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Higher Dimensional CFTs as 2D Conformally-Equivariant Topological Field Theories
Two and three-point functions of primary fields in four dimensional CFT have simple space-time dependences factored out from the combinatoric...
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Building New Einstein Spaces by Deforming Symmetric Einstein Spaces
We introduce an approach to determine new pseudo-Riemannian Einstein spaces by deforming symmetric pseudo-Riemannian Einstein spaces. The metrics of...
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Polyanalytic Toeplitz Operators: Isomorphisms, Symbolic Calculus and Approximation of Weyl Operators
We discuss an extension of Toeplitz quantization based on polyanalytic functions. We derive isomorphism theorem for polyanalytic Toeplitz operators...
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mu-Brownian Motion, Dualities, Diffusions, Transforms, and Reproducing Kernel Hilbert Spaces
Replacing the Lebesgue measure on an interval by a Stieltjes positive non-atomic measure, we study the corresponding counterpart of the Brownian...
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The Dirichlet Space
The notes below are a copy of a set of three lectures presented online in July 2021, during the Fields Institute Focus Program Analytic Function...
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Gibbs Measures of Nonlinear Schrödinger Equations as Limits of Quantum Many-Body States in Dimension d ≤ 3
Gibbs measures of nonlinear Schrödinger equations are a fundamental object used to study low-regularity solutions with random initial data. In the...
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Tail algebras for monotone and q-deformed exchangeable stochastic processes
We compute the tail algebras of exchangeable monotone stochastic processes. This allows us to prove the analogue of de Finetti’s theorem for this...
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Renormalization
In this chapter, we address some applications of the theory of Hopf algebras that have been popular recently, starting essentially in the late 1990s...
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An Invitation to the Drury–Arveson Space
This is an extended version of a three part mini course on the Drury–Arveson space given as part of the Focus Program on Analytic Function Spaces and...
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Classical field theory limit of many-body quantum Gibbs states in 2D and 3D
We provide a rigorous derivation of nonlinear Gibbs measures in two and three space dimensions, starting from many-body quantum systems in thermal...
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Q-space Representation of Boson Fock Space
We review the so-called Q-space representation (a probability theoretical representation) of the boson Fock space over a Hilbert space. This...
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Mathematical Reflections on Locality
Starting from the principle of locality in quantum field theory, which states that an object is influenced directly only by its immediate...
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Invariant Gibbs measures for the three dimensional cubic nonlinear wave equation
We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional cubic wave equation, which is also known as the hyperbolic
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The two weight T1 theorem for fractional Riesz transforms when one measure is supported on a curve
Let σ and ω be locally finite positive Borel measures on ℝ n . We assume that at least one of the two measures σ and ω is supported on a regular C 1, δ ...
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Toeplitz Operators on CR Manifolds and Group Actions
Let X be a connected orientable compact CR manifold with non-degenerate Levi form. In this paper, we study the algebra of Toeplitz operators on X and...
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Spinors in Inner Product Spaces
This chapter builds on Chapters 3 and 4, and uses the material in Sections 1.4 and 1.5. Any knowledge of representation theory is helpful, but the...
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Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space
We consider the nonlinear Schrödinger equation with multiplicative spatial white noise and an arbitrary polynomial nonlinearity on the...