David Spivak
Visiting Assistant Professor
University of Oregon
Department of Mathematics
Office: 317 Fenton Hall
Email: dspivak at uoregon
Teaching.
Curriculum
Vitae.
Research
Statement.
Derived
Smooth Manifolds A reworking of my PhD dissertation. The category
of derived manifolds contains arbitrary intersections of manifolds, even
if they are not transverse, while retaining enough structure so that
every compact derived manifold has a fundamental class in cobordism.
[To appear in Duke Mathematical Journal, tentatively April 2010.]
Here
is a slide talk I gave
on the subject in Vancouver, BC.
Rigidification of
quasi-categories and Mapping spaces in
quasi-categories -- joint with
Dan Dugger. In these papers we give several new ways to construct
mapping spaces in a quasi-category, for example as nerves of categories,
and show that they are all equivalent to the ones presented in Lurie's
book. We then give a self-contained proof of Lurie's result that the
Joyal model structure on simplicial sets is Quillen equivalent to
Bergner's model structure on simplicial categories.
Anomaly-Free
Sets of Fermions. A physics paper I coauthored. [Published
in the Journal of Mathematical Physics.]
The problem
I was given: find integer solutions to the system
x_1 + x_2 + ... + x_n = 0,
x_1^3 + x_2^3 + ... + x_n^3 = 0.
Categorical and topological
methods in computer science. This page includes a sheaf-theoretic model of
databases, a way to categorize higher-dimensional networks, and some
proposals that explain my interest in these types of ideas.
I also helped to organize a session of a conference relating to these
ideas at IPAM in October 2009. See the schedule and slides here.
Other files Includes
some papers of mine and others (some brief or unfit for publication, but
possibly of interest), a program for doing calculations in a group-ring,
some LaTeX guides I use, and other random stuff.
The Google.
The wiki.
MathSciNet.
Math arXiv.
Category theory
reprints.
Dan Dugger's page.
Jacob Lurie's page.
John Baez's blog.
UO Math department.
UO Math
Library.
UO Computer Science
Department.
UO.
This
work by David I. Spivak is licensed under a
Creative Commons
Attribution-Share Alike 3.0 Unported License.