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.

One of the larger endeavors I am working on is the development of a suitable framework for (infinite dimensional) derived differential geometry, tailored towards applications to field theory. This project is supported by a joint NSF topology grant, with Owen Gwilliam. This builds upon (still ongoing) work of mine with D. Roytenberg centered around modeling derived manifolds using differential graded manifolds.

I have also been actively researching the interaction between étale and motivic homotopy theory.

Finally, I have been working in the field of log geometry with Sarah Scherotzke, Nicolo Sibilla, and Mattia Talpo. We are currently investigating log étale K-theory.

I have many other projects as well.

Published Papers

1. Higher Orbifolds and Deligne-Mumford Stacks as Structured Infinity Topoi. Memoirs of the American Mathematical Society 264 (2020), no. 1282 arXiv link

1. Étale Stacks as Prolongations. Advances in Mathematics Volume 352, 20 August 2019, Pages 56-132 arXiv link

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

4. On The Homotopy Type of Higher Orbifolds and Haefliger Classifying Spaces. Advances in Mathematics, Volume 294, 14 May 2016, Pages 756–818 arXiv link

5. Correction to the article : An étalé space construction for stacks. Algebraic & Geometric Topology 16(1):541-546, February 2016

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

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

8. 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

On the Universal Property of Derived Manifolds with Steffens P.

On the profinite homotopy type of log schemes Scherotzke S., Sibilla N., and Talpo M.

Relative Étale Realizations of Motivic Spaces and Dwyer-Friedlander K-Theory of Noncommutative Schemes with Elmanto E.

On the étale homotopy type of higher stacks

Homological Algebra for Superalgebras of Differentiable Functions with Roytenberg D.

Sheaf Theory for Étale Geometric Stacks

Additional Material

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

PhD Thesis

 

Math 639 Homotopy Theory (fall 2020)

Math 114 Discrete Mathematics, sections 3 and 4 (spring 2020)

Math 649 Category Theory (fall 2019)

Math 114 Discrete Mathematics, section 5 (fall 2019)

Math 639 Moduli Spaces and Invariant Theory (spring 2018)

Math 114 Calculus II GMU, section 6 (spring 2018)

Math 114 Calculus II GMU, sections 4 and 5 (fall 2017)

Math 629 Algebraic Topology I GMU (spring 2017)

Math 649 Category Theory GMU (fall 2016)

Math 631 Graduate Topology GMU (spring 2016)

Math 321 Abstract Algebra GMU (fall 2015)

Math 101 (Calc II), Sec. 205 (UBC 2015)

Master's Course on Topos Theory (University of Bonn 2013)

I was on sabbatical at the Max Planck Institute for Mathematics in Bonn, Germany from summer 2018 until fall 2019.

I was a visiting scientist as the Max Planck Institute for Mathematics during the summers of 2016 and 2017.

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."

Topology, Algebraic Geometry, and Dynamics Seminar (TADS) (organizer)

Past Seminars

Higher Differential Geometry Seminar (co-organizer, w/ Christian Blohmann and Peter Teichner)

Student Seminar on Higher Categories I

Student Seminar on Higher Categories II

                                                                                    ©2013 David Carchedi     ©2013 Smoking Hen Studios