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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

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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