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Geometric Analysis Seminar, Gauge Theory Learning Seminar

Semi-Fredholm Gluing Methods and Applications in Gauge Theory

Greg Parker (Stanford University)

Location:  Hill 705 and Zoom
Date & time: Tuesday, 30 January 2024 at 2:50PM - 3:50PM

Abstract: The construction of most moduli spaces in modern differential geometry requires gluing results, which have a reputation for being technical. More recent gluing problems require importing even more technical details from different areas of analysis to deal with issues like loss of regularity and the appearance of degenerate operators which do not admit Fredholm extensions. In this talk, I will present a unified framework for dealing with this type of gluing problem that extends the alternating method to these new settings. I will then explain how this framework is utilized to prove a new gluing result in gauge theory that provides a key step towards using Fueter sections and (mathbb Z_2)-harmonic spinors to compactify the moduli spaces of solutions to generalized Seiberg—Witten equations.

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