Michael A. Warren

Member
School of Mathematics
Institute for Advanced Study

Contact information

School of Mathematics
Institute for Advanced Study
Einstein Drive
Princeton, New Jersey 08540
USA

Office : Fuld Hall 419

☎ : 609-734-8185
✉ : m(insert-surname-here)@math.ias.edu

Research interests

• Category theory
• Homotopy theory
• Mathematical logic

Publications and preprints

• A characterization of representable intervals, Theory and Applications of Categories, vol 26 (8), pp. 204-232, 2012.
  [TAC]
• The strict ω-groupoid interpretation of type theory, in Models, Logics and Higher-Dimensional Categories: A Tribute to the Work of Mihály Makkai, AMS and Centre de Recherches Mathématiques publications, 2011.
  [PDF] [AMS]
• Martin-Löf Complexes, with S. Awodey and P. Hofstra, submitted, 2009.
  Preprint on the arXiv as arXiv:0906.4521 (math.LO).
  [PDF] [arXiv]
• Lawvere-Tierney sheaves in algebraic set theory, with S. Awodey, N. Gambino and P. L. Lumsdaine, Journal of Symbolic Logic, 74(3), pp. 862-890, 2009.
  [PDF] [arXiv]
• Homotopy theoretic models of identity types, with S. Awodey, Mathematical Proceedings of the Cambridge Philosophical Society, 146, pp. 45-55, 2009.
  [PS] [PDF] [arXiv]
• Coalgebras in a category of classes, Annals of Pure and Applied Logic, 146(1), pp. 60-71, 2007.
  [PS]
• Predicative algebraic set theory, with S. Awodey, Theory and Applications of Categories, volume 15, pp. 1-39, 2005.
  [TAC]

Some conference recent talks

• Homotopy and type theory, a series of three tutorial lectures, Logic and Interactions 2012, Algebra and Computation Week, February 27 - March 2, 2012.
  [Lecture notes coming soon!]
• Some connections between homotopy theory and logic, School of Mathematics Short Postdoc Talks, IAS, October 7, 2011. A slightly truncated version of my slides is available below.
  [PDF]
• Recent advances relating homotopy theory and type theory, 2011 Summer Meeting of the Canadian Mathematical Society, Special Session on Homotopy and Categories, University of Alberta (Edmonton), June 4, 2011.
• A combinatorial realizability model of type theory, Oberwolfach Mini-Workshop on the Homotopy Interpretation of Constructive Type Theory, March 4, 2011.
• Combinatorial realizability models of type theory, 2010 Category Theory Octoberfest, Dalhousie University (Halifax), October 23, 2010.
• Strict intervals in monoidal categories, 2010 Summer Meeting of the Canadian Mathematical Society, Special Session on Tensor Categories, University of New Brunswick (Fredericton), June 6, 2010.
• Martin-Löf Complexes as a model of homotopy types, Workshop on Homotopy and Type Theory, Carnegie Mellon University (Pittsburgh), February 5, 2010.

Notes and other output

• Homotopy theoretic aspects of constructive type theory, Ph.D. thesis, Carnegie Mellon University, 2008.
  [PDF]
• Algebraic models of sets and classes in categories of ideals with S. Awodey and H. Forssell, 2006.
  [PS]
• Predicative categories of classes, M.Sc. thesis, Carnegie Mellon University, 2004.
  [PS] [PDF]

Conference websites

Local website for the 26th iteration of Mathematical Foundations of Programming Semantics (MFPS):
[MFPS XXVI]

Websites for the Fields-Ottawa workshop on Smooth Structures in Logic, Category Theory and Physics:
[Local Website] [Fields Institute Website]

Abbreviated CV

• AARMS Postdoctoral Fellow in the Department of Mathematics and Statistics at Dalhousie University, where I was a member of the Atlantic Category Theory Group.
• Postdoctoral Fellow (supported by the Fields Institute) in the Department of Mathematics and Statistics at the University of Ottawa, where I was a memeber of the Logic and Foundations of Computing Group.
• Ph.D. in Logic, Carnegie Mellon University.
• M.Sc. in Mathematics, Carnegie Mellon University.
• M.A. (Honours) in Philosophy, University of St. Andrews.