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Seminars

Below are the future seminars organised by the School of Mathematics.

Please note that only some seminar series are advertised here.

Past archives: 2024, 2025.

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Results 11 to 20 of 23

Andries Salm (University of Oxford) – Metric perturbations of degenerate Z/2-harmonic 1-forms

Date
@ Roger Stevens Lecture Theatre 11
Category

Z/2 harmonic 1-forms are generalizations of harmonic 1-forms that allow topological twisting around a subspace of codimension 2. These objects were introduced by Taubes to compactify the moduli spaces of solutions to generalized Seiberg-Witten equations, and they show up in many other gauge theoretical problems.

Donaldson showed there is a deformation theory for so-called non-degenerate Z/2-harmonic 1-forms. In this presentation metric we study the perturbations of the remaining degenerate solutions. For a natural class of degenerate examples, we prove that after a suitable perturbation of the ambient Riemannian metric, the form can be deformed to a nearby non-degenerate Z/2-harmonic 1-form.

Pavel Turek (Okinawa Institute of Science and Technology) – Field-independent decomposition columns of Hecke algebras

Date
@ MALL, online
Category

Abstract: Let Hn be a Hecke algebra over an arbitrary field, and let e be its quantum characteristic. A central open problem in the representation theory of Hn is describing composition factors of Specht modules (which are irreducible if e=0) for e>1. We provide new elementary formulas for many entries of decomposition matrices of Hn - matrices that give these composition factors. The new formulas provide at least one column in every block and are independent of the underlying field, making them highly applicable and insightful. The talk is based on results proved with David Hemmer and with Bim Gustavsson, Stacey Law, Lorenzo Putignano and Liron Speyer.