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Abstracts, Operator and Spectral Theory

12:30-12:50 K.-M. Perfekt: “Poincaré fundamental functions
Abstract: I will discuss the spectral decomposition of the double layer potential for the Laplacian, operating within the framework of symmetrisation. I will also indicate a recent result on the spectrum of this operator for domains in 3D with conical points. Based on joint work with Johan Helsing.

13:00-13:50 A. Pushnitski, “Schmidt subspaces of Hankel operators
Abstract: A Schmidt subspace of a bounded (not necessarily self-adjoint) operator A in a Hilbert space is an eigenspace of |A|. In this talk, I will describe the structure of Schmidt spaces of Hankel operators. This is recent joint work with Patrick Gerard (Orsay).

14:00-14:50 L. Scardia, “Equilibrium measures for nonlocal energies: The effect of anisotropy
Abstract: Nonlocal energies are continuum models for large systems of particles with long-range interactions. Under the assumption that the interaction potential is radially symmetric, several authors have investigated qualitative properties of energy minimisers​. But what can be said in the case of anisotropic kernels? Motivated by the example of dislocation interactions in materials science, we pushed the methods developed for nonlocal energies beyond the case of radially symmetric potentials, and discovered surprising connections with random matrices and fluid dynamics.​

15:30-16:20 J.R. Partington, “Properties of restricted shift operators”
Abstract: We discuss numerical ranges of restricted shift operators and their unitary dilations, and we link these with the theory of truncated Toeplitz operators (TTO) and Hankel operators. Further results on the norm of a TTO are derived, and a conjecture on the existence of continuous symbols for compact TTO is resolved. This is joint work with Pamela Gorkin (Bucknell) and others.

16:30-17:20 O.F. Brevig, “Hilbert–type inequalities and operator theory in the Hardy space of Dirichlet series
Abstract: We present two instances where inequalities related to the classical Hilbert inequality appear in the operator theory of the Hardy space of (ordinary) Dirichlet series with square summable coefficients. After some preliminaries, we will discuss a canonical Hankel form which is a multiplicative analogue of the Hilbert matrix. We will then explain how a family of Hilbert–type inequalities are related to sharp norm estimates for composition operators. Some related open problems will also be discussed. Some of the material presented is based on joint work with F. Bayart and joint work with K.-M. Perfekt, K. Seip, A. G. Siskakis and D. Vukotić.

Operator and Spectral Theory

University of Reading, 12:30, April 4, 2018
Funded by an LMS Scheme 9 grant.
Travel support available for UK research students without other means of support.

The aim of the meeting is to highlight the interplay between operator and spectral theory, and to illustrate modern problems relevant to both areas.

Speakers
Ole Fredrik Brevig (Norwegian University of Science and Technology)
Jonathan Partington (University of Leeds)
Alexander Pushnitski (King’s College London)
Lucia Scardia (University of Bath)
Karl-Mikael Perfekt (University of Reading)

Abstracts.

Schedule
11:30 Lunch (for early arrivers), at Eat at the Square (building 7 on the map).

Talks in Mathematics room 314:
12:30-12:50 K.-M. Perfekt: “Poincaré fundamental functions”
13:00-13:50 A. Pushnitski, “Schmidt subspaces of Hankel operators”
14:00-14:50 L. Scardia, “Equilibrium measures for nonlocal energies: The effect of anisotropy”
14:50-15:20 Break
15:30-16:20 J.R. Partington, “Properties of restricted shift operators”
16:30-17:20 O.F. Brevig, “Hilbert–type inequalities and operator theory in the Hardy space of Dirichlet series”

17:20 Wine reception in Mathematics room 112.

19:00 Dinner at Franco Manca.

Venue:
Whiteknights Campus
University of Reading

Travel:
From London Paddington, take the train to Reading [RDG] (25 minutes). From Heathrow, take the bus to Reading (45-minute nonstop service, see www.railair.com). From the Reading Train Station, take the bus (21 or 21a) to Reading University (Whiteknights campus). Map of Whiteknights campus. Mathematics is Building 4 on the map.

Accommodation:
Hotel ibis Reading (town center)
The Cedars Hotel (on campus)
Hillingdon Prince (15-minute walk)

Registration fee:
10 GBP

Contact:
Karl-Mikael Perfekt, k.perfekt (at) reading.ac.uk