Research lectures, seminars and events
The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but wish to enquire about attending one of the events please contact the organiser or host department.
|October 2019||December 2019|
Events for 14 November 2019
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Automorphic Lie algebras are a class of infinite-dimensional Lie algebras that are closely related to a wide variety of algebraic structures that appear in integrable systems theory, mathematical physics and geometry. They can be viewed as a certain generalisation of the well-studied (twisted) loop algebras and current algebras. It can often be difficult to immediately gain an intuitive understanding of the algebraic structure behind an automorphic Lie algebra. However, this task can be made easier using techniques in representation theory. Associated to an automorphic Lie algebra is a commutative algebra of functions. Studying automorphic Lie algebras via evaluation maps parameterised by the representations of the associated commutative algebra provides a descending chain of ideals of the automorphic Lie algebra. A detailed study of this chain of ideals immediately shows that the representation theory of automorphic Lie algebras is wild, and enables us to describe the local Lie structure of the automorphic Lie algebra.
Marek Schoenherr: The electroweak sector of the Standard Model and precision calculations for the LHC
The LHC has completed its second run at the unprecedented energy of 13 TeV and prepares for the upcoming Run-3, with the High-Luminosity upgrade on the horizon. While the search for new physics continues in the soon-to-be-accessible high-energy regime, precision measurements of inclusive observables are likewise on the experiments physics programme. In this presentation I will review the role and properties of the electroweak half of the Standard Model and detail how its precise understanding is crucial to the success of both objectives in these seemingly so very dissimilar regimes.
Jean-Claude Cuenin: Improved eigenvalue bounds for SchrÃ¶dinger operators with slowly decaying potentials
We extend a result of Davies and Nath  on the location of eigenvalues of SchrÃ¶dinger operators $-\Delta+V$ with slowly decaying complex-valued potentials to higher dimensions. We also discuss examples related to the Laptev--Safronov conjecture , which stipulates that the absolute value of any complex eigenvalue can be bounded in terms of the $L^q$ norm of $V$, for a certain range of exponents $q$. The talk is based on .
Davies, E. B. and Nath, J. SchrÃ¶dinger operators with slowly decaying potentials J. Comput. Appl. Math., 2002, 148, 1-28
Laptev, A. and Safronov, O. Eigenvalue estimates for SchrÃ¶dinger operators with complex potentials Comm. Math. Phys., 2009, 292, 29-54
Cuenin, J.-C. Improved eigenvalue bounds for Schr\"odinger operators with slowly decaying potentials arXiv e-prints, 2019, arXiv:1904.03954
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Matthias Taeufer: A robust initial scale estimate and localization at band edges of the Anderson model
We prove that Anderson localization near band edges of ergodic continuum
random Schroedinger operators with periodic background potential in in
dimension two and larger is universal.
In particular, Anderson localization holds without extra decay
assumptions on the random variables and independently of regularity or
degeneracy of the Floquet eigenvalues of the background operator.
Our approach is based on a robust initial scale estimate the proof of
which avoids Floquet theory altogether and uses instead an interplay
between quantitative unique continuation and large deviation estimates.
Furthermore, our reasoning is sufficiently flexible to prove this
initial scale estimate in a non-ergodic setting, which promises to be an
ingredient for understanding band edge localization also in these
Based on joint work with Albrecht Seelmann (TU Dortmund).