Workshop on Non-linear integral transforms: Fourier-Mukai and Nahm

CRM, Montreal, Canada, August 27-31, 2007.

Speakers:
Claudio Bartocci (Genova)
David Ben-Zvi (Texas, Austin)
Philip Boalch (École Normale Supérieure, Paris)
Ugo Bruzzo (SISSA)
Andrei Caldararu (Wisconsin)
Sergei Cherkis (Trinity College, Dublin)
Gabor Etesi (BUTE)
Chris Ford (independant)
Oscar Garcia-Prada (CSIC)
Daniel Hernández-Ruipérez (Salamanca)
Ruxandra Moraru (Waterloo)
Tomasz Mrowka (MIT)
Tom Nevins (UIUC)
Daniel Nogradi (Wuppertal)
Paul Norbury (Boston)
Tony Pantev (Pennsylvania)
Nuno Romao (MIT)
Justin Sawon (SUNY Stony Brook)
Mark Stern (Duke)
Szilard Szabo (Renyi Institute)
Carlos Tejero Prieto (Salamanca)
Richard Thomas (Imperial College) (to be confirmed)
Misha Vertbitsky (Glasgow)
Kota Yoshioka (Kobe)

Organizers:
Benoit Charbonneau (McGill)
Jacques Hurtubise (McGill)
Marcos Jardim (Campinas, Brazil)
Eyal Markan (UMASS Amherst)

Website: http://www.crm.umontreal.ca/FourierMukaiNahm07/index_e.shtml

Funding: We regret that no further funding is available.

Scientific content:
The transforms that are to be the subject of this workshop operate on
moduli spaces, either of holomorphic objects or of gauge fields, and
have been extensively developed over the past 20 years as privileged
tools in the area.

The Nahm transform was initially introduced by Nahm in the early 80’s to
study magnetic monopoles. It developed over the years into a duality
among instantons which are invariant under the action of a subgroup of
translations of R4. On the other hand, the Fourier–Mukai transform was
also introduced in the early 80’s by Mukai as a duality among sheaves on
abelian varieties. In the late 80’s it was realized that both
constructions are actually equivalent in certain circumstances. Another
common feature is their role in mathematical physics, notably gauge
theory and string theory.

The aim of this workshop is to gather together a diverse group of people
working on this fairly focused but current topic. It will attract a
broad variety of participants: algebraic geometers, differential
geometers and mathematical physicists. The mixture of algebraic and
analytic technique required by the two transforms will lead to fruitful
interaction between the participants, and to solutions of some open
questions in both areas.

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