Events Archive

Mathematical Physics Seminar

Math Physics Seminar, Roland Bauerschmidt, Harvard, "Local eigenvalue statistics for random regular graphs"

Tue, Nov 10, 2015, 4:30 pm to 6:00 pm
I will discuss results on local eigenvalue statistics for uniform random regular graphs. Under mild growth assumptions on the degree, we prove that the local semicircle law holds at the optimal scale, and that the bulk eigenvalue statistics (gap statistics and averaged energy correlation functions) are given by those of the GOE. Joint work with J...

Math Physics Seminar, Bertrand Duplantier, Ins. Phys. Théorique, Saclay, "Schramm -- Loewner Evolution and Liouville Quantum Multifractality"

Tue, Oct 27, 2015, 4:30 pm to 5:30 pm
We describe some recent advances in the study of the fundamental coupling of a canonical model of random paths, the Schramm--Loewner Evolution (SLE), to a canonical model of random surfaces, Liouville Quantum Gravity (LQG). The latter is expected to be the conformally invariant continuum limit of various models of random planar maps.

Math Physics Seminar, Daniel Sternheimer, Rikkyo & Bourgogne U's, "The reasonable effectiveness of mathematical deformation theory in physics, .......

Tue, Oct 6, 2015, 4:30 pm to 5:30 pm
In 1960 Wigner marveled about ``the unreasonable effectiveness of mathematics in the natural sciences," referring mainly to physics. In that spirit we shall first explain how a posteriori relativity and quantum mechanics can be obtained from previously known theories using the mathematical theory of deformations.

Math Physics Seminar, Pavel Exner, Inst. for Math. Physics, Prague, "Quantum Graphs and Neumann Networks"

Tue, Sep 29, 2015, 4:30 pm to 5:30 pm
Quantum graph models are extremely useful but they also have some drawbacks. One of them concerns the physical meaning of the vertex coupling. The self-adjointness requirement leaves a substantial freedom expressed through parameters appearing in the conditions matching the wave function at the graph vertices.

Math Physics Seminar, Yoshiko Ogata, U of Tokyo, "A class of gapped Hamiltonians on quantum spin chains and its classification"

Tue, Apr 28, 2015, 4:30 pm to 5:30 pm
"The MPS (matrix product state) formalism gives a recipe to construct Hamiltonians in quantum spin chains from $n$-tuples of $k\times k$- matrices. This $n$-tuple defines a completely positive map and the existence of the uniform spectral gap of the Hamiltonian is related to the spectral property of the associated CP map.

Math Physics Seminar, Barry Simon, Caltech, "Singular Eigenvalue Perturbation Theory"

Math Physics Seminar, Wendelin Werner, ETS, Zurich, "'A simple renormalization flow setup for FK-percolation models"

Tue, Apr 7, 2015, 4:30 pm to 5:30 pm
We will present a simple setup in which one can make sense of a renormalization flow for FK-percolation models in terms of a simple Markov process on a state-sace of discrete weighted graphs.

Math Physics Seminar, Grisha Falkovich, Weizmann Inst., "When the Dust Settles"

Tue, Mar 31, 2015, 4:30 pm to 5:30 pm
Small aerosols drift down a temperature or turbulence gradient since faster particles fly longer distances before equilibration. That fundamental phenomenon is known since Maxwell and it was universally believed that particles moving down the kinetic energy gradient must concentrate in minima (say, on walls in turbulence).

Math Physics Seminar, Simone Warzel, TU-Munich, "On the decay rates of determinantal correlation functionals"

Tue, Mar 24, 2015, 4:30 pm to 5:30 pm
Determinantal correlation functionals arise as the correlation functions of non-interacting fermions, and also in other determinantal point processes, such as the eigenvalues of random matrices, and the zeros of random polynomials.

Math Physics Seminar, Senya Shlosman, U Marseille, "Airy diffusion and N^{1/3} fluctuations in the 2D Ising model"

Tue, Mar 3, 2015, 4:30 pm to 5:30 pm
For the two-dimensional Ising model at low temperatures consider a floating droplet of the (+) phase floating in the sea of (-) phase, pressed against a horizontal wall within a box of linear size N. I will explain that the fluctuations of the boundary of the droplet near the contact with the wall are of the order of N^{1/3}.

Math Physics Seminar, Subhro Ghosh, Princeton, "Rigidity phenomena in random point sets"

Tue, Feb 24, 2015, 4:30 pm to 5:30 pm
In several naturally occurring (infinite) point processes, the number the points inside a finite domain can be determined, almost surely, by the point configuration outside the domain. There are also other processes where such ''rigidity'' extends also to a number of moments of the mass distribution.

Math Physics Seminar, Michael Kiessling, Rutgers, "A novel quantum-mechanical interpretation of the Dirac equation"

Tue, Feb 10, 2015, 4:30 pm to 5:30 pm
A novel interpretation is given of Dirac's ``wave equation for the relativistic electron'' as a quantum-mechanical one-particle equation in which electron and positron are merely the two different ``topological spin'' states of a single more fundamental particle, not distinct particles in their own right.

Math Physics Seminar, Alessandro Giuliani, U. of Rome 3, "Height Fluctuations in Interacting Dimers"

Tue, Feb 3, 2015, 4:30 pm to 6:00 pm
Perfect matchings of Z^2 (also known as non-interacting dimers on the square lattice) are an exactly solvable 2D statistical mechanics model. It is known that the associated height function behaves at large distances like a massless gaussian field, with the variance of height gradients growing logarithmically with the distance. As soon as dimers...

Math Physics Seminar, Ivan Corwin, Columbia, "Stochastic higher spin vertex models on the line"

Tue, Dec 9, 2014, 4:30 pm to 6:00 pm
We show how transfer matrices of higher spin vertex models (generalizing the six-vertex model) can be conjugated into stochastic matrices describing interacting particle systems. Bethe ansatz produces eigenfunctions and we prove their completeness on the line.

Math Physics Seminar, Jakob Yngvason, U. of Vienna, "Superfluid behavior of a Bose-Einstein condensate in a random potential"

Tue, Nov 18, 2014, 4:30 pm to 5:30 pm
We investigate the relation between Bose-Einstein condensation

Math Physics Seminar, Christian Fronsdal, UCLA, "The Structure of flow in Hyrdrodynamics, Thermodynamics and General Relativity, from Navier Stokes

Tue, Nov 11, 2014, 4:30 pm to 5:30 pm
"The structure of flow in Hydrodynam:wqics, Thermodynamics and General Relativity, from Navier Stokes to Tolman."

Math Physics Seminar, John Inbrie, "A rigorous result on many-body localization "

Tue, Oct 14, 2014, 4:30 pm to 6:00 pm
A one-dimensional spin chain with random interactions exhibits many-body localization. I will discuss a proof under a physically reasonable assumption that limits the amount of level attraction in the system.

Math Physics Seminar: Amir Dembo, "Statistical Mechanics on Sparse Random Graphs: Mathematical Perspective"

Tue, Sep 23, 2014, 4:30 pm to 5:30 pm
Theoretical physics studies of disordered materials lead to challenging mathematical problems with applications to random combinatorial problems and coding theory. The underlying structure is that of many discrete variables that are strongly interacting according to a mean field model determined by a random sparse graph.

Math Physics Seminar, Frank Hansen, "Regular operator mappings and multivariate geometric means"

Tue, Sep 16, 2014, 4:30 pm to 5:30 pm
We introduce the notion of regular operator mappings of several variables generalising the notion of spectral function. This setting is convenient for studying maps more general than what can be obtained from the functional calculus, and it allows for Jensen type inequalities and multivariate non-commutative perspectives.

Math Physics Seminar, Hugo Duminil, "From conformal invariance of parafermionic observables to conformal invariance of interfaces of planar random-clu

Tue, May 20, 2014, 4:30 pm to 6:00 pm
In this talk we will explain how the determination of the scaling limit of parafermionic observables can be used to deduce the conformal invariance of interfaces in planar random-cluster models with cluster-weight 1 ≤ Q ≤ 4 (1\leq Q \leq 4).

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