Topology Seminar, Spring 2016

Next Talk(s)

Next talk: TBA

Upcoming talks: 

We will have a little mini-conference on April 7th on the homotopy type of embedding spaces, and configuration spaces.  Speakers include:

  • Paul Arnaud Songhafouo Tsopmene (U.Regina)
  • Don Stanley (U.Regina)
  • Pascal Lambrechts (Universite catholique de Louvain)
  • Victor Turchin (Kansas State)

The mailing list for the topology seminar is: Topology-talks@lists.uvic.ca

Previous Talks 2016-2017

Speaker: Tom Baird (Memorial, Newfoundland)

Title: Kirwan surjectivity in real symplectic geometry and moduli spaces of vector bundles over a real curve

Abstract:  In the early 80s, Kirwan proved a relationship between the equivariant cohomology of a Hamiltonian action on a symplectic manifold, and the cohomology of its symplectic quotient. I present a version of this relationship for symplectic manifolds equipped with an anti-symplectic involution, relating the cohomology of corresponding fixed point Lagrangian submanifolds. I then apply this result to study the topology of moduli spaces of vector bundles and a real algebraic curve, in the style of Atiyah-Bott.

Date / Time: October 21st, 1:30pm

Location: CLE C108


Speaker: Bala Krishnamoorthy (Washington State University, Vancouver)

Title: Linear Programming in Geometric Measure Theory

Abstract: We present results on two problems related to shapes in geometric
measure theory (GMT) that employ techniques from algebraic topology
and linear programming. Currents represent generalized surfaces in
GMT, and were introduced to study area minimizing surfaces and other
related problems. The flat norm provides a natural distance in the
space of currents, and works by decomposing a d-dimensional current
into d- and (the boundary of) (d+1)-dimensional pieces. A natural
question about currents is the following. If the input is an integral
current, i.e., a current with integer multiplicities, can its flat
norm decomposition be integral as well?  Surprisingly, the answer is
not known in general. On the other hand, for the discretization of the
flat norm on a finite simplicial complex, the analogous statement is
true for d-chains in a (d+1)-complex. This result is implied by the
boundary matrix of the simplicial complex being totally unimodular,
guaranteeing integer solutions for an associated integer linear
program. We develop an analysis framework that extends the result in
the simplicial setting to that for d-currents in (d+1)-dimensional
space, provided a suitable triangulation result holds. We also prove
this result holds in 2D. In the second problem, we consider a notion
of average shape defined as the median shape of currents using the
flat norm distance. In the corresponding simplicial version of the
problem, the median chain of a set of input chains in a finite
simplicial complex is computed using linear programming.

Date / Time: Friday October 14th, 1:30pm

Location: CLE C108


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