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.





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