Dynamical Systems seminar: Dynamics in 2-Morse Theory

Speaker- Bowen Chen (SIMIS)

Time: May 27, 16:00
Location – 1710, SIMIS
Zoom Meeting ID: 844 0594 7424 (Passcode: 076895)

Abstract:
2-Morse theory is the study of 2 commuting Morse vector fields on Riemannian manifold. We give a geometric description on the moduli space of film in order to apply it into higher enumerative problems, which generalize the method from standard Morse theory.
In this talk, we will review some dynamics of gradient flow in standard Morse theory, then investigate the dynamics of the film in 2-Morse theory by showing 2 main families of examples explicitly: $\mathbb{RP}^n$ case and $\mathbb{T}^n$ case. We end up with the dimension counting fomula for general 2-Morse moduli space and point out the relation between 2-Morse theory with Morse-Bott theory and convex polygonal subdivision.