email: jmourao@tecnico.ulisboa.pt
Keywords: Mathematical physics, quantum gravity, theories of connections, rigorous quantum theory, symplectic geometry, algebraic geometry, functional analysis, difeomorphism invariant theories
Member of the Center for Mathematical Analysis, Geometry, and Dynamical Systems, CAMGSD.
President of the Mathematics Department of IST
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.
April 2018: Non-uniqueness
of quantization, (no-)reality conditions, complex time evolution and
generalized coherent state transforms
Radboud
University
December 2016: Complexified
Hamiltonian Symplectomorphisms and Solutions of the Homogeneous
Complex Monge-Ampere Equation
Hong
Kong Geometry Colloquium
December 2015: Quantum
Mechanics versus Complex Geometry: Lecture
Notes.
Lectures at the Physics
Department of the Beijing Normal University.
Fall 2015: Imaginary time in Kähler geometry, quantization
and tropical amoebas: Notes for the
Seminar
(overview of the course) and
Lectures: Index,
L1,
L2,
L3,
L4,
L5.
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
quantization,
Seminar at the Mini-Workshop
on Geometry, Chinese
University of Hong Kong.
October 16, 2013: Complex
time evolution in geometric quantization,
Seminar
at the 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.
(1990-1994)
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
constrained systems.
(1990-1993; 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.
(1990-1993; co-supervisor. The supervisor was Alfredo
B. Henriques)
Paulo
Sá, Associate Professor at Área Departamental de Física,
Universidade do Algarve on:
Inflationary models.
(1995-2001; supervisor. The co-supervisor was Nenad
Manojlovic)
José
Manuel 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 theory.
(2000 - 2002)
Fernando Passos on:
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.