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 2020||March 2020|
Events for 6 February 2020
Aperiodic sequences over finite alphabets are ubiquitous in the study of topological dynamics, and as such, it's important that we have tools for studying such sequences. We're able to use methods from algebraic topology, such as Cech cohomology to provide invariants for these sequences, especially when the sequences have additional structure such as those generated by substitutions. One first builds a topological space associated with the sequence, called the tiling space for which cohomology can then be computed. These spaces are interesting in their own right and rather different to the standard beasts that a topologist might usually encounter. I will give a brief introduction to tiling spaces and explain how we are sometimes able to calculate cohomology for sequences over other (infinite) alphabets such as compact Lie groups.
NOTE: exceptionally, this talk will take place in CG93.
We provide examples of initial data which saturate the enhanced diffusion rates proved
for general shear flows which are Hölder regular or Lipschitz continuous with critical points, and
for regular circular flows, establishing the sharpness of those results. The proof makes use of a
probabilistic interpretation of the dissipation of solutions to advection diffusion equations.
Contact email@example.com for more information about this event.
The pioneering work of Bekenstein and Hawking in the 70s showed that black holes have a thermodynamic behavior. They produced a universal area law for black hole entropy valid in the limit that the black hole is infinitely large. Quantum effects induce finite-size corrections to this formula, thus providing a window into the fundamental microscopic theory of gravity and its deviations from classical general relativity. In this talk I will discuss recent advances in high-precision computations of quantum black hole entropy in supersymmetric theories of gravity, using new localization techniques. These calculations allow us to test the suggestion that black holes are really ensembles of microscopic states in a very detailed manner, much beyond the semi-classical limit.
I will then discuss how one can independently verify these calculations using explicit models of microscopic ensembles for black holes in string theory constructed in the 90s. These investigations throw up a surprising link to number theory and the so-called Mock modular forms of Ramanujan. I will end by sketching some research directions that these ideas lead to.