Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Research & business

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.


 

November 2019
SunMonTueWedThuFriSat
October 2019 December 2019
1 2
3 4 5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30

Events for 28 November 2019

DEI Seminar Series: People Power: creating a just energy transition

1:00pm to 2:00pm, E101, Engineering, Emma Bridge, Community Energy England

Contact lynn.gibson@durham.ac.uk for more information about this event.


Antonin Monteil: Ginzburg-Landau relaxation for harmonic maps valued into manifolds

2:00pm, CM301

We will look at the classical problem of minimizing the Dirichlet energy of a map $u :\Omega\subset\mathbb{R}^2\to N$ valued into a compact Riemannian manifold $N$ and subjected to a Dirichlet boundary condition $u=\gamma$ on $\partial\Omega$. It is well known that if $\gamma$ has a non-trivial homotopy class in $N$, then there are no maps in the critical Sobolev space $H^1(\Omega,N)$ such that $u=\gamma$ on $\partial\Omega$. To overcome this obstruction, a way is to rather consider a relaxed version of the Dirichlet energy leading to singular harmonic maps with a finite number of topological singularities in $\Omega$. This was done in the 90's in a pioneering work by Bethuel-Brezis-Helein in the case $N=\mathbb{S}^1$, related to the Ginzburg-Landau theory. In general, we will see that minimizing the energy leads at main order to a non-trivial combinatorial problem which consists in finding the energetically best topological decomposition of the boundary map $\gamma$ into minimizing geodesics in $N$. Moreover, we will introduce a renormalized energy whose minimizers correspond to the optimal positions of the singularities in $\Omega$.

Contact djoko.wirosoetisno@durham.ac.uk for more information about this event.