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July 2018
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Forthcoming events in the School of Mathematical Sciences

Expand or collapse all abstracts.

Comparison Theorems under Weak Assumptions
11:10 Fri 29 Jun, 2018 :: EMG06 :: Kwok Kun Kwong :: National Cheng Kung University

TBA
The topology and geometry of spaces of Yang-Mills-Higgs flow lines
11:10 Fri 27 Jul, 2018 :: Barr Smith South Polygon Lecture theatre :: Graeme Wilkin :: National University of Singapore

Given a smooth complex vector bundle over a compact Riemann surface, one can define the space of Higgs bundles and an energy functional on this space: the Yang-Mills-Higgs functional. The gradient flow of this functional resembles a nonlinear heat equation, and the limit of the flow detects information about the algebraic structure of the initial Higgs bundle (e.g. whether or not it is semistable). In this talk I will explain my work to classify ancient solutions of the Yang-Mills-Higgs flow in terms of their algebraic structure, which leads to an algebro-geometric classification of Yang-Mills-Higgs flow lines. Critical points connected by flow lines can then be interpreted in terms of the Hecke correspondence, which appears in Witten’s recent work on Geometric Langlands. This classification also gives a geometric description of spaces of unbroken flow lines in terms of secant varieties of the underlying Riemann surface, and in the remaining time I will describe work in progress to relate the (analytic) Morse compactification of these spaces by broken flow lines to an algebro-geometric compactification by iterated blowups of secant varieties.
TBA
11:10 Fri 3 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Brett Chenoweth :: University of Ljubljana

TBA
11:10 Fri 10 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Hang Wang :: University of Adelaide

TBA
11:10 Fri 17 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Siye Wu :: National Tsinghua University

TBA
11:10 Fri 31 Aug, 2018 :: Barr Smith South Polygon Lecture theatre :: Vanessa Robins :: Australian National University

TBA
11:10 Fri 5 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Scott Morrison :: Australian National University