David Carchedi, Assistant Professor of Mathematics

I am an assistant professor of mathematics at George Mason University.

I completed my PhD in 2011 under the supervision of Ieke Moerdijk at Utrecht University, in the Netherlands. My thesis title was "Categorical Properties of Topological and Differentiable Stacks."

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Thesis

Categorical Properties of Topological and Diffentiable Stacks

Prezi

A prezi outlining some of my research areas. It was part of my presentation in MPI's Oberseminar in 2012

(Outdated)

Curriculum vitae

                                                                                                                                               

Research

A central theme of my research is applications of higher category theory to topology and differential and algebraic geometry. In particular, I am interested in derived geometry. I also maintain an active interest in field theory.

I am currently involved in many different research projects. One of the larger endeavors I am working on is an active collaboration with Dima Roytenberg centered around modeling derived manifolds using differential graded manifolds. I am also working with Hiro Tanaka on extended these ideas to the infinite dimensional setting.

Publications

Published Papers

Erratum: "An Étalé Space Construction for Stacks" Journal of Algebraic and Geometric Topology (To Appear).

On Theories of Superalgebras of Differentiable Functions. Theory and Applications of Categories, Vol. 28, 2013, No. 30, pp 1022-1098. with Roytenberg D.

An Étalé Space Construction for Stacks. Journal of Algebraic and Geometric Topology 13(2):831-903, 2013

Compactly Generated Stacks: A Cartesian closed theory of topological stacks. Advances in Mathematics, Volume 229, Issue 6, April 1 2012, Pages 3339-3397 arXiv link

Preprints

Kato-Nakayama spaces, infinite root stacks, and the profinite homotopy type of log schemes with Scherotzke S., Sibilla N., and Talpo M.

On The Homotopy Type of Higher Orbifolds and Haefliger Classifying Spaces

Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity Topoi

Homological Algebra for Superalgebras of Differentiable Functions with Roytenberg D.

Étalé Stacks as Prolongations

Sheaf Theory for Étale Geometric Stacks

Articles in Preparation

Étale homotopy types of higher stacks.

Homotopy theory of orbispaces (with D. Gepner and A. Henriques)

Additional Material

Informal notes about Étale stacks I wrote for Alan Weinstein: A Quick Note on Étale Stacks

PhD Thesis

 

Teaching

Positions

I was a postdoc with Kai Behrend at the University of British Columbia from 2014-2015.

I was a postdoc at the Max Planck Institute for Mathematics from 2011-2014.

I was a Visiting Scholar at UC Berkeley from Jan.-May of 2014 with Alan Weinstein.

I was a Visiting Scholar at MIT during the summers of 2009, 2010, 2012, and 2013.

Before starting my PhD at Utrecht, I spent a year in Utrecht as a participant in the Master Class in Symplectic Geometry from 2006-2007.

I also participated quite a bit in the Master Class in Calabi-Yau Geometry from 2008-2009.

In Fall of 2002, I was a participant in the "Math in Moscow Program."

Seminars

                                                                                    ©2013 David Carchedi     ©2013 Smoking Hen Studios