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24-27 Jun 2024 Metz (France)
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Program
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‹ Tuesday, June 25, 2024 › |
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09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
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9:00 - 10:00 (1h)
M. Ballesteros
 Amphi
Miguel Ballesteros
10:00 - 10:30 (30min)
Coffee break
Coffee Room
10:30 - 11:30 (1h)
M. Grillakis
Amphi
Manoussos Grillakis
›11:30 (1h)
S. Cenatiempo: Quantum Mechanics at our scale: a mathematical challenge
While the theory of quantum mechanics describes interactions between constituents of matter at the microscopic scale, the effects of these interactions may lead to fascinating quantum mechanics phenomena at a macroscopic scale. The discovery of such phenomena, including superfluidity and superconductivity as two pioneering examples, has led to extraordinary developments in realizing new materials that exploit the principles of quantum mechanics to exhibit innovative behaviours. In these lectures, we will discuss the challenge of developing mathematical models that rigorously describe how these macroscopic effects emerge from the microscopic scale, focusing on the paradigmatic example of the interacting Bose gas. › Amphi
11:30 - 12:30 (1h)
S. Cenatiempo: Quantum Mechanics at our scale: a mathematical challenge
Amphi
While the theory of quantum mechanics describes interactions between constituents of matter at the microscopic scale, the effects of these interactions may lead to fascinating quantum mechanics phenomena at a macroscopic scale. The discovery of such phenomena, including superfluidity and superconductivity as two pioneering examples, has led to extraordinary developments in realizing new materials that exploit the principles of quantum mechanics to exhibit innovative behaviours. In these lectures, we will discuss the challenge of developing mathematical models that rigorously describe how these macroscopic effects emerge from the microscopic scale, focusing on the paradigmatic example of the interacting Bose gas.
12:30 - 14:30 (2h)
Lunch
Restaurant Universitaire
›14:30 (1h)
M. Falconi: Scaling limits in quantum models of particle-field interaction
In these lectures I will review a series of recent results on the interaction between quantum particles and fields, in different scaling regimes (all somewhat related to Bohr's correspondence principle). From a mathematical perspective, infinite dimensional semiclassical analysis lies at the backbone of our results; we will review its main developments and connect them with the study of systems of quantum particles in interaction with a semiclassical field, as well as with the equations of classical electrodynamics. › Amphi
14:30 - 15:30 (1h)
M. Falconi: Scaling limits in quantum models of particle-field interaction
Amphi
In these lectures I will review a series of recent results on the interaction between quantum particles and fields, in different scaling regimes (all somewhat related to Bohr's correspondence principle). From a mathematical perspective, infinite dimensional semiclassical analysis lies at the backbone of our results; we will review its main developments and connect them with the study of systems of quantum particles in interaction with a semiclassical field, as well as with the equations of classical electrodynamics.
›15:30 (1h)
I. M. Sigal: Ginzburg-Landau equations
The Ginzburg-Landau equations (Nobel prize 2003) is perhaps the most successful PDE system in condensed matter physics. Originating in the theory superconductivity (Nobel prizes 1972 and 2003), it was extended to various other areas of condensed matter physics, such as theories of liquid crystals and fractional Hall effect (Nobel prizes 1991 and 1998). Independently, these equations appeared in particle physics providing the simplest U(1)-gauge theory. Their non-abelian generalization, the Yang- Mills-Higgs equations (Nobel prizes 1999, 2013) is a fundamental ingredient of the standard model of particle physics. GLE have also a natural geometrical interpretation coupling the section and connections of line bundles. In this lecture, I describe the basic properties of the GLE, its key solutions (magnetic vortices and vortex lattices), discuss recent results and say a few words on the extension of this equation to Riemann surfaces. › Amphi
15:30 - 16:30 (1h)
I. M. Sigal: Ginzburg-Landau equations
Amphi
The Ginzburg-Landau equations (Nobel prize 2003) is perhaps the most successful PDE system in condensed matter physics. Originating in the theory superconductivity (Nobel prizes 1972 and 2003), it was extended to various other areas of condensed matter physics, such as theories of liquid crystals and fractional Hall effect (Nobel prizes 1991 and 1998). Independently, these equations appeared in particle physics providing the simplest U(1)-gauge theory. Their non-abelian generalization, the Yang- Mills-Higgs equations (Nobel prizes 1999, 2013) is a fundamental ingredient of the standard model of particle physics. GLE have also a natural geometrical interpretation coupling the section and connections of line bundles. In this lecture, I describe the basic properties of the GLE, its key solutions (magnetic vortices and vortex lattices), discuss recent results and say a few words on the extension of this equation to Riemann surfaces.
16:30 - 18:00 (1h30)
Posters
Poster room
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