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

University of San Diego The University of San Diego (USD) is a Private university, private Catholic Church, Catholic research university in San Diego, California, United States. Chartered in 1949 as the independent San Diego College for Women and San Diego University ...

who works in

category theory Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. 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 morphism, arrows in order to be able to explicitly study the structure behind those equalities. H ...

homotopy theory In mathematics, homotopy theory is a systematic study of situations in which Map (mathematics), maps can come with homotopy, homotopies between them. It originated as a topic in algebraic topology, but nowadays is learned as an independent discipli ...

, logic as applied to set theory, and

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

Work

Shulman did his undergraduate work at the

California Institute of Technology The California Institute of Technology (branded as Caltech) is a private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small group of institutes ...

and his postgraduate work at the

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

and the

University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, 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 U.S. National Science Foundation (NSF) is an Independent agencies of the United States government#Examples of independent agencies, independent agency of the Federal government of the United States, United States federal government that su ...

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 Univalent foundations are an approach to the foundations of mathematics in which mathematical Structuralism (philosophy of mathematics), structures are built out of objects called ''types''. Types in univalent foundations do not correspond exactly ...

and

homotopy type theory In mathematical logic and computer science, homotopy type theory (HoTT) refers to various lines of development of intuitionistic type theory, based on the interpretation of types as objects to which the intuition of (abstract) homotopy theory ap ...

. 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 Univ ...

that was awarded a $7.5M grant from the

Air Force Research Laboratory The Air Force Research Laboratory (AFRL) is a scientific research and development detachment of the United States Air Force Air Force Materiel Command, Materiel Command dedicated to leading the discovery, development, and integration of direct- ...

for homotopy type theory.

Blogs

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

GitHub GitHub () is a Proprietary software, proprietary developer platform that allows developers to create, store, manage, and share their code. It uses Git to provide distributed version control and GitHub itself provides access control, bug trackin ...

, 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 Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessme ...

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 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