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Drafts and Work in Progress Descriptions
of some current research projects and some old drafts.
Undergraduate Research Supervised
Lecture
Notes Notes
from some lectures I've given.
Research
Papers
(With Thomas Baird) Smooth approximation in algebraic sets and the topological Atiyah-Segal map.
Submitted (September 2012). arXiv:1206.3341.
Abstract
(With Rufus Willett and Guoliang Yu) A finite dimensional approach to the strong Novikov conjecture.
Submitted (May 2012). arXiv:1203.6168.
Abstract
(With Romain
Tessera and Guoliang Yu) Finite decomposition complexity and the
integral Novikov conjecture for higher algebraic K-theory.
To appear in J. Reine Angew. Math. (Crelle's Journal). arxiv:1111.7022.
Abstract
Periodicity
in the stable representation theory of crystallographic groups.
To appear in Forum Math. (published on-line 11/4/11).
arxiv:1007.0406.
Abstract
Invariant
tubular neighborhoods in infinite-dimensional Riemannian
geometry, with applications to Yang-Mills theory. Arch. Math.
(Basel) 96 (2011) no. 6, 589--599. arXiv:1006.0063
Abstract
On
The Yang-Mills stratification for surfaces. Proc. Amer.
Math. Soc. 139 (2011), no. 5., 1851-1863. Abstract
(With
Nan-Kuo Ho and Chiu-Chu Melissa Liu) Orientability in Yang-Mills
Theory over Nonorientable Surfaces. Communications
in Analysis and Geometry 17 (2009), no. 5, 903--954.
arXiv:0810.4882
Abstract
The stable
moduli space of flat connections over a surface. Trans. Amer.
Math. Soc. 363 (2011), no. 1, 1061-1100. arXiv:0810.4882
Abstract
Yang-Mills
theory over surfaces and the Atiyah-Segal theorem. Algebraic
& Geometric Topology 8 (2008) 2209--2251.
arXiv:0710.0681
Abstract
Excision for
deformation K-theory of free products. Algebraic
& Geometric Topology 7 (2007) 2239--2270.
arXiv:math/0703463
Abstract
Stable
Representation Theory of Infinite Discrete Groups. This is
the final version of my Ph.D. thesis, posted 7/27/2007. Abstract
Connectivity
of the coset poset and the subgroup poset of a group. J.
Group Theory 8 (2005), no. 6, 719--746. arXiv:math/0210001
Abstract
Connectivity
of the coset poset. Senior Honors Thesis, Cornell University
(2002). arXiv:math/0208176
Abstract
(With Anant
Godbole and Sam Greenberg) Cliques and independent neighbor sets
in random graphs. Proceedings of the Thirty-second Southeastern
International Conference on Combinatorics, Graph Theory and
Computing (Baton Rouge, LA, 2001). Congr. Numer. 153 (2001),
113--128.
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