Well we've reached the end of the LMS symposium in Durham, and I, for one, am really looking forward to going back home, and thinking about my own work problems. That said it has been a lot of fun to be here, and I may even try and learn something about derived categories off the back of all the talks related to them, and the enthusiasm of the categorists. I'm feeling pretty tired today, so I'm just going to list the last set of talks, starting with yesterday (a cold and miserably damp day).
In the morning the key-note speaker was Tom Bridgeland from the University of Sheffield, another of the enthusiastic categorists mentioned above, and he was talking under the title: "Spaces of stability conditions". He used words such as bounded coherent sheaf, topological B-model, elliptic curve, the Mukai transformation, T-duality, topological conformal field theory, Michael Douglas' Pi stability condition, Fukaya categories, special lagrangians (or slags), Richard Thomas and the McKay correspondence. Somehow all these words were related, and despite Tom Bridgeland being an excellent speaker (I do have a very good set of notes to work with from this talk), I'm afraid I know too little about algebraic geometry to be able to understand the topics. It has been suggested that a good place for me to start would be Serge Lang's book, "Introduction to Algebraic Geometry", and I'm giving it some consideration, although, at £364.27, I don't think I will be buying a copy any time soon. I believe many of the ideas discussed in the talk can be found in Tom Bridgeland's papers "Stability conditions on triangulated categories" and "Stability conditions on K3 surfaces".
In the afternoon we had a talk from Alexei Bondal entitled "Derived categories of toric varieties", and a second key-note speaker in the form of Ron Donagi who spoke about "Geometric transitions, Calabi-Yau integrable systems, and open GW invariants". Ron Donagi's talk was based on the papers "Geometric transitions and integrable systems" and "Geometric Transitions and Mixed Hodge Structures". After these talks we had a wine reception and a seven(!)-course banquet, which might explain some of my lethargy today :)
This morning we heard from Boris Dubrovin who gave the last talk of the symposium to an audience suffering from the morning-after effects of the banquet (principally the wine's effects) under the title "Frobenius manifolds and integrable hierarchies of the topological type". I refer the interested reader to his paper "Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants" for a flavour of the talk.
Now I have an afternoon to work in Durham and will catch my train home tomorrow, at which point I will catch up on my sleep. So ends my missives from the front here in Durham :)
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