Evolution of statistically inhomogeneous degenerate water wave quartets

at a workshop on Nonlinear Water Waves – an Interdisciplinary Interface at the Erwin Schrödinger International Institute for Mathematics and Physics in Vienna.

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Title: “Donaldson Uhlenbeck compactification for the moduli space of framed sheaves on a Deligne-Mumford stack”

Abstract: Framed sheaves over surfaces first appeared as a generalisation of framed SU(r) instantons on S^4. Later, Uhlenbeck provided a compactification for the moduli space of framed SU(r) instantons which through the Donaldson correspondence and the work of Li and Morgan produced the so called Donaldson-Uhlenbeck compactification of the moduli space of framed sheaves. We want to focus on a further generalisation to the moduli space of framed sheaves on Deligne-Mumford stacks and construct an analogous compactification. This is work in progress with U. Bruzzo.

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https://aimath.org/workshops/upcoming/singularhiggs/

Marina’s research is on the geometry of singular curves as used in physics theories in and beyond the Standard Model.

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There will be a poster from CMS at the lunch time session.

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The __LMS__ Summer School, held at the University of Manchester, consisted of six short lecture courses designed to give an introduction to areas of higher mathematics unlikely to have been encountered as part of a typical undergraduate mathematics degree.

The topics were fairly evenly split between pure and applied mathematics to reflect the varying interests of the participants. Accompanying each lecture course were group based problem sessions, giving us a chance to talk about and develop the concepts that had been discussed in the lectures. I found the discussion element of these sessions particularly enjoyable, owing to the diversity of the other participants’ interests (that is, I learned about a lot of exotic physical principles with cool names).

In addition to these more formal lecture courses, there were daily colloquia, again on a range of pure and applied mathematical topics. These were often more (mind-__blowingly__) difficult to follow and didn’t go into as much detail, but were extremely interesting nonetheless, with topics including the Radon transform (with applications in the reconstruction of __CT__ scan images) and Alexander __Grothendieck’s__ “__Dessins__ __d’Enfants__” (a type of combinatorial graph which supposedly resembles a child’s drawing, hence the name).

Most days also included some sort of entertainment (live music __etc__.), organised by Dr. James __Montaldi__ of Manchester University, and there were weekend excursions to the Museum of Science and Industry and to the Peak District.

After attending the summer school I’m certain I’d like to continue my study of mathematics after my undergraduate degree, and if you are thinking about doing the same then I’d highly recommend speaking to a lecturer about the summer school; I loved it!

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The title of the work is “Exploring Botnet Evolution via Multidimensional Models and Visualisation” and is published in the LNCS series.

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This work is supported by a Royal Society grant.

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