Speaker: Norton Lee
Title: Quantum spin spin system and supersymmetric gauge theory
Abstract: We exploit many aspects of relation between supersymmetric gauge theories in four dimensions and quantum spin systems. We first find an explicit formula for the subleading factor of surface defect partition function, which is identified as the Jost function of the N site sl_2 XXX spin chain, which reduces, in a limiting case, to that of the N-particle periodic Toda chain.
Using the non-perturbative Dyson-Schwinger equations of supersymmetric gauge theory in the presence of a surface defect, we reconstruct the monodromy matrix of the spin system, and establish relations between the spin chain commuting Hamiltonians with the expectation value of the twisted chiral ring of gauge theory.
Speaker: Matt Gursky [University of Notre Dame]
Speaker: Sean Keel [The University of Texas at Austin]
Title: Q&A about online teaching
Speaker: Kimberly Bell, Carol Hernandez [Center for Excellence in Learning and Teaching (CELT)]
Abstract: Kimberly Bell and Carol Hernandez both work at the Center for Excellence in Learning and Teaching (CELT). They will tell you briefly about some of the resources CELT has to offer for your online teaching, and then answer questions. Your chance to get some advice if you are teaching online this semester!
Speaker: Kenji Fukaya
Title: Equivariant Lagrangian Floer homology
Abstract: For a symplectic manifold with a compact group action and its invariant Lagrangian submanifolds, one can define an equivariant version of Lagrangian Floer homology. Its (potential) application includes:
Defining symplectic side of Atiyah-Floer conjecture,
Study of Floer homology of symplectic quotient,
I want to discuss some of such applications and certain examples of equivariant Lagrangian Floer homology together with idea of its construction.
Title: Recent results on random walk on a group
Speaker: Robert Hough [Stony Brook University]
Abstract: I will discuss several break-thoughs on statistical physics models from the late 80s and early 90s, all of which can be viewed as random walks on groups. The models include the abelian sandpile model on the torus, the Kac model modeling many colliding particles, and the mixing of the 15 puzzle.
Speaker: Bernhard Reinke, Aix-Marseille University
Title: The Weierstrass root-finder is not generally convergent
Speaker: Bernhard Reinke [Aix-Marseille University]
Abstract: We will give an overview of root-finding methods and their interpretation as complex dynamical systems. The main focus will be the Weierstrass/Durand-Kerner method and its similarities and differences to the Newton and the Ehrlich-Aberth methods.
In particular, we will show how to use methods from computer algebra to investigate (and/or establish) the existence of attracting periodic cycles, as well as diverging orbits, and present explicit examples of both phenomena for the Weierstrass method.
This talk is based on joint work with Dierk Schleicher and Michael Stoll.
Monday September 28, 9.30 AM EST: Sameer Murthy (King’s College London)
Speaker: John Lott [Berkeley University]