SPEAKER: Joseph Palmer (University of Illinois at Urbana-Champaign)



TITLE: Lifting complexity one torus actions to integrable systems



ABSTRACT: A complexity-one space is a symplectic 2n-manifold equipped with Hamiltonian action of a torus of dimension n-1. The momentum map for such an action can be identified with n-1 real valued functions. On the other hand, an integrable system on such a manifold is the data of n functions. This motivates several natural questions: given a complexity-one space, when can an additional function be found to produce an integrable system? When can the resulting system be chosen to be toric? When can it be chosen to have no degenerate singularities?



In this talk, I will discuss answers to various versions of these questions, both in dimension four and higher. In particular, I will mention previous results of Karshon and Hohloch-Sabatini-Sepe-Symington in dimension four, and describe new results in higher dimensions. Parts of the new work that I will present are joint with Sonja Hohloch, Susan Tolman, and Jason Liu.



DATE: Thursday, 16 November 2023

TIME:? 4pm GMT

            8am San Francisco

11am Toronto

1pm Rio

4pm UK

5pm Central Europe

12am (day+1) Hong Kong

10am Urbana



ZOOM: https://unige.zoom.us/j/61237795215?pwd=T2toTHF4eWhCOGgrVndUYlJGc0IwUT09

MEETING ID: 612 3779 5215

PASSCODE: 6512684158
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FROM 202.120.11.*