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.
|January 2019||March 2019|
Events for 22 February 2019
Compact manifolds with the exceptional holonomy group G2 can be used in
M-Theory to geometrically engineer 4D theories with minimal
supersymmetry, as well as 3D N=2 theories from type II strings. I will
review recent progress in the construction of such geometries, the
associated physics, and dualities between compactifications. By
exploiting various fibration structures, I will show to find large
classes of M-Theory/heterotic duals, as well as examples of G2 mirrors
in the context of type II strings.
Consider a mixture of M non-interacting immiscible fluids under isothermal conditions
at thermal equilibrium. The configurations seen in the experiments can be described as the (local)
minimizers of a Gibbs free energy introduced by Van der Waals (later rediscovered by Cahn and Hilliard).
In this model, a parameter $\epsilon$ describes the typical size of the interface regions
separating areas of pure phases.
A mathematical challenge of the 80s was to understand the behaviour of the model as $\epsilon \to 0$.
It was proved by Modica that the Van der Waals energy converges, in the sense of Gamma-convergence,
to the surface energy of the interfaces separating the stable phases, as conjectured by Gurtin
some years earlier.
In this talk a variant of the above model allowing for small scale heterogeneities in the fluids
is presented. In particular, the case where the scale $\epsilon$ of the small homogeneities is of
the same order of the scale governing the phase transition is considered.
The interaction between homogenization and the phase transitions process will lead, in the
limit as $\epsilon \to 0$, to an anisotropic interfacial energy.
The talk is based on a work in collaboration with Irene Fonseca (CMU), Adrian Hagerty (CMU), and Cristina Popovici (Loyola University).
Contact email@example.com for more information about this event.