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Talks in Mathematical Physics
in the Stockholm area
This is a seminar series which specializes in mathematical physics, including random matrix theory, spectral theory, classical and quantum dynamics, etc., and it is organized jointly between the mathematics and physics departments in the Stockholm area. What we suggest is a meeting approximately every two weeks and to keep discussions at a pedagogical level, aiming for a better interaction between different communities.

Organization
Please contact Douglas or Maurice if you would like to contribute. Here is a temporary doodle for interest and schedule preference. We are leaning towards Thursdays 15-16.

Topics
Some suggested topics:
Lower-dimensional particle systems, Coulomb gases, CFT (Hardy, Lundholm, Langmann, Lenells, Viklund...)
Coherent states, correspondence principle and quantization (Hynek, Lundholm, Hoppe?, Lenells?...)

Past and planned seminars
 2017 17/1- KTH Course: SF2724 Topics in mathematics IV: Methods of modern mathematical physics During the spring 2017 a master-level course (which may also be credited by PhD students) will be given about mathematical methods in quantum mechanics. Starting from a precise mathematical formulation of the latter, including in particular the famous uncertainty and exclusion principles, we will aim to rigorously prove the stability of ordinary matter. This is something which most of us take for granted and physics textbooks rarely discuss but which is quite subtle and requires proper analysis of the above principles. Various useful inequalities such as the Hardy, Sobolev and Lieb-Thirring inequalities will be introduced and proved during the course. More information can be found here: https://www.kth.se/social/course/SF2724/ 2016 17/318/319/3 KTH / Stockholm University / Institut Mittag-Leffler Session in Mathematical Physics at the 27th Nordic Congress of Mathematicians Confirmed speakers: Farrokh Atai (KTH Royal Institute of Technology) Thomas Bäckdahl (Chalmers University of Technology) Matthias Christandl (Copenhagen University) Horia Cornean (Aalborg University) Jan Derezinski (University of Warsaw) Tobias Ekholm (Institut Mittag-Leffler and Uppsala University) Maria Esteban (CNRS and University Paris-Dauphine) Magnus Goffeng (University of Gothenburg) Arne Jensen (Aalborg University) Thordur Jonsson (University of Iceland) Antti Kupiainen (University of Helsinki) Hans Ringström (KTH Royal Institute of Technology) See the page of the session for schedule and abstracts. 9/313:15-14:15 KTH 3721 Analysis seminar Singular systems on manifolds Teoman Turgut (Bogaziçi University) Abstract: We discuss a singular extension of Laplacian on a two or three dimensional manifold. Under certain mild assumptions, we show that the bottom of the spectrum becomes a non-degenerate eigenvalue. We define an oversimplified version of the Lee model, in which a two level system is interacting with bosonic particles on a three dimensional manifold. We show that this system can be understood by an associated operator, after removing an infinity (renormalization). We indicate that this operator contains all the information about the dynamics and the spectrum is bounded from below. We explain that there is a well defined self-adjoint Hamiltonian defined by this operator. We sketch the proof that on a compact manifold the lowest eigenstate of this operator is unique, using the theory of positivity improving semigroups. 2015 28/1013:15-14:15 KTH 3721 Analysis seminar Anyons in the average field approximation D. Lundholm (KTH) Abstract: Quantum systems confined to planar geometries may exhibit effective particles with unusual statistics, called anyons. These can be modeled as identical particles (bosons or fermions) in 2D with magnetic flux attached to them. In this talk I will discuss the validity of the average field approximation for anyons, in which the resulting magnetic field is replaced by that of the mean distribution of the particles. In a certain limit this turns out to be a correct description and the particles then behave like independent, identically distributed bosons interacting via a self-consistent magnetic field. The resulting non-linear energy functional is being studied in joint work with Michele Correggi, Romain Duboscq and Nicolas Rougerie. 9/910:30-11:30 SU 306 Analysis/Mathematical physics seminar On the generations of monic polynomials obtained by replacing the coefficients of the polynomials of the next generation with the zeros of a polynomial of the previous generation Francesco Calogero (Physics Department, University of Rome) Abstract: Generations of monic polynomials, all of arbitrary degree N, are obtained from a seed polynomial of degree N by identifying the coefficients of the polynomials of the next generation with the zeros of a polynomial of the previous generation; and Diophantine properties are reported of the zeros of the polynomials thereby obtained when the seed polynomial is the Hermite polynomial of degree N. This is joint work in progress with Oksana Bihun. 3/909:15-10:15 KTH 3721 Analysis/special seminar Critical exponents for FK random planar maps Nathanael Berestycki (Cambridge) Abstract: We consider random planar maps weighted by the critical Fortuin--Kasteleyn percolation model with parameter $q \in (0,4)$. The study of these surfaces is central to the theory of Liouville quantum gravity. We obtain rigorously the value of the critical exponent associated with the length of cluster interfaces, which is shown to be $$\frac{4}{\pi} \arccos \left( \frac{\sqrt{2 - \sqrt{q}}}{2} \right).$$ This is consistent with physics predictions; in particular, applying the KPZ formula we recover the dimension of SLE curves. Joint work with Benoit Laslier and Gourab Ray (Cambridge). 11/613:00-14:00 KTH 3733 Enhanced Quantization M. Hynek (KTH) Abstract: I will discuss a certain generalization of Canonical Quantization proposed by John R. Klauder which is believed to solve some of the problems arising in quantization (in particular for systems with an infinite number of degrees of freedom). 27/515:15-16:15 KTH 3721 Conformal Field Theory, and Schramm-Loewner Evolution Nam-Gyu Kang (Seoul National University) Abstract: I will present an elementary introduction to conformal field theory in the context of complex analysis and probability theory. Introducing Ward functional as an insertion operator under which the correlation functions are transformed into their Lie derivatives, I will explain several formulas in conformal field theory including Ward's equations. This presentation will also include relations between conformal field theory and Schramm–Loewner evolutions. For these relations, the so-called neutrality conditions of vertex fields on the charges play an important role. I explain two neutrality conditions: first, the linear combination of bosonic fields is to be a well-defined Fock space field; second, the Coulomb gas correlation function is to be conformally invariant. To reconcile these two neutrality conditions, one needs to place the background charge at the marked interior point, the target point of SLE. This is joint work with Nikolai Makarov. 21/515:15-16:15 KTH 3721 Geodesics on Ellipsoids (II) J. Hoppe (KTH) This is a continuation of the previous talk by the same speaker, concerning new methods related to the study of length-minimizing paths on ellipsoids. 13/510:30-11:30 SU 306 Analysis/Mathematical physics seminar Three-coloured chessboards Hjalmar Rosengren (Chalmers and Gothenburg Univ) Abstract: I will discuss some mathematics and physics related to what I call three-coloured chessboards. These seemingly simple combinatorial objects turn out to have intriguing relations to topics such as elliptic functions and modular forms, solvable models of statistical mechanics, affine Lie algebras and Painlevé equations. The lecture should be accessible to a wide audience. 7/515:15-16:15 KTH 3721 Geodesics on Ellipsoids J. Hoppe (KTH) Abstract: Various methods will be presented to study length-minimizing paths on ellipsoids. Mathematical Physics would not be what it is today without Jacobi's work on geodesics on ellipsoids, with the invention of elliptical coordinates, and one of the prime examples for what we nowadays call Hamilton-Jacobi theory. 23/415:15-16:15 KTH 3721 2D Coulomb gases and particles in magnetic fields D. Lundholm (KTH) Abstract: I will outline how one is led to study a classical 2D Coulomb gas, starting from a quantum theory of electrons moving in a magnetic field and confined to a plane (but interacting with their usual 3D Coulomb repulsion). This is also a part of Laughlin's Nobel Prize-awarded work on the fractional quantum Hall effect. If time permits we can look at related, more complicated many-particle wave functions and the problem of computing their correlation functions. 16/415:15-16:15 KTH 3721 Gaussian and non-Gaussian Limit theorems for some determinantal systems of particles G. Lambert (KTH) Abstract: First, I will review the central limit theorem for linear statistics of the sine point process from Random Matrix theory. Then, I will explain how the proof can be generalized to a class of determinantal measures in one dimension which interpolate between Poisson and Random Matrix statistics. An example of such a process comes from considering a grand canonical ensemble of free fermions in a quadratic well at positive temperature. For this model, we obtain different limit theorems for linear statistics depending on the density of the process and the temperature. In particular, in a critical regime, we can observe some non-Gaussian limits. This is a joint work with K. Johansson. 26/315:15-16:15 KTH 3721 Various aspects on Coulomb gases A. Hardy (KTH) Abstract: I will introduce (classical) Coulomb gases, which are statistical gases of particles on R^d interacting according to the laws of electrostatic, and provide various aspects of their asymptotic analysis. More precisely, I'll discuss the convergence, large deviations, and the possible fluctuations for such particle systems, and the asymptotic expansion for the partition function as well. I'll also describe the connection to random matrices and orthogonal polynomials when d=2. 18/310:30-11:30 SU 306 Analysis/Mathematical physics seminar E. Langmann (KTH) Kernel functions and Calogero-Moser type systems 25/210:30-11:30 SU 306 Analysis/Mathematical physics seminar B.L.G. Jonsson (KTH) A bandwidth limitation for certain array antennas and its connection to sum-rules 28/110:30-11:30 SU 306 Analysis/Mathematical physics seminar Boris Shapiro (SU) On spectral asymptotics of quasi-exactly solvable quartic and Yablonskii-Vorob'ev polynomials 2014 10/1211:00-12:00 SU 306 Analysis/Mathematical physics seminar Markus Grassl SIC-POVMs and MUBs: Sets of Quantum States with Special Properties

Participants
The following have expressed their interest in participating in the seminars (which are of course open to everyone):

Annemarie Luger
Anthony Metcalfe
Björn Gustafsson
Douglas Lundholm
Edwin Langmann
Farrokh Atai
Fredrik Viklund
Jan Boman
Jens Hoppe
Jonatan Lenells
Gaultier Lambert
Kurt Johansson
Mariusz Hynek
Maurice Duits
Pavel Kurasov
Per Moosavi
Rostyslav Kozhan
Simon Larson