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 halfinteger multiple of pi square. The
halfinteger 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 higherorder stability in the configuration spaces of a manifold
Let F_k(M) denote the ordered kpoint 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 higherorder "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 
TBA
TBA

September 13 
Natalie Hobson University of Georgia 
TBA
TBA

September 20 
Lei Song University of Kansas 
TBA
TBA

September 27 
Aaron Bertram University of Utah 
TBA
TBA

October 4 
Chi Li Purdue University 
TBA
TBA

October 11 
Fall Break 

October 18 
Tom Alberts University of Utah 
The Geometry of the Last Passage Percolation Model
Last passage percolation is a wellstudied 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 longtime 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 detropicalizing our approach and using it to analyze
the socalled directed polymer problem.

October 25 


November 1 
Calum Spicer UC San Diego 
TBA

November 8 


November 15 


November 22 


November 29 


December 6 


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