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Geometry and Mathematical Physics

∙ Integrable systems in relation with differential, algebraic and symplectic geometry, as well as with the theory of random matrices, special functions and nonlinear waves, Frobenius manifolds • Deformation theory, moduli spaces of sheaves and of curves, in relation with supersymmetric gauge theories, strings, Gromov-Witten invariants, orbifolds and automorphisms
• Quantum groups, noncommutative Riemannian and spin geometry, applications to models in mathematical physics
• Mathematical methods of quantum mechanics
• Mathematical aspects of quantum Field Theory and String 
Theory
• Symplectic geometry, sub-riemannian geometry

• Geometry of quantum fields and strings

Geometry and quantization of moduli spaces of Higgs bundles

 The ubiquity of moduli spaces of semi-stable higgs bundles on a smooth projective curve both in mathematics and physics is rather impressive. These moduli spaces have proven to be grounds of extremely fruitful interaction between the two disciplines. As an example, the techniques developed by physicists to quantize a symplectic manifold and to quantize a com- pletely integrable Hamiltonian system when applied to these moduli spaces yield remarkable mathematical results. E.

Analysis, Math-Phys, and Quantum Seminars 2014-2015

This Seminar is run within the mathematics division of SISSA as a part of SISSA's research activities on the Mathematical Methods of Quantum Mechanics, and is partially funded by the 2014-2017 FIR-MIUR grant "COND-MATH, Condensed Matter in Mathematical Physics".

The Seminar presents a selection of recent advances in the current mathematical research driven primarily by models and emergent effects from condensed matter and ultra-cold atoms physics, statistical physics, and theoretical physics. This involves methods and tools from functional analysis, PDE, and operator theory, and in particular: quadratic forms, spectral and scattering theory, non-linear and dispersive PDEs, singular perturbations of elliptic differential operators, self-adjoint extension theory, scaling and kinetic limits, C*-algebraic formulation of Quantum Mechanics, semi-classical analysis, numerics, and topological and geometrical methods for solid state physics.

Date Speaker Seminar
October 30 László Zsidó (Rome Tor Vergata) On Woronowicz's approach to the Tomita-Takesaki theory
November 6 Paolo Antonelli (GSSI L'Aquila) On a class of non-linear Schrödinger equations with non-linear damping

Analysis, Math-Phys, and Quantum Seminars 2015-2016

This Seminar is run within the mathematics division of SISSA as a part of SISSA's research activities on the Mathematical Methods of Quantum Mechanics, and is partially funded by the 2014-2017 FIR-MIUR grant "COND-MATH, Condensed Matter in Mathematical Physics".

The Seminar presents a selection of recent advances in the current mathematical research driven primarily by models and emergent effects from condensed matter and ultra-cold atoms physics, statistical physics, and theoretical physics. This involves methods and tools from functional analysis, PDE, and operator theory, and in particular: quadratic forms, spectral and scattering theory, non-linear and dispersive PDEs, singular perturbations of elliptic differential operators, self-adjoint extension theory, scaling and kinetic limits, C*-algebraic formulation of Quantum Mechanics, semi-classical analysis, numerics, and topological and geometrical methods for solid state physics.

Date Speaker Seminar
October 29 Pavel Exner (Rome Tor Vergata) Schrödinger operators exhibiting a parameter-dependent spectral transition.
October 10 Antti Knowles (ETH Zurich) Local eigenvalue statistics for random regular graphs

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