Wednesday, May 29, 2024 - 10:10 in V2-210
Rough Uhlenbeck Compactness with Application to 2D Yang-Mills Measure
A talk in the SPDEvent series by
Abdulwahab Mohamed from University of Edinburgh
| Abstract: |
In this talk we provide a possible rough extension of Uhlenbeck compactness theorem on the square under boundedness of lasso fields in a suitable H\"older-besov norm. The main ingredient is a singular elliptic SPDE to obtain a Coulomb gauge which we solve using regularity structures. Furthermore, our result yields the same regularity results as obtained Chevyrev (2019) and as such it can be seen as the first gauge fixed representation of 2D YM using elliptic PDE. Finally, we give a sketch on the techniques and introduce the concept of rough additive functions, which provides the base of defining line integrals of distributional 1-forms, controlled gauge transformations and corresponding holonomies. This is a joint work with Ilya Chevyrev and Tom Klose.
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