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Mathematical Challenges in Quantum Mechanics - Online Seminars
from
Friday, November 1, 2024 (9:00 AM)
to
Saturday, May 31, 2025 (11:00 PM)
Monday, October 28, 2024
Tuesday, October 29, 2024
Wednesday, October 30, 2024
Thursday, October 31, 2024
Friday, November 1, 2024
Saturday, November 2, 2024
Sunday, November 3, 2024
Monday, November 4, 2024
Tuesday, November 5, 2024
Wednesday, November 6, 2024
11:30 AM
MCQM PhD Lecture: Benjamin Alvarez
MCQM PhD Lecture: Benjamin Alvarez
11:30 AM - 12:30 PM
Title: An introduction to non relativistic QED Abstract: This talk is dedicated to presenting the fundamental notions to adress non relativistic QED models. The general framework of quantum field theory will be presented together with the Hamiltonian of non relativistic QED. In addition, we aim to give a taste of important works that have been done in the field together with some open problems.
2:30 PM
MCQM Seminar: Volker Bach
MCQM Seminar: Volker Bach
2:30 PM - 3:30 PM
Title: TBA Abstract: TBA
Thursday, November 7, 2024
Friday, November 8, 2024
Saturday, November 9, 2024
Sunday, November 10, 2024
Monday, November 11, 2024
Tuesday, November 12, 2024
Wednesday, November 13, 2024
Thursday, November 14, 2024
Friday, November 15, 2024
Saturday, November 16, 2024
Sunday, November 17, 2024
Monday, November 18, 2024
Tuesday, November 19, 2024
Wednesday, November 20, 2024
Thursday, November 21, 2024
Friday, November 22, 2024
Saturday, November 23, 2024
Sunday, November 24, 2024
Monday, November 25, 2024
Tuesday, November 26, 2024
Wednesday, November 27, 2024
Thursday, November 28, 2024
Friday, November 29, 2024
Saturday, November 30, 2024
Sunday, December 1, 2024
Monday, December 2, 2024
Tuesday, December 3, 2024
Wednesday, December 4, 2024
Thursday, December 5, 2024
Friday, December 6, 2024
Saturday, December 7, 2024
Sunday, December 8, 2024
Monday, December 9, 2024
Tuesday, December 10, 2024
Wednesday, December 11, 2024
Thursday, December 12, 2024
Friday, December 13, 2024
Saturday, December 14, 2024
Sunday, December 15, 2024
Monday, December 16, 2024
Tuesday, December 17, 2024
Wednesday, December 18, 2024
11:30 AM
MCQM PhD Lecture: Angelo Lucia
MCQM PhD Lecture: Angelo Lucia
11:30 AM - 12:30 PM
Title: Locality and spectral gaps in quantum spin systems Abstract: In this lecture, I will give a brief introduction to the mathematical framework used to describe quantum spin systems on lattices. The main goal will be to connect the study of models defined over finite volumes to an idealized infinite volume limit called the thermodynamic limit. A key role will be played by locality estimates known as Lieb-Robinson bounds. I will then focus on the spectral gap of the model, the difference between the two lowest energy levels, and I will explain how it is related to the problem of phase classification of quantum phases of matter.
2:30 PM
MCQM Seminar: David Pérez García
MCQM Seminar: David Pérez García
2:30 PM - 3:30 PM
Title: Spectral gaps in many body quantum systems Abstract: How does the spectral gap of a quantum many body system scale with the system size? This turns out to be a very relevant question both in condensed matter physics and in quantum computing. However, there are very few available techniques to give bounds of that scaling. In the first part of this talk, we will review recent results which explain why: it is undecidable to know if the spectral gap will vanish or not with the system size. In the second part, we will review complementary results which show that, despite this general impossibility result, one can still prove spectral gap estimates in a rather wide family of systems. As a consequence, one obtains new bounds on the lifetime of quantum memories.
Thursday, December 19, 2024
Friday, December 20, 2024
Saturday, December 21, 2024
Sunday, December 22, 2024
Monday, December 23, 2024
Tuesday, December 24, 2024
Wednesday, December 25, 2024
Thursday, December 26, 2024
Friday, December 27, 2024
Saturday, December 28, 2024
Sunday, December 29, 2024
Monday, December 30, 2024
Tuesday, December 31, 2024
Wednesday, January 1, 2025
Thursday, January 2, 2025
Friday, January 3, 2025
Saturday, January 4, 2025
Sunday, January 5, 2025
Monday, January 6, 2025
Tuesday, January 7, 2025
Wednesday, January 8, 2025
Thursday, January 9, 2025
Friday, January 10, 2025
Saturday, January 11, 2025
Sunday, January 12, 2025
Monday, January 13, 2025
Tuesday, January 14, 2025
Wednesday, January 15, 2025
11:30 AM
MCQM PhD Lecture: Benjamin Hinrichs
MCQM PhD Lecture: Benjamin Hinrichs
11:30 AM - 12:30 PM
Title: An Invitation to Path Measure Methods for Polaron Models Abstract: This talk gives an introduction to the connection between the Hamiltonian formulation of quantum mechanics and its probabilistic counterpart. We first discuss this in terms of Feynman-Kac formulas for Schrödinger operators together with some applications. Then, we move to their analogues for polaron models, i.e., models of quantum particles linearly coupled to a quantum field. We also sketch how the named applications extend to the polaron, e.g., when studying ground states or the effective mass.
2:30 PM
MCQM Seminar: Robert Seiringer
MCQM Seminar: Robert Seiringer
2:30 PM - 3:30 PM
Title: Spectral analysis of polaron models in the strong coupling limit Abstract: The Fröhlich polaron and related models of quantum field theory have played a prominent role in mathematical physics over several decades. In this talk, we shall explain recent bounds on the quantum corrections to the (classical) Pekar approximation of the ground state energy of the Fröhlich polaron model in the strong coupling limit, and their consequence on the existence of excited states and the polaron's effective mass.
Thursday, January 16, 2025
Friday, January 17, 2025
Saturday, January 18, 2025
Sunday, January 19, 2025
Monday, January 20, 2025
Tuesday, January 21, 2025
Wednesday, January 22, 2025
Thursday, January 23, 2025
Friday, January 24, 2025
Saturday, January 25, 2025
Sunday, January 26, 2025
Monday, January 27, 2025
Tuesday, January 28, 2025
Wednesday, January 29, 2025
Thursday, January 30, 2025
Friday, January 31, 2025
Saturday, February 1, 2025
Sunday, February 2, 2025
Monday, February 3, 2025
Tuesday, February 4, 2025
Wednesday, February 5, 2025
Thursday, February 6, 2025
Friday, February 7, 2025
Saturday, February 8, 2025
Sunday, February 9, 2025
Monday, February 10, 2025
Tuesday, February 11, 2025
Wednesday, February 12, 2025
Thursday, February 13, 2025
Friday, February 14, 2025
Saturday, February 15, 2025
Sunday, February 16, 2025
Monday, February 17, 2025
Tuesday, February 18, 2025
Wednesday, February 19, 2025
Thursday, February 20, 2025
Friday, February 21, 2025
Saturday, February 22, 2025
Sunday, February 23, 2025
Monday, February 24, 2025
Tuesday, February 25, 2025
Wednesday, February 26, 2025
Thursday, February 27, 2025
Friday, February 28, 2025
Saturday, March 1, 2025
Sunday, March 2, 2025
Monday, March 3, 2025
Tuesday, March 4, 2025
Wednesday, March 5, 2025
Thursday, March 6, 2025
Friday, March 7, 2025
Saturday, March 8, 2025
Sunday, March 9, 2025
Monday, March 10, 2025
Tuesday, March 11, 2025
Wednesday, March 12, 2025
11:30 AM
MCQM PhD Lecture: Andrew Rout
MCQM PhD Lecture: Andrew Rout
11:30 AM - 12:30 PM
Title: A (brief) introduction to Gibbs measures for the nonlinear Schrödinger equation Abstract: In this talk I will give an introduction to Gibbs measures for the nonlinear Schrödinger equation. The construction of global solutions to dispersive PDEs usually relies on the conservation of quantities like the energy and the mass. For lower regularity functions, these quantities are infinite, so cannot be used. Instead one introduces an invariant measure, which can act as a substitute for the conserved quantities. I give the heuristic ideas for the construction the Gibbs measure, and also sketch the details of the rigorous construction. I will also discuss how to use the Gibbs measure to construct global solutions to the nonlinear Schrödinger equation.
Thursday, March 13, 2025
Friday, March 14, 2025
Saturday, March 15, 2025
Sunday, March 16, 2025
Monday, March 17, 2025
Tuesday, March 18, 2025
Wednesday, March 19, 2025
Thursday, March 20, 2025
Friday, March 21, 2025
Saturday, March 22, 2025
Sunday, March 23, 2025
Monday, March 24, 2025
Tuesday, March 25, 2025
Wednesday, March 26, 2025
Thursday, March 27, 2025
Friday, March 28, 2025
Saturday, March 29, 2025
Sunday, March 30, 2025
Monday, March 31, 2025
Tuesday, April 1, 2025
Wednesday, April 2, 2025
Thursday, April 3, 2025
Friday, April 4, 2025
Saturday, April 5, 2025
Sunday, April 6, 2025
Monday, April 7, 2025
Tuesday, April 8, 2025
Wednesday, April 9, 2025
2:30 PM
MCQM Seminar: Rafael Benguria
MCQM Seminar: Rafael Benguria
2:30 PM - 3:30 PM
Title: Bound on the Excess Charge of Generalized Thomas-Fermi-Weizsäcker functionals Abstract: We bound the number of electrons Q that an atom can bind in excess of neutrality for density functionals generalizing the classical Thomas-Fermi-Weizsäcker functional: instead of the classical power 5/3 more general powers p are considered. For 3/2 < p <2 we prove the excess charge conjecture, i.e., that Q is uniformly bounded in the atomic number Z. The case p = 3/2 is critical: the behavior changes from a uniform bound in Z to a linear bound at the critical coupling 4 √ π of the nonlinear term. We also improve the linear bound for all p ≥ 6/5. This is joint work with Heinz Siedentop, LMU, Munich.
Thursday, April 10, 2025
Friday, April 11, 2025
Saturday, April 12, 2025
Sunday, April 13, 2025
Monday, April 14, 2025
Tuesday, April 15, 2025
Wednesday, April 16, 2025
Thursday, April 17, 2025
Friday, April 18, 2025
Saturday, April 19, 2025
Sunday, April 20, 2025
Monday, April 21, 2025
Tuesday, April 22, 2025
Wednesday, April 23, 2025
Thursday, April 24, 2025
Friday, April 25, 2025
Saturday, April 26, 2025
Sunday, April 27, 2025
Monday, April 28, 2025
Tuesday, April 29, 2025
Wednesday, April 30, 2025
Thursday, May 1, 2025
Friday, May 2, 2025
Saturday, May 3, 2025
Sunday, May 4, 2025
Monday, May 5, 2025
Tuesday, May 6, 2025
Wednesday, May 7, 2025
Thursday, May 8, 2025
Friday, May 9, 2025
Saturday, May 10, 2025
Sunday, May 11, 2025
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