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Mathematical Physics Seminar

Shadi Tahvildar-Zadeh - Covariant Quantum Theory of Guided Fields

Shadi Tahvildar-Zadeh

Location:  Hill Center room 705
Date & time: Thursday, 13 February 2020 at 12:00PM - 1:00PM


HILL 705

Shadi Tahvildar-Zadeh - Rutgers University

Thursday, February 13th , 12:00pm; Hill 705

 "Covariant Quantum Theory of Guided Fields"

After recalling the deformation procedure that allows one to start with classical Hamilton-Jacobi theory of particle mechanics and arrive at Schroedinger's equation for the wave function that provides the quantum law of motion for those particles,  I will show how one can use a similar procedure to arrive at a quantum version of the classical scalar field theory, in which the evolution of the quantized field is guided by a wave function defined on a finite-dimensional field configuration space, and that all this can be accomplished without breaking the Lorentz covariance of the theory.  This is joint work with Maaneli Derakhshani and Michael Kiessling.


Jeffry Kahn - Rutgers University

Thursday, February 13th, 2:00pm; Hill 705

"Thresholds vs. fractional expectation-thresholds"

The threshold, p_c(F), for an increasing family F contained in {0,1}^n is the (unique) p for which mu_p(F) = 1/2, where mu_p is the natural p-biased product measure on {0,1}^n.  Thresholds have been central to the study of random discrete structures (e.g. random graphs and hypergraphs) since the work of Erdos and Renyi in 1960, with, in particular, estimation of thresholds for various specific properties the subject of some of the most powerful work in the area.


In 2006, Gil Kalai and I conjectured that a natural lower bound q(F) (the "expectation-threshold") on p_c(F) is never too far from the true value.  In this talk I'll focus on a recent result proving a fractional version of this conjecture suggested about ten years ago by Michel Talagrand.?


This easily implies several previously difficult results and conjectures in probabilistic combinatorics, including thresholds for perfect hypergraph matchings (Johansson–Kahn–Vu) and bounded-degree spanning trees (Montgomery).  We also resolve (and vastly extend) the ``axial'' version of the random multi-dimensional assignment problem, proving a 2005 conjecture of Martin, Mezard and Rivoire.?


Our approach builds on a recent breakthrough of Alweiss, Lovett, Wu and Zhang on the Erdos–Rado “Sunflower Conjecture.”?


Joint with Keith Frankston, Bhargav Narayanan and Jinyoung Park.


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