5:00pm - NS 1201 - Mathematical PhysicsAnton Kapustin - (Caltech)Exact bosonization in two spatial dimensions and a new class of lattice gauge theories We describe a 2d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 2d lattice to a lattice gauge theory while preserving the locality of the Hamiltonian. When the space is simply-connected, this bosonization map is an equivalence. We describe several examples of 2d bosonization, including free fermions on square and honeycomb lattices and the Hubbard model. We describe Euclidean actions for the corresponding lattice gauge theories and find that they contains Chern-Simons-like terms. |

10:00am - Natural Sciences II, Room 1201 - Advancement to Candidacy ExaminationDaniel Bergman - (University of California, Irvine - Department of Mathematics)A Multiscale Model of the Paradoxical Roles of the Immune System in EMT-Mediated Cancer |

2:00pm - Rh 340P - Mathematical PhysicsYunfeng Shi - (Fudan University)Spectral gaps for quasi-periodic Schrodinger operators with Liouville frequencies III We consider the spectral gaps of quasi-periodic Schrodinger operators with Liouville frequencies. By establishing quantitative reducibility of the associated Schrodinger cocycle, we show that the size of the spectral gaps decays exponentially. This is a joint work with Wencai Liu. |