Aisenstadt Chair

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Michael Aizenman (Princeton University)
Stay: September 17- November 16, 2018

Michael Aizenman delivered his lectures on September 24, 25 and 27, 2018 in the Pavillon André-Aisenstadt, room 1140 at 4:00 pm.

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AizenmanDATE
Monday, September 24, 2018 / 4:00 pm

LOCATION
Centre de recherches mathématiques
Pavillon André-Aisenstadt, Université de Montréal
Rooom 1140

A mathematical physicist's perspective on Statistical Mechanics

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Statistical mechanics explains and quantifies the process by which structure emerges from chaos. Its genesis is in Boltzmann's explanation of thermodynamical behavior and in particular of the concept of entropy. The statistic mechanical perspective was instrumental for Planck's theory of the light quantization and Einstein's calculation of the Avogadro number. More recent developments include links between the physics of critical phenomena and the mathematics of conformally invariant random structures, stochastic integrability, and representation theory. The talk will focus on examples of observations and conjectures which turned out to point in fruitful directions.

A reception will follow the lecture at the Salon Maurice-L'Abbé, Pavillon André-Aisenstadt (room 6245).

DATE
Tuesday, September 25, 2018 / 4:00 pm

LOCATION
Centre de recherches mathématiques
Pavillon André-Aisenstadt, Université de Montréal
Room 1140

Emergent structures in statistical mechanics and quantum systems

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Equilibrium states of classical and quantum systems can often be understood in terms of spontaneously emergent structures. Examples can be seen in: i) the emergent fermionic and spinor degrees of freedom in planar models, ii) the spontaneous organization of Ising and Potts spins into cliques, whose statistics are given by the Fortuin-Kasteleyn random cluster models, iii) the random current representation of the equilibrium Gibbs states of Ising and related field theoretic models, and iv) loop based organization of certain quantum spin chains into clusters of total S^z=0 spin. Uncovering the hidden stochastic geometric features allows insights on the model's phase structure, the nature of its correlation functions, and details of its critical behavior.

DATE
Thursday, September 27, 2018 / 4:00 pm

LOCATION:
Centre de recherches mathématiques Pavillon André-Aisenstadt,
Université de Montréal
Room 1140

The Imry-Ma effect and the decay of correlations under quenched random field

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The famed discontinuity of the magnetization in the two dimensional Ising model is unstable to the addition of quenched random magnetic field of uniform variance, even if that is small. The talk will focus on a quantitative version of the statement established in a previous work with J. Wehr. The result is a power-law upper bound on the decay of the effects of boundary conditions on the magnetization in finite systems, as function of the distance to the boundary. The analysis applies to all field strengths and all temperatures, including T =0. However the result does not resolve the question of possible transition to exponential decay at weak disorder. The corresponding questions concerning disorder effects on systems with continuous symmetry in three and four dimensions also remain open. The talk is based on a recent joint work with Ron Peled (TAU).

BIOGRAPHY

Michael Aizenman is a mathematical physicist at Princeton University. He received a PhD degree in 1975 at Yeshiva University (Belfer Graduate School of Science), New York. After postdoctoral positions, he was appointed assistant professor at Princeton. In 1982, he moved to Rutgers University as associate professor and then full professor. In 1987, he moved to the Courant Institute and in 1990 returned to Princeton as professor of mathematics and theoretical physics. He was awarded the Norbert Wiener Prize (1990) of the AMS and SIAM for “his outstanding contribution of original and non-perturbative mathematical methods in statistical mechanics by means of which he was able to solve several long open important problems concerning critical phenomena, phase transitions, and quantum field theory.” More recently he has been working on quantum effects of quenched disorder. Member of the National Academy of Sciences since 1997, he is also the recipient of the Brouwer Medal (2002) of the Dutch Royal Mathematical Society (KWG) and Royal Netherlands Academy of Arts and Sciences (KNAW), and doctor honoris causa of Université de Cergy-Pontoise (2009). He is the principal organizer of the joint CRM–PCTS workshop that will be held at Princeton in October 2018.