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Jason Lotay: Lectures

June 6, 2018
TITLE: The G2 Laplacian flow: progress and outlook

ABSTRACT: I will discuss some recent progress in understanding the G2 Laplacian flow, particularly in the presence of symmetries, and describe some open problems and questions.

June 5, 2018
TITLE: The G2 Laplacian flow: introduction and overview

ABSTRACT: The G2 Laplacian flow was introduced by Bryant as a potential tool for studying the challenging problem of existence of holonomy G2 metrics. I will give an introduction to the flow and a brief survey of the general theory.

September 10, 2017
TITLE: Invariant coassociative 4-folds via gluing

ABSTRACT: Coassociative 4-folds in R7 with symmetry have been studied by several authors, including Harvey-Lawson and Bryant. Such submanifolds with S1-symmetry locally exist in abundance, but few global examples are known. I will describe joint work with Nicos Kapouleas which produces infinitely many embedded, asymptotically conical, S1-invariant coassociative 4-folds in R7 by a gluing method.

June 8, 2017
TITLE: Calibrated submanifolds of G2 and Spin(7) manifolds with conical singularities

ABSTRACT: I will give a brief survey of known results in the study of compact calibrated submanifolds with conical singularities in exceptional holonomy manifolds. In particular, I will describe their deformation theory, desingularization results and applications, including the construction of examples and potential connections to calibrated fibrations.