Home
Welcome to my webpage! Here you can find more information about me
and my research.
Research interests
My research is in algebra (category theory and homotopical algebra),
logic (categorical logic and type theory), and
mathematical foundations of computer science (logic in CS and formal
verification).
Research
Below you will find, organized roughly by research area, an assortment of links to my papers, preprints and
other notes. Preprint versions may differ from journal versions.
Category theory and homotopical algebra

Bicategorical
fibration structures and stacks, with Dorette Pronk, Theory
and Applications of Categories, 29(29), pp. 836873, 2014.

Model structures from a monad on presheaves, preprint, 2013.

A
characterization of representable intervals, Theory and
Applications of Categories, 26(8), pp. 204232, 2012.
Preprint on the arXiv.
Type theory

The local universes model:
an overlooked coherence construction for dependent type
theories, with Peter LeFanu Lumsdaine, to appear in ACM
Transactions on Computational Logic, 2015. Preprint on the
arXiv.

A
univalent formalization of the padic numbers, with
Álvaro Pelayo and Vladimir Voevodsky, Mathematical
Structures in Comptuer Science, 2015. Coq code is available
here.

Homotopy
type theory, with Álvaro Pelayo, Gazette des Mathématiciens, no. 142, 95110, October, 2014.

Voevodsky's Univalence Axiom in homotopy type theory, with Steve Awodey and Álvaro Pelayo, Notices of the American Mathematical Society, 60(08), 11641167, October, 2013.

Homotopy type theory and Voevodsky's univalent foundations, with Álvaro Pelayo, Bulletin of the American Mathematical Society, 51, 597648, 2014.
Associated Coq code is available here.

Combinatorial
realizability models of type theory, with Pieter Hofstra, Annals of Pure and Applied Logic, 164(10), pp. 957988, 2013. Preprint available on the arXiv.

MartinLöf Complexes, with Steve Awodey and Pieter Hofstra,
Annals of Pure and Applied Logic, 164(10), pp. 928956, 2013. Preprint available on the arXiv.

The
strict ωgroupoid interpretation of type theory, in Models,
Logics and HigherDimensional Categories, CRM Proc. Lecture Notes 53, Amer. Math. Soc., 291340, 2011.

A combinatorial realizability model of 1truncated type
theory, in Oberwolfach Reports 11/2011, pp. 630633,
2011. Available here.

Homotopy theoretic models of identity types, with Steve Awodey, Mathematical Proceedings of the Cambridge Philosophical Society, 146, pp. 4555, 2009. Preprint available on the arXiv.

Homotopy
theoretic aspects of constructive type theory, Ph.D. Thesis in
Logic, Carnegie Mellon University, 2008.

Homotopy models of intensional type theory, Ph.D. Thesis
Prospectus, 2006.
Mathematical logic and topos theory

LawvereTierney sheaves in algebraic set theory, with Steve Awodey, Nicola Gambino and Peter LeFanu Lumsdaine, Journal of Symbolic Logic, 74(3), pp. 862890, 2009. Preprint on the arXiv.

Coalgebras in a category of classes, Annals of Pure and Applied Logic, 146(1), pp. 6071, 2007. Preprint available here.

Algebraic models of sets and classes in categories of ideals, with Steve Awodey and Henrik Forssell, unpublished note, 2006.

Predicative algebraic set theory, with Steve Awodey, Theory and Applications of Categories, 15, pp. 139, 2005.

Predicative
categories of classes, M.Sc. Thesis in Logic, Carnegie Mellon
University, 2004.
About
Here you can find my contact and biographical information.
Contact information
maw@mawarren.net
Previous academic positions
 Member, School of Mathematics, Institute for Advanced Study,
Princeton, USA, 2011  2013.
 Postdoctoral fellow, Department of Mathematics and Statistics,
Dalhousie University, Halifax, Canada, 2010  2011.
 Postdoctoral fellow, Department of Mathematics and Statistics,
University of Ottawa, Ottawa, Canada, 2008  2010.
Education
 Ph.D. in Logic, Computation and Methodology, Carnegie Mellon
University, Pittsburgh, USA, 2008.
 M.Sc. in Mathematical Sciences, Carnegie Mellon University, 2006.
 M.Sc. in Logic and Computation, Carnegie Mellon University, 2004.
 M.A. (honours, first) in Philosophy, University of
St. Andrews, Scotland, UK, 2002.
Nationality
USA
Photograph