|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
The Yang-Mills Lagrangian in supercritical dimensions
If you have a question about this talk, please contact Neshan Wickramasekera.
The small energy regularity for Yang-Mills solutions in dimension 4 was the key to the concentration-compactness result for Yang-Mills fields by Karen Uhlenbeck. This result, proven about 3 decades ago, was relevant for the construction of 4-manifold invariants by Simon Donaldson. The study is based on the theory of Sobolev connections over smooth bundles. I will describe in what sense dimension 4 is critical for Uhlenbeck’s approach.
I will then introduce a notion of weak curvatures on possibly very singular bundles. Such class allows to apply a variational approach to the Yang-Mills Lagrangian in superctitical dimensions, where we don’t have a priori control on the topology of the bundle. This measure-theoretic notion of bundles allowing wild topological singularities bears analogies to integral currents. The integer multiplicity condition of Herbert Federer and Wendell Fleming is replaced in our setting by the integrality of relevant Chern classes.
I will present the solution to the Yang-Mills-Plateau problem in the abelian case. In particular I will describe a closure theorem for abelian weak curvatures on singular bundles and the successive regularity result for the Yang-Mills-Plateau minimizers. These results are part of an ongoing project in collaboration with my advisor Tristan Rivière.
This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsFriends of Scott Polar Research Institute lecture series Palestinians in Israel: Segregation, Discrimination and Democracy Neuropsychiatry discussion group
Other talksNumerical Methods for (Quasi)Variational Inequalities - Part II Evolution and development of early land plant rooting systems Meditation Session at the Botanical Gardens Numerical Methods for (Quasi)Variational Inequalities - Part I First Bolashak Educational Forum: Contemporary changes in Kazakhstan’s education system Sequential Monte Carlo methods for graphical models