## Geometry and Topology

•  Jesse Madnick , McMaster University
•  Bubble Tree Convergence of Parametrized Associative Submanifolds
•  10/17/2019
•  2:00 PM - 3:00 PM
•  C304 Wells Hall

In symplectic geometry, part of Gromov's Compactness Theorem asserts that sequences of holomorphic curves with bounded energy have subsequences that converge to bubble trees, and that both energy and homotopy are preserved in this "bubble tree limit." In $G_2$ geometry, the analogues of holomorphic maps are the "associative Smith maps." In this talk, we'll see that familiar analytic features of holomorphic maps also hold for associative Smith maps. In particular, we'll describe how sequences of associative Smith maps give rise to bubble trees, and how energy and homotopy are again preserved in the limit. This is joint work with Da Rong Cheng and Spiro Karigiannis.

## Contact

Department of Mathematics
Michigan State University