Algebraic Geometry Seminar

Fall 2016 — Tuesdays 3:30 - 4:30 PM, location: JFB 102

Date Speaker Title — click for abstract (if available)
August 30 Grigory Mikhalkin
University of Geneva
Quantum index of real plane curves and refined enumerative geometry
We note that under certain conditions, the area bounded by the logarithmic image of a real plane curve is a half-integer multiple of pi square. The half-integer number can be interpreted as the quantum index of the real curve and used to refine enumerative invariants.
August 31 (special RTG seminar)
room: TBA
Jenny Wilson
Stanford University
Representation theory and higher-order stability in the configuration spaces of a manifold
Let F_k(M) denote the ordered k-point configuration space of a connected open manifold M. Work of Church and others shows that for a given manifold, as k increases, this family of spaces exhibits a phenomenon called homological "representation stability" with respect to the natural symmetric group actions. In this talk I will explain what this means, and describe a higher-order "secondary stability" phenomenon among the unstable homology classes. The project is work in progress, joint with Jeremy Miller.
September 6 Chung Ching Lau
University of Utah
September 13 Natalie Hobson
University of Georgia
September 20 Lei Song
University of Kansas
September 27 Aaron Bertram
University of Utah
October 4 Chi Li
Purdue University
October 11 Fall Break
October 18 Tom Alberts
University of Utah
The Geometry of the Last Passage Percolation Model
Last passage percolation is a well-studied model in probability theory that is simple to state but notoriously difficult to analyze. In recent years it has been shown to be related to many seemingly unrelated things: longest increasing subsequences in random permutations, eigenvalues of random matrices, and long-time asymptotics of solutions to stochastic partial differential equations. Much of the previous analysis of the last passage model has been made possible through connections with representation theory of the symmetric group that comes about for certain exact choices of the random input into the last passage model. This has the disadvantage that if the random inputs are modified even slightly then the analysis falls apart. In an attempt to generalize beyond exact analysis, recently my collaborator Eric Cator (Radboud University, Nijmegen) have started using tools of tropical geometry to analyze the last passage model. The tools we use to this point are purely geometric, but have the potential advantage that they can be used for very general choices of random inputs. I will describe the very pretty geometry of the last passage model, our work in progress to use it to produce probabilistic information, and our goal of eventually de-tropicalizing our approach and using it to analyze the so-called directed polymer problem.
October 25
November 1 Calum Spicer
UC San Diego
November 8
November 15
November 22
November 29
December 6

Archive of previous seminars.

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