One hundred and second meeting of the
University of Sheffield
Monday 27th February 2017
The talks will take place in various rooms on floor F of the Hicks Building - see below.
Tea/coffee will be in the Common Room (I15) on I floor of the Hicks Building.
There are various places for lunch - follow a group of locals if in doubt.
A group is likely to be going for drinks and an early dinner after the last talk - all are welcome to join.
10:30 - 11:00
|11:00 - 12:00|
|Nick Kuhn (University of Virginia)|
Hurewicz maps for infinite loopspaces.
|12:00 - 14:00||Lunch|
|14:00 - 15:00|
|Dirk Schuetz (Durham)|
Computing Steenrod Squares in Khovanov Cohomology
|15:00 - 16:00||Tea/coffee|
|16:00 - 17:00|
|Jeff Giansiracusa (Swansea)|
Exterior algebra and Plucker coordinates in tropical geometry
Abstracts of talks
Title: Exterior algebra and Plucker coordinates in tropical geometry
Any Grassmannian Gr(d,n) admits an embedding in projective space called
the Plucker embedding, and exterior algebra provides an elegant
description of this embedding, In this talk I will present an
of this picture for the combinatorial objects called (valuated)
matroids, which are the basic building blocks of tropical geometry. A
valuated matroid can be thought of as an object defined over
the tropical idempotent semiring T by a tropical analogue of
Plucker coordinates. I will describe how to define
a tropical analogue
of exterior algebra and use this to give a new cryptomorphic
description of valuated matroids. The main result is that a
d-multivector w is a valuated matroid if and only if the quotient of
T^n that is dual to the kernel of wedging with w has d-th exterior
power free of rank 1. This gives a projective embedding of the Dressian
(the space of all valuated matroids) in a tropical projective space and
also provides it with a modular interpretation.
Title: Hurewicz maps for infinite loopspaces.
In a 1958 paper, Milnor observed that then new work by Bott allowed him
to show that the n-sphere admits a vector bundle with non-trivial top
Stiefel-Whitney class precisely when n=1,2,4, 8. This can be
interpreted as a calculation of the mod 2 Hurewicz map for the
classifying space BO, which has the structure of an infinite
have been studying such Hurewicz maps for generalized homology theories
by relating the Adams filtration of the domain to a filtration of the
range coming from Andre-Quillen homotopy calculus. When
specialized to ordinary mod p homology, my general results have some
tidy consequences, including Milnor's theorem and a variant with ko
replaced by tmf.
Title: Computing Steenrod Squares in Khovanov Cohomology
recent work Lipshitz and Sarkar constructed a stable homotopy type for
Khovanov cohomology, thus introducing cohomology operations to it. They
showed that the second Steenrod square is non-trivial for many
non-alternating knots, and used it to refine the Rasmussen invariant.
Nevertheless, computations become very time-intensive once a knot has
more than 15 crossings. We will discuss techniques to improve
computations for more complicated knots and how they can be used to
identify the resulting stable homotopy types.
Everyone who wishes to participate is welcome, particularly
postgraduate students. The usual criteria for
assistance with travel expenses apply. Beneficiaries will need to
complete the standard forms, which are available at the