and tropicalization,
Felix Klein Seminar at the Mathematics Department of the University of Notre Dame.
- January 24, 2014: Imaginary time flow in geometric quantization and in Kähler geometry, degeneration to real polarizations and tropicalization,
Seminar at the Mathematics Department of the University of Michigan.
- December 18, 2013: Imaginary time flow in geometric quantization, degeneration to real polarizations and tropicalization,
Seminar at the WaGaRy workshop of the Institute of Mathematics of the Polish Academy of Sciences.
- November 2, 2013: Decomplexification of integrable systems,
quantization and Kähler geometry,
Minicourse given at the
International School on
Geometry, Grupoids and Quantization,
University of Hong Kong..
- October 17, 2013: Geodesics on the space of Kähler
metrics, geometric tropicalization and
Seminar at the
Mini-Workshop on Geometry,
Chinese University of Hong Kong.
- October 16, 2013:
Complex time evolution in geometric
Faculty of Sciences and Technology,
University of Macau.
- September 5, 2013: Tropicalization in symplectic geometry
and degeneration to real polarizations,
Seminar at the Conference on Tropical Aspects in Geometry and
Topology, Max Planck Institute for Mathematics, Bonn.
Supervision of Ph.D. Thesis
Supervised or co-supervised PhD thesis of:
João Nuno Tavares, Associate
Professor at the
Departamento de Matematica Pura,
Faculdade de Ciencias, Universidade do Porto on:
Mathematical methods on the quantization of first class
co-supervisor. The supervisor was Paulo Crawford)
Paulo Moniz, Full Professor at the Departamento
de Fisica da Universidade da Beira Interior on:
Symmetries in general relativity and exact solutions.
co-supervisor. The supervisor was
Alfredo B. Henriques)
Associate Professor at Área Departamental de
Física, Universidade do Algarve on:
supervisor. The co-supervisor was
Velhinho Assistant Professor at the Departamento de Fisica da Universidade da Beira Interior on:
Quantization of systems with non-trivial phase spaces.
- (2003 - 2006)
Pedro Matias on:
Application of geometric quantization techniques to quantum field
Supervision of M.Sc. Thesis
Supervised the M.Sc. thesis of:
(2000 - 2002)
Representations of the Virasoro Algebra and Conformal Field Theories.
I completed my undergraduate studies in June 1986 in
the Physics Department of
Moscow State University (MSU).
Wrote a a M.Sc. thesis on propagation of electromagnetic waves in crystals
under the supervision of Vladimir Ivanovich Grigoriev.
In 1985 I was very lucky to meet and attend classes
on differential geometry, Lie groups and Lie algebras by
Yuri Kubyshin and Igor Volobuev. They, together with
Dmitrii Vassilievitch Shirkov, became in September 1986 the supervisors of
my PhD thesis which I completed
in MSU in June 1988.
Defended habilitation in Physics at the IST in June 1995.