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Mathematical Challenges in Quantum Mechanics - Online Seminars
from
Friday, 1 November 2024 (09:00)
to
Saturday, 31 May 2025 (23:00)
Monday, 28 October 2024
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Tuesday, 29 October 2024
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Wednesday, 30 October 2024
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Thursday, 31 October 2024
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Friday, 1 November 2024
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Saturday, 2 November 2024
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Sunday, 3 November 2024
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Monday, 4 November 2024
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Tuesday, 5 November 2024
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Wednesday, 6 November 2024
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11:30
MCQM PhD Lecture: Benjamin Alvarez
MCQM PhD Lecture: Benjamin Alvarez
11:30 - 12:30
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.
14:30
MCQM Seminar: Volker Bach
MCQM Seminar: Volker Bach
14:30 - 15:30
Title: TBA Abstract: TBA
Thursday, 7 November 2024
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Friday, 8 November 2024
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Saturday, 9 November 2024
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Sunday, 10 November 2024
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Monday, 11 November 2024
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Tuesday, 12 November 2024
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Wednesday, 13 November 2024
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Thursday, 14 November 2024
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Friday, 15 November 2024
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Saturday, 16 November 2024
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Sunday, 17 November 2024
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Monday, 18 November 2024
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Tuesday, 19 November 2024
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Wednesday, 20 November 2024
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Thursday, 21 November 2024
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Friday, 22 November 2024
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Saturday, 23 November 2024
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Sunday, 24 November 2024
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Monday, 25 November 2024
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Tuesday, 26 November 2024
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Wednesday, 27 November 2024
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Thursday, 28 November 2024
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Friday, 29 November 2024
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Saturday, 30 November 2024
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Sunday, 1 December 2024
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Monday, 2 December 2024
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Tuesday, 3 December 2024
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Wednesday, 4 December 2024
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Thursday, 5 December 2024
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Friday, 6 December 2024
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Saturday, 7 December 2024
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Sunday, 8 December 2024
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Monday, 9 December 2024
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Tuesday, 10 December 2024
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Wednesday, 11 December 2024
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Thursday, 12 December 2024
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Friday, 13 December 2024
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Saturday, 14 December 2024
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Sunday, 15 December 2024
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Monday, 16 December 2024
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Tuesday, 17 December 2024
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Wednesday, 18 December 2024
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11:30
MCQM PhD Lecture: Angelo Lucia
MCQM PhD Lecture: Angelo Lucia
11:30 - 12:30
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.
14:30
MCQM Seminar: David Pérez García
MCQM Seminar: David Pérez García
14:30 - 15:30
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, 19 December 2024
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Friday, 20 December 2024
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Saturday, 21 December 2024
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Sunday, 22 December 2024
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Monday, 23 December 2024
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Tuesday, 24 December 2024
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Wednesday, 25 December 2024
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Thursday, 26 December 2024
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Friday, 27 December 2024
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Saturday, 28 December 2024
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Sunday, 29 December 2024
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Monday, 30 December 2024
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Tuesday, 31 December 2024
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Wednesday, 1 January 2025
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Thursday, 2 January 2025
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Friday, 3 January 2025
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Saturday, 4 January 2025
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Sunday, 5 January 2025
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Monday, 6 January 2025
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Tuesday, 7 January 2025
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Wednesday, 8 January 2025
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Thursday, 9 January 2025
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Friday, 10 January 2025
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Saturday, 11 January 2025
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Sunday, 12 January 2025
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Monday, 13 January 2025
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Tuesday, 14 January 2025
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Wednesday, 15 January 2025
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11:30
MCQM PhD Lecture: Benjamin Hinrichs
MCQM PhD Lecture: Benjamin Hinrichs
11:30 - 12:30
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.
14:30
MCQM Seminar: Robert Seiringer
MCQM Seminar: Robert Seiringer
14:30 - 15:30
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, 16 January 2025
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Friday, 17 January 2025
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Saturday, 18 January 2025
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Sunday, 19 January 2025
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Monday, 20 January 2025
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Tuesday, 21 January 2025
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Wednesday, 22 January 2025
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Thursday, 23 January 2025
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Friday, 24 January 2025
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Saturday, 25 January 2025
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Sunday, 26 January 2025
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Monday, 27 January 2025
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Tuesday, 28 January 2025
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Wednesday, 29 January 2025
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Thursday, 30 January 2025
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Friday, 31 January 2025
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Saturday, 1 February 2025
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Sunday, 2 February 2025
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Monday, 3 February 2025
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Tuesday, 4 February 2025
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Wednesday, 5 February 2025
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Thursday, 6 February 2025
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Friday, 7 February 2025
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Saturday, 8 February 2025
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Sunday, 9 February 2025
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Monday, 10 February 2025
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Tuesday, 11 February 2025
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Wednesday, 12 February 2025
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Thursday, 13 February 2025
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Friday, 14 February 2025
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Saturday, 15 February 2025
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Sunday, 16 February 2025
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Monday, 17 February 2025
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Tuesday, 18 February 2025
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Wednesday, 19 February 2025
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Thursday, 20 February 2025
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Friday, 21 February 2025
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Saturday, 22 February 2025
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Sunday, 23 February 2025
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Monday, 24 February 2025
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Tuesday, 25 February 2025
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Wednesday, 26 February 2025
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Thursday, 27 February 2025
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Friday, 28 February 2025
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Saturday, 1 March 2025
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Sunday, 2 March 2025
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Monday, 3 March 2025
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Tuesday, 4 March 2025
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Wednesday, 5 March 2025
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Thursday, 6 March 2025
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Friday, 7 March 2025
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Saturday, 8 March 2025
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Sunday, 9 March 2025
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Monday, 10 March 2025
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Tuesday, 11 March 2025
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Wednesday, 12 March 2025
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11:30
MCQM PhD Lecture: Andrew Rout
MCQM PhD Lecture: Andrew Rout
11:30 - 12:30
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, 13 March 2025
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Friday, 14 March 2025
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Saturday, 15 March 2025
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Sunday, 16 March 2025
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Monday, 17 March 2025
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Tuesday, 18 March 2025
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Wednesday, 19 March 2025
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Thursday, 20 March 2025
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Friday, 21 March 2025
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Saturday, 22 March 2025
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Sunday, 23 March 2025
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Monday, 24 March 2025
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Tuesday, 25 March 2025
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Wednesday, 26 March 2025
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Thursday, 27 March 2025
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Friday, 28 March 2025
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Saturday, 29 March 2025
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Sunday, 30 March 2025
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Monday, 31 March 2025
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Tuesday, 1 April 2025
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Wednesday, 2 April 2025
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Thursday, 3 April 2025
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Friday, 4 April 2025
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Saturday, 5 April 2025
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Sunday, 6 April 2025
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Monday, 7 April 2025
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Tuesday, 8 April 2025
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Wednesday, 9 April 2025
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11:30
MCQM PhD Lecture: Konstantin Merz
MCQM PhD Lecture: Konstantin Merz
11:30 - 12:30
Title: The Ionization Conjecture in Quantum Mechanics and Density Functional Theory: An Introduction Abstract: Quantum mechanics accurately describes physics on atomic length scales. However, many fundamental questions about the structure of matter remain unanswered. A prominent example is the Ionization Conjecture. It asserts that an atom with nuclear charge Z can bind at most Z+1 electrons. Although this has been experimentally documented since the 1970s, a mathematical proof is not in sight. In this lecture, we introduce the Ionization Conjecture and review some landmark results and recent progress. Although the conjecture for the full many-body problem seems out of reach, significant progress has been made in certain effective single-particle models. These models are easier to study yet still capture key aspects of the full many-body system. Among these are density functional theories such as the classic Thomas–Fermi model, which effectively describe the energy and particle distribution of large atoms and molecules. Remarkably, despite describing the bulk of the electrons, these models also provide insights into the outermost electrons—the key objects in the Ionization Conjecture.
14:30
MCQM Seminar: Rafael Benguria
MCQM Seminar: Rafael Benguria
14:30 - 15:30
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, 10 April 2025
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Friday, 11 April 2025
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Saturday, 12 April 2025
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Sunday, 13 April 2025
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Monday, 14 April 2025
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Tuesday, 15 April 2025
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Thursday, 17 April 2025
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Friday, 18 April 2025
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Saturday, 19 April 2025
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Tuesday, 22 April 2025
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Wednesday, 23 April 2025
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Thursday, 24 April 2025
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Friday, 25 April 2025
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Saturday, 26 April 2025
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Sunday, 27 April 2025
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Tuesday, 29 April 2025
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Wednesday, 30 April 2025
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Thursday, 1 May 2025
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Friday, 2 May 2025
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Sunday, 4 May 2025
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Monday, 5 May 2025
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Tuesday, 6 May 2025
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Wednesday, 7 May 2025
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Thursday, 8 May 2025
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Friday, 9 May 2025
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Saturday, 10 May 2025
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Sunday, 11 May 2025
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Monday, 12 May 2025
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Tuesday, 13 May 2025
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Wednesday, 14 May 2025
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11:30
MCQM PhD Lecture: TBA
MCQM PhD Lecture: TBA
11:30 - 12:30
Title: TBA Abstract: TBA
14:30
MCQM Seminar: Nicola Pinamonti
MCQM Seminar: Nicola Pinamonti
14:30 - 15:30
Title: TBA Abstract: TBA
Thursday, 15 May 2025
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Friday, 16 May 2025
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Saturday, 17 May 2025
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Sunday, 18 May 2025
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Monday, 19 May 2025
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Tuesday, 20 May 2025
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Wednesday, 21 May 2025
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Thursday, 22 May 2025
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Tuesday, 27 May 2025
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Wednesday, 28 May 2025
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Thursday, 29 May 2025
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Friday, 30 May 2025
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Saturday, 31 May 2025
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