Michael "Mike" Shulman (; born 1980) is an American associate professor of mathematics at the

University of San Diego The University of San Diego (USD) is a private Roman Catholic research university in San Diego, California. Chartered in July 1949 as the independent San Diego College for Women and San Diego University (comprising the College for Men and Sc ...

who works in category theory and

higher category theory In mathematics, higher category theory is the part of category theory at a ''higher order'', which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. Higher ca ...

homotopy theory In mathematics, homotopy theory is a systematic study of situations in which maps can come with homotopies between them. It originated as a topic in algebraic topology but nowadays is studied as an independent discipline. Besides algebraic topol ...

, logic as applied to set theory, and

computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includin ...

Work

Shulman did his undergraduate work at the

California Institute of Technology The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

and his postgraduate work at the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

and the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

, where he received his Ph.D. in 2009. His doctoral thesis and subsequent work dealt with applications of category theory to homotopy theory. In 2009, he received a

National Science Foundation The National Science Foundation (NSF) is an independent agency of the United States government that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National ...

Mathematical Sciences Postdoctoral Research Fellowship. In 2012–13, he was a visiting scholar at the Institute for Advanced Study, where he was one of the official participants in the ''Special Year on Univalent Foundations of Mathematics''. Shulman was one of the principal authors of the book ''Homotopy type theory: Univalent foundations of mathematics'', an informal exposition on the basics of univalent foundations and homotopy type theory. In 2014, Shulman was part of a team headed by

Steve Awodey Steven M. Awodey (; born 1959) is an American mathematician and logician. He is a Professor of Philosophy and Mathematics at Carnegie Mellon University. Biography Awodey studied mathematics and philosophy at the University of Marburg and the ...

that was awarded a $7.5M grant from the

Air Force Research Laboratory The Air Force Research Laboratory (AFRL) is a scientific research organization operated by the United States Air Force Materiel Command dedicated to leading the discovery, development, and integration of aerospace warfighting technologies, p ...

for homotopy type theory.

Blogs

Shulman is a supporter of using web-based software systems, such as

GitHub GitHub, Inc. () is an Internet hosting service for software development and version control using Git. It provides the distributed version control of Git plus access control, bug tracking, software feature requests, task management, co ...

, to promote collaborative work by mathematicians—the six-hundred-page ''Homotopy type theory'' book being a notable example. He is a prolific contributor to the ''n''Lab (and a member of its steering committee), and a co-host of the homotopy type theory blog and of the ''n''-Category Cafe, a blog focusing on higher category theory.Shulman postings to ''n''-Category Cafe blog
/ref>

Selected publications

* Michael Shulman;
Synthetic Differential Geometry
' May 31, 2006 * Daniel Licata and Michael Shulman;
Calculating the fundamental group of the circle in homotopy type theory
' January 15. 2013 * Benedikt Ahrens, Chris Kapulkin, and Michael Shulman;
Univalent categories and the Rezk completion
' March 4. 2013 * Michael Shulman – In Cambridge Journals Special Issue: From type theory and homotopy theory to Univalent Foundations of Mathematics;
Univalence for inverse diagrams and homotopy canonicity
' November 23, 2013 *

John C. Baez John Carlos Baez (; born June 12, 1961) is an American mathematical physics, mathematical physicist and a professor of mathematics at the University of California, Riverside (UCR) in Riverside, California, Riverside, California. He has worked o ...

and Michael Shulman;
Lectures on ''n''-categories and cohomology
' In

References

External links

Shulman's home page
at University of San Diego *

Shulman postings to Homotopy Type Theory blog
{{DEFAULTSORT:Shulman, Michael 21st-century American mathematicians Category theorists University of San Diego faculty University of Chicago alumni Institute for Advanced Study visiting scholars California Institute of Technology alumni Living people 1980 births