David Spivak

Last updated
David Isaac Spivak
David MIT 20190110.jpg
Spivak in December 2019
Born
Los Angeles, California
NationalityAmerican
Alma mater
Known for Ologs
Scientific career
Fields Mathematics
Category theory
Applied category theory
Institutions Topos Institute

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.

Contents

Early life and education

Spivak received his PhD in mathematics from UC Berkeley in 2007 under the supervision of Peter Teichner and Jacob Lurie. [2] His thesis was on derived manifolds, [3] Spivak worked as a postdoc at the University of Oregon and Massachusetts Institute of Technology. [4]


Work

Spivak and Robert Kent developed a human-readable categorical system of knowledge representation called ologs. [5] These were applied, in a series of collaborations with the materials scientist Markus Buehler, to different problems in that materials science. [6] [7] [8] Ologs have been also used by researchers at NIST. [9] 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." [10]

Spivak has also studied dynamical systems and operads, originating the operadic approach to wiring diagram syntax. [11] [12] [13] His unpublished work "Metric realization of fuzzy simplicial sets" was cited by the authors of UMAP as inspirational for that work.

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. [14] The two, together with Rémy Tuyeras, wrote the first article using category theory to understand the structure of deep learning, called "Backprop as functor". [15]

Spivak is an editor of a diamond open access journal, Compositionality. [16]

Bibliography

References

  1. ↑ "Team". Topos Institute . Retrieved March 30, 2023.
  2. ↑ David Spivak at the Mathematics Genealogy Project
  3. ↑ Spivak, David I. (2008). "Derived Smooth Manifolds". Duke Mathematical Journal. 153: 55–128. arXiv: 0810.5174 . Bibcode:2008PhDT.......449S. CiteSeerX   10.1.1.244.3704 . doi:10.1215/00127094-2010-021. S2CID   18483726.
  4. ↑ "David I. Spivak" (PDF). David Spivak. Retrieved July 10, 2023.
  5. ↑ Spivak, David I.; Kent, Robert E. (31 January 2012). "Ologs: A Categorical Framework for Knowledge Representation". PLOS ONE . 7 (1): e24274. arXiv: 1102.1889 . Bibcode:2012PLoSO...724274S. doi: 10.1371/journal.pone.0024274 . PMC   3269434 . PMID   22303434.
  6. ↑ Brehm, Denise (8 December 2011). "Researchers link patterns seen in spider silk, melodies". news.mit.edu.
  7. ↑ Chandler, David L. (28 November 2012). "The music of the silks". news.mit.edu.
  8. ↑ Damrad, Kelsey (11 September 2015). "A new molecular design approach". news.mit.edu.
  9. ↑ Padi, Sarala; Breiner, Spencer; Subrahmanian, Eswaran; Sriram, Ram D. (June 2018). "Modeling and Analysis of Indian Carnatic Music Using Category Theory". IEEE Transactions on Systems, Man, and Cybernetics: Systems. 48 (6): 967–981. doi:10.1109/TSMC.2016.2631130. S2CID   21722758.
  10. ↑ Spivak, David I. (2014). Category Theory for the Sciences. MIT Press. ISBN   978-0-262-02813-4.[ page needed ]
  11. ↑ Spivak, David I.; Tan, Joshua (4 September 2016). "Nesting of dynamical systems and mode-dependent networks". Journal of Complex Networks: cnw022. doi:10.1093/comnet/cnw022.
  12. ↑ Giesa, Tristan; Jagadeesan, Ravi; Spivak, David I.; Buehler, Markus J. (September 2015). "Matriarch: A Python Library for Materials Architecture". ACS Biomaterials Science & Engineering. 1 (10): 1009–1015. doi:10.1021/acsbiomaterials.5b00251. PMC   4996638 . PMID   27570830.
  13. ↑ Spivak, David I.; Ernadote, Dominique; Hammammi, Omar (2016). "Pixel matrices: An elementary technique for solving nonlinear systems". 2016 IEEE International Symposium on Systems Engineering (ISSE). pp. 1–5. arXiv: 1605.00190 . doi:10.1109/SysEng.2016.7753120. ISBN   978-1-5090-0793-6. S2CID   1156200.
  14. ↑ Fong, Brendan; Spivak, David I. (2019). An Invitation to Applied Category Theory: Seven Sketches in Compositionality. Cambridge University Press. doi:10.1017/9781108668804. ISBN   978-1-108-66880-4. S2CID   199139551.[ page needed ]
  15. ↑ Fong, Brendan; Spivak, David I.; Tuyéras, Rémy (2019). "Backprop as functor: A compositional perspective on supervised learning". IEEE Computer Society Press. Proceedings of the Thirty fourth Annual IEEE Symposium on Logic in Computer Science (LICS 2019): 1–13.
  16. ↑ Editorial Board, Compositionality. Accessed August 16, 2019.
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