TopComb Seminar - Fall 2010

 
This page is outdated. Click here for info regarding the Spring 2011 seminar.
 
The seminar is on hiatus for the holidays, we will resume in the Spring Semester. Happy New Year!
 

The link to the Google Group is here.

We meet on Thursdays at 10:00 AM (sharp) in room Evans 939.

Organizers: Anton Dochtermann and Alex Engstrom .

This semester we are studying Davis-Januszkiewicz spaces, and related constructions in toric geometry/topology and algebra. We're loosely following the text `Torus Actions and Their Applications in Topology and Combinatorics' by Buchstaber and Panov. Click on the title to download an early draft of the book.

Some other interesting papers along these lines:

`Moment-angle complexes, monomial ideals, and Massey products' by Denham and Suciu.

`Moment-angle manifolds and complexes' (lecture notes) by Panov.

`Cup-products in generalized moment-angle complexes' by Bahri, Bendersky, Cohen, and Gitler.

Also, a whole page devoted to Toric Topology in Manchester, with more relevant material.

Some other ideas for future topics include:

Please email one of us if feel strongly about any of these topics, or if you have other ideas!

Here is the list of talks
Date Topic Speaker
Aug 19, 2010
  • Intro/organizational meeting
  • DJ spaces
Alex E.
Aug 26, 2010
  • More DJ spaces (from [BP])
Anton
Sept 2, 2010
  • Cubical Complexes (as presented in [BP])
Jacob
Sept 9, 2010
  • Obstructions to combinatorial maps [Z]
Benjamin
Sept 16, 2010
  • Homotopy colimits ([WZZ], [S])
Matthew
Sept 23, 2010
  • Homotopy colimits and generalized DJ spaces [BBCG]
Matthew
Sept 30, 2010
  • Hamiltonian actions, moment maps (from [P])
Chris
Oct 21, 2010
  • The cohomology algebra of moment angle complexes - faces rings, Tor-algebras, etc(from [P, P2])
Anton
Oct 28, 2010
  • The cohomology algebra cont., additive structure
Anton
Nov 4, 2010
  • The cohomology algebra cont., multiplicative structure
Alex P.
Nov 11, 2010
  • Applications to (complements of) subspace arrangements
Jacob
Nov 18, 2010
  • MSRI workshop (no seminar)
Nov 25, 2010
  • Giving thanks (no seminar)
Not the turkey

Literature
[BBCG] Bahri, Bendersky, Cohen, Gitler "The polyhedral product functor".
[BP] Buchstaber, Panov, "Torus Actions and Their Applications in Topology and Combinatorics".
[BH] Bruns, Herzog, "Cohen-Macaulay rings".
[BHV] Brenner, Herzog, Villamayor et al., "Three Lecture on Commutative Algebra".
[P] Panov, "Moment-angle manifolds and complexes" (lecture notes).
[P2] Panov, "Cohomology of face rings, and torus actions".
[WZZ] Welker, Ziegler, Zivaljevic, "Homotopy colimits - comparison lemmas for combinatorial applications".
[S] Shulman, Michael "Homotopy limits and colimits and enriched homotopy theory".
[MS] Miller, Sturmfels, "Combinatorial commutative algebra".
[St] Stanley "Combinatorics and Commutative Algebra", Second Edition.
[Z] Zivaljevic, "Combinatorial groupoids, cubical complexes, and the Lovasz conjecture".