Special Speakers
Graeme Wilkin (National University of Singapore)
When: 2017.02.21 Title: The reverse Yang-Mills-Higgs flow in the neighbourhood of a critical point Abstract: The Yang-Mills-Higgs flow was originally studied by Simpson in the context of constructing Hermitian-Einstein metrics on Higgs bundles. Methods of Donaldson and Simpson show that the Yang-Mills-Higgs flow resembles a nonlinear heat equation on the space of Hermitian metrics on the bundle and therefore the downwards flow is well-behaved with respect to existence and uniqueness, and it also has nice smoothing properties. On the other hand, the reverse flow is ill-posed and therefore even existence of solutions is problematic.
In this talk I will describe a new method to construct long-time solutions to the reverse Yang-Mills-Higgs flow that converge to a given critical point. The methods naturally lead to an algebraic criterion for two critical points to be connected by a flow line and a geometric condition to distinguish between broken and unbroken flow lines in terms of secant varieties of the underlying curve. If time permits I will talk about work in progress to describe the compactification of the space of flow lines in terms of the geometry of secant varieties.
Topology Day 2017 (2017.03.14)
Topics
A comprehensive plan for the term can be found here: Plan
Overview of Spectra
- Speaker: Agnès Beaudry (CU Boulder)
- When: 2017.01.17
- Notes
Cohomology Theories and Brown Representability
- Speakers: Sebastian Bozlee and Cherry Ng (CU Boulder)
- When: 2017.01.24
Prespectra and Spectra
- Speakers: Nikki Sanderson and Katharine Adamyk (CU Boulder)
- When: 2017.01.31
The Stable Homotopy Category as a Triangulated Symmetric Monoidal Category
- Speaker: Matthew Pierson (CU Boulder)
- When: 2017.02.07
Vector Bundles and the Thom Isomorphism Theorem
- Speaker: Jordan Watts (CU Boulder)
- When: 2017.02.14
Thom Spectra and the Pontryagin-Thom Theorem
- Speaker: Andy Riddle (CU Boulder)
- When: 2017.02.21
Quillen's Theorem: MU and Formal Group Laws
- Speaker: Cliff Blakestad (CU Boulder)
- When: 2017.02.28
K-Theory
- Speaker: Markus Pflaum (CU Boulder)
- When: 2017.03.07
- Notes
S-Modules
- Speaker: Agnès Beaudry (CU Boulder)
- When: 2017.03.21
Symmetric Spectra
- Speaker: Paul Lessard (CU Boulder)
- When: 2017.04.11,18
Infinity Categories
- Speaker: Jonathan Wise (CU Boulder)
- When: 2017.04.25