David Spivak Explained

David Isaac Spivak
Birth Place:	Los Angeles, California
Nationality:	American
Fields:	Mathematics Category theory Applied category theory
Workplaces:	Topos Institute
Known For:	Ologs

David Isaac Spivak is an American mathematician and senior scientist at the Topos Institute.^[1] He has worked on applications of category theory, in particular ologs and operadic compositionality of dynamical systems. He authored and coauthored the introductory texts on category theory and its applications, Category Theory for the Sciences and An Invitation to Applied Category Theory.

Early life and education

Spivak received his PhD in mathematics from UC Berkeley in 2007 under the supervision of Peter Teichner and Jacob Lurie. His thesis was on derived manifolds,^[2] Spivak worked as a postdoc at the University of Oregon and Massachusetts Institute of Technology.^[3]

Work

Spivak and Robert Kent developed a human-readable categorical system of knowledge representation called ologs.^[4] These were applied, in a series of collaborations with the materials scientist Markus Buehler, to different problems in that materials science.^{[5] [6] [7]} Ologs have been also used by researchers at NIST.^[8] The goal of ologs, and of Spivak's book, was to show that category theory can be made relatively easy and thus be understood by a wider audience. Piet Hut endorsed the book saying, "This is the first, and so far the only, book to make category theory accessible to non-mathematicians."^[9]

Spivak has also studied dynamical systems and operads.^{[10] [11] [12]}

Spivak and Brendan Fong wrote a book that summarizes the developments in applied category theory for a wide audience, and started a nonprofit applied category theory research institute called Topos Institute, located in Berkeley, California.^[13]

Spivak is an editor of a diamond open access journal, Compositionality.^[14]

Bibliography

• Spivak. Category Theory for the Sciences, MIT Press, 2014
• Schultz & Spivak. Temporal Type Theory: a Topos-Theoretic Approach to Systems and Behavior, Springer-Verlag, 2019,
• Fong & Spivak. An Invitation to Applied Category Theory: Seven Sketches in Compositionality, Cambridge University Press, 2019,

External links

• Spivak's former MIT Homepage

Notes and References

1. Web site: Team . . March 30, 2023.
2. 2008PhDT.......449S . 10.1.1.244.3704 . Derived Smooth Manifolds . Spivak . David I. . Duke Mathematical Journal . 2008 . 153 . 55–128 . 10.1215/00127094-2010-021 . 0810.5174 . 18483726 .
3. Web site: David I. Spivak . David Spivak . July 10, 2023.
4. Spivak . David I. . Kent . Robert E. . Ologs: A Categorical Framework for Knowledge Representation . . 31 January 2012 . 7 . 1 . e24274 . 10.1371/journal.pone.0024274 . 22303434 . 3269434 . 2012PLoSO...724274S . 1102.1889 . free .
5. Web site: Researchers link patterns seen in spider silk, melodies . news.mit.edu . Denise . Brehm . 8 December 2011.
6. Web site: The music of the silks . news.mit.edu . David L. . Chandler . 28 November 2012.
7. Web site: A new molecular design approach . news.mit.edu . Kelsey . Damrad . 11 September 2015.
8. Padi . Sarala . Breiner . Spencer . Subrahmanian . Eswaran . Sriram . Ram D. . Modeling and Analysis of Indian Carnatic Music Using Category Theory . IEEE Transactions on Systems, Man, and Cybernetics: Systems . June 2018 . 48 . 6 . 967–981 . 10.1109/TSMC.2016.2631130 . 21722758 .
9. Book: 978-0-262-02813-4 . Category Theory for the Sciences . Spivak . David I. . 2014 . MIT Press.
10. Spivak . David I. . Tan . Joshua . Nesting of dynamical systems and mode-dependent networks . Journal of Complex Networks . 4 September 2016 . cnw022 . 10.1093/comnet/cnw022 .
11. Giesa . Tristan . Jagadeesan . Ravi . Spivak . David I. . Buehler . Markus J. . Matriarch: A Python Library for Materials Architecture . ACS Biomaterials Science & Engineering . September 2015 . 1 . 10 . 1009–1015 . 10.1021/acsbiomaterials.5b00251 . 27570830 . 4996638 .
12. Book: 10.1109/SysEng.2016.7753120 . Pixel matrices: An elementary technique for solving nonlinear systems . 2016 IEEE International Symposium on Systems Engineering (ISSE) . 1–5 . 2016 . Spivak . David I. . Ernadote . Dominique . Hammammi . Omar . 978-1-5090-0793-6 . 1156200 .
13. Book: Fong . Brendan . Spivak . David I. . An Invitation to Applied Category Theory: Seven Sketches in Compositionality . Cambridge University Press . 2019 . 978-1-108-66880-4 . 10.1017/9781108668804. 199139551 .
14. http://www.compositionality-journal.org Editorial Board