Spring 2024
The Seminar runs on Tuesdays at STRAND BLDG S4.29. This term, some talks will run from 15:00 to 16:00, and others will be in two parts – an introductory talk from 15:00 to 15:40 and a research talk from 15:45 to 16:30.
23 April, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Dan Kaplan (University of Hasselt)
Title: Quiver varieties for the working geometer
Abstract: This talk is divided into two related, yet self-contained sections. The first section is an elementary introduction to (Nakajima) quiver varieties, beginning with representations of quivers and emphasizing small examples. The second section shifts gears to symplectic resolutions of singularities, including the minimal resolutions of du Val singularities and the Springer resolution of the nilpotent cone of a Lie algebra.
The sections unite as we construct symplectic resolutions for quiver varieties by varying a stability parameter. In joint work with Travis Schedler, we leverage these symplectic resolutions to build resolutions for spaces that are (analytically) locally quiver varieties. The key idea here is to choose local resolutions at the most singular points and then demonstrate that certain compatible, monodromy-free choices extend and glue to a global resolution.
30 April, 15:00-16:00, STRAND BLDG S4.29
Speaker: Ulrike Tillmann (University of Oxford)
Title: Homology stability for generalised Hurwitz spaces and asymptotic monopoles
Abstract: Configuration spaces have played an important role in mathematics and its applications. In particular, the question of how their topology changes as the cardinality of the underlying configuration changes has been studied for some fifty years and has attracted renewed attention in the last decade.
While classically additional information is associated “locally” to the points of the configuration, there are interesting examples when this additional information is “non-local”. With Martin Palmer we have studied homology stability in some of these cases, including Hurwitz space and moduli spaces of asymptotic monopoles.
7 May, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Ilaria Di Dedda (King’s College London)
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21 May, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Anna Felikson (Durham University)
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28 May, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Nick Lindsay (University of Cologne)
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11 June, Part I: 15:00-15:40, Part II: 15:45-16:30, STRAND BLDG S4.29
Speaker: Filippo Baroni (University of Oxford)
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