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Research

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.


 

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Events for 27 November 2017

Codina Cotar: Equality of the Jellium and Uniform Electron Gas next-order asymptotic terms for Coulomb and Riesz potentials

12:00am, CM221
We consider two sharp next-order asymptotics problems, namely the asymptotics for the minimum energy for optimal point con figurations and the asymptotics for the many-marginals Optimal Transport, in both cases with Coulomb and Riesz costs with inverse power-law long-range interactions. The first problem describes the ground state of a Coulomb or Riesz gas, while the second appears as a semi-classical limit of the Density Functional Theory energy modelling a quantum version of the same system. Recently the second-order term in these expansions was precisely described, and corresponds respectively to a Jellium and to a Uniform Electron Gas model. The present work shows that for inverse-power-law interactions with power d-2<= s= 3, the two problems have the same minimum. For the Coulomb potential in d=3, s=1, our result disproves a conjecture from 2014 of Lewin and Lieb, and shows that, whereas minimizers may be different, the minimum values are equal. Furthermore, provided that the crystallization hypothesis in d = 3 analogous to Abrikosov's conjecture holds, then our result verifies the physicists' conjectured1.4442 lower bound on the famous Lieb-Oxford constant. Our result rigorously confirms the predictions made by the physicists decades ago, regarding the optimal value of the Uniform Electron Gas next-order asymptotic term. This is based on joint works with Mircea Petrache (ETH/Santiago).

Contact sunil.chhita@durham.ac.uk for more information about this event.


Jennifer Uzzell: Personal Religious History and Research (Postgraduate Research Seminar 4)

11:30am, Seminar Room C (D/TH107), Dept. of Theology & Religion, Abbey House, DH1 3RS, Durham

Contact jonathan.miles-watson@durham.ac.uk, m.j.guest@durham.ac.uk for more information about this event.


IAS Fellow's Seminar - Is it a good idea to use iron containing nanoparticles for water treatment?

1:00pm to 2:00pm, IAS Seminar Room, Palace Green, Professor Christian Ruby (University of Lorraine, France)

Contact enquiries.ias@durham.ac.uk for more information about this event.


Kaveh Mousavand: A Gentle Introduction to Auslander-Retien Theory

4:00pm, CM221

Adachi-Iyama-Reiten recently introduced the notion of tau-tilting theory, a generalization of the classical tilting theory, which heavily relies on the Auslander-Reiten theory. This generalization, as its precursor, soon found many applications and established new connections between different areas, including representation theory of algebras, geometry, combinatorics, lattice theory, etc. String and gentle algebras, however, have received a lot of attention in the past few decades. In particular, the work of Butler-Ringel (in 1987) bolstered their phenomenal growth. Due to their fruitful combinatorics, providing a tractable framework and including a vast family of algebras, gentle algebras have prominent applications in diverse areas, including representation theory, cluster algebra, symplectic geometry, etc.

In this talk, after a short explanation of the above-mentioned topics, we will look at some interactions between them to show how one sheds light on the study of the other. Recapping some preliminaries in the first half, in the remainder I will introduce a canonical method to embed every arbitrary gentle algebra into a well-behaved gentle algebra, where we can find an explicit combinatorial description of Hom(M,\tau(N)) and Ext(N,M), for each pair of string modules M and N. If time permits, we will see some aspects of \tau-tilting theory and further use our results to describe the lattice of (functorially finite) torsion classes of gentle algebras by means of kisses between strings and also analyze the notion of mutation in terms of concrete combinatorics.

Contact anna.felikson@durham.ac.uk for more information about this event.


Dr Stephen Barton: The Mission of Jesus in Constitutional Perspective

4:15pm, Seminar Room C (D/TH107), Dept. of Theology & Religion, Abbey House, DH1 3RS, Durham

Contact francis.watson@durham.ac.uk for more information about this event.