Classifying toric and semitoric fans by lifting equations from SL(2, Z)

We present an algebraic method to study four-dimensional toric varieties by lifting matrix equations from the special linear group SL(2, Z) to its preimage in the universal cover of SL(2, R). With this method we recover the classification of two dimensional toric fans, and obtain a description of their semitoric analogue. As an application to symplectic geometry of Hamiltonian systems, we give a concise proof of the connectivity of the moduli space of toric integrable systems in dimension four, recovering a known result, and extend it to the case of semitoric integrable systems with a fixed number of focus-focus points. (joint work with Daniel Kane and Alvaro Pelayo) Please note: There will be a pre-talk for graduate students from 2:30 3:00. The regular talk will begin at 3:00. Advisor: Alvaro Pelayo Monday, November 23, 2015 3:00 PM AP&M 7218 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *