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Geometric Analysis Seminar, Gauge Theory Learning Seminar


Antonella Marini (Yeshiva University)

Location:  Hill 705 and Zoom
Date & time: Tuesday, 20 February 2024 at 2:50PM - 3:50PM

Abstract. The aims of this talk are to motivate the study of boundary value
problems in non-abelian gauge theories over compact Riemannian manifolds
with boundary, in light of the possible different applications to the fields
of geometric analysis and mathematical physics (in particular, in quantum
field theory), and to define a range of well-posed boundary value problems,
analyzed in comparison to other contexts, such as that of harmonic maps,
H-surface equations, and with possible applications to the study of the non-
linear sigma model. A Morse theory for the Yang-Mills Dirichlet problem is
outlined. This talk includes results derived by the author, individually and
collaboratively, over the course of many years1.


1precisely, with T. Isobe, on the existence of local minima and min-max-type solutions,
with V. Moncrief and R. Maitra, for applications to QFT, with T. Otway, to frame those
results in the context of a nonlinear Hodge-de Rham theory