David I. Spivak
Massachusetts Institute of Technology
Department of Mathematics
Cambridge, MA 02139
Phone:
Email:
Homepage:
(510) 684-6425
dspivak@math.mit.edu
http://math.mit.edu/∼dspivak
Education
Ph.D. Mathematics, University of California, Berkeley, 2007.
Advisor: Peter Teichner.
Thesis title: Quasi-smooth derived manifolds.
B.S. Mathematics, University of Maryland, College Park, 2000.
Employment
MIT (Mathematics): Research scientist. Spring 2013 – Present.
MIT (Mathematics): Postdoctoral associate. Spring 2010 – Spring 2013.
University of Oregon (Mathematics): Paul Olum Visiting Assistant Professor. Fall 2007 – Spring 2010.
University of Oregon (Computer and Information Sciences): guest instructor. Spring 2008, Fall 2008.
University of California, Berkeley (Mathematics): Graduate Student Instructor. 2001 – 2005, 2006 –
2007.
University of California, Berkeley (Mathematics): Graduate Student Researcher. 2005 – 2006.
University of Maryland, College Park (Mathematics): Strauss Teaching Assistant. 1999 – 2000.
Grants
Current
As Principal Investigator
Air Force Office of Scientific Research (AFOSR) grant FA9550-14-1-0031, “Categorical Approach to
Agent Interaction”, in the amount of $180,000 per year for 5 years (2013/12 – 2018/12).
National Science Foundation (NSF) grant 1611699, “I-Corps: Solving Information-Integration Problems
Using Category Theory", in the amount of $50,000 for 6 months (2016/01 – 2016/06).
As Co-PI
National Aeronautics and Space Administration (NASA) grant NNH13ZEA001N, “Category-theoretic
Approaches for the Analysis of Distributed Systems”, in the amount of $100,000 per year for 3 years
(2014/06 – 2017/05).
David I. Spivak
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Previous
As Principal Investigator
Office of Naval Research (ONR) grant N000141310260, “Categorical informatics,” in the amount of
$180,000 per year for 3 years (2013/02 – 2015/10).
Office of Naval Research (ONR) grant N000141010841, “Categorical Information Theory,” in the amount
of $120,000 per year for 3 years (2010/06 – 2013/05).
Office of Naval Research (ONR) grant N000140910466, “Databases and Networks,” in the amount of
$100,000 per year (2009/01 – 2010/06).
Honors and awards
Outstanding Graduate Student Instructor (UC Berkeley 2002).
VIGRE fellowship (UC Berkeley 2000-2001).
Graduated Magna Cum Laude, and with Honors in Mathematics (U. Maryland 2000).
Outstanding Senior Award (U. Maryland 2000).
Carol Karp award for Outstanding Logic student (U. Maryland 2000).
Publications, preprints, and presentations
Book
Spivak, D.I. (2014) Category Theory for the Sciences. Cambridge: MIT Press. 486 pages.
Journal Articles
Vagner, D.; Spivak, D.I.; Lerman, E. (2015) “Algebras of Open Dynamical Systems on the Operad of
Wiring Diagrams”. Accepted for publication: Theory and Application of Categories. Available online
http://arxiv.org/abs/1408.1598
Giesa, T.; Jagadeesan, R.; Spivak, D.I.; Buehler, M.J. (2015) “Matriarch: a Python library for materials architecture.” ACS Biomaterials Science & Engineering, http://pubs.acs.org/doi/full/10.1021/
acsbiomaterials.5b00251.
Brommer D.B.; Giesa T.; Spivak, D.I.; Buehler, M.J. (2015) “Categorical Prototyping: Incorporating
Molecular Mechanisms into 3D printing". Nanotechnology, article reference: NANO-108127.
Spivak, D.I. (2014) “Database queries and constraints via lifting problems.” Mathematical structures in
computer science. Available online: http://arxiv.org/abs/1202.2591
Spivak, D.I. (2012) “Functorial Data Migration”. Information and Communication. Vol 217, pp. 31 – 51.
Available online: http://arxiv.org/abs/1009.1166
Giesa, T.; Spivak, D.I.; Buehler, M.J. (2012) “Category theory based solution for the building block replacement problem in materials design”. Advanced Engineering Materials. DOI: 10.1002/adem.201200109
Spivak, D.I.; Kent, R.E. (2012) “Ologs: a categorical framework for knowledge representation”. PLoS
ONE 7(1): e24274. doi:10.1371/journal.pone.0024274.
Wong, J.Y.; McDonald, J.; Taylor-Pinney, M.; Spivak, D.I.; Kaplan, D.L.; Buehler, M.J. (2012) “Materials
by design: Merging proteins and music”. Nano Today 7, issue 6, pp. 488 – 495.
David I. Spivak
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Giesa, T.; Spivak, D.I.; Buehler M.J. (2011) “Reoccurring patterns in hierarchical protein materials and
music: The power of analogies”. BioNanoScience 1 no. 4, pp. 153-161.
Spivak, D.I.; Giesa, T.; Wood, E.; Buehler, M.J. (2011) “Category Theoretic Analysis of Hierarchical
Protein Materials and Social Networks.” PLoS ONE 6(9): e23911. doi:10.1371/journal.pone.0023911
Dugger, D.; Spivak, D.I. (2011) “Rigidification of quasi-categories.” Algebraic and Geometric Topology 11
pp. 225-261.
Dugger, D.; Spivak, D.I. (2011) “Mapping spaces in quasi-categories.” Algebraic and Geometric Topology
11 pp. 263-325.
Spivak, D.I. (2010) “Derived Smooth Manifolds.” Duke Mathematical Journal 153, no. 1, pp. 55-128.
Batra, P.; Dobrescu, B.A.; Spivak, D.I. (2006) “Anomaly-free sets of fermions.” Journal of Mathematical
Physics, 47, 082301.
Refereed conference papers and technical reports
Forssell, H.; Gylterud, H.K.; Spivak, D.I. (2016) “Type theoretical databases”. Logical Foundations of
Computer Science. Available online http://arxiv.org/abs/1406.6268
Wisnesky, R.; Spivak, D.I.; Schultz, P.; Subrahmanian, E. (2015) “Functorial data migration: from theory
to practice”. NIST Interagency/Internal Report (NISTIR). Available online: http://arxiv.org/abs/1502.
05947.
Morton, J.; Spivak, D.I. (2015) “A operad-based normal form for morphism expressions in a closed
compact category". Higher-dimensional rewriting and applications, http://hdra15.gforge.inria.fr.
Spivak, D.I.; Wisnesky, R. (2015) “Relational Foundations for Functorial Data Migration.” Proceedings of
the International Symposium on Database Programming Languages (DBPL), ACM. Available online: http:
//arxiv.org/abs/1212.5303.
Gross, J.; Chlipala, A.; Spivak, D.I. (2014) “Experience Implementing a Performant Category-Theory
Library in Coq”. 5th conference on interactive theorem proving (ITP’14). Available online: http://arxiv.
org/abs/1401.7694
Spivak, D.I.; Wisnesky, R. (2013) “A Functorial Query Language”. Data-Centric Programming workshop
(DCP2014). Available online: http://research.microsoft.com/en-us/events/dcp2014/wisnesky.
pdf
Preprints
Schultz, P.; Spivak, D.I.; Vasilakopoulou, C.; Wisnesky, R. (2016) "Algebraic databases". Available
online: http://arxiv.org/abs/1602.03501
Lerman, E.; Spivak, D.I. (2016) "An algebra of open continuous time dynamical systems and networks".
Spivak, D.I. (2015) “The steady states of coupled dynamical systems compose according to matrix
arithmetic". Available online: http://arxiv.org/abs/1512.00802
Schultz, P.; Spivak, D.I.; Wisnesky, R. (2015) “QINL: Query-integrated Languages". Available online:
http://arxiv.org/abs/1511.06459
Spivak, D.I.; Schultz, P.; Rupel, D. (2015) “String diagrams for traced and compact categories are
oriented 1-cobordisms”. Submitted. Available online: http://arxiv.org/abs/1508.01069
Pérez, M.; Spivak, D.I. (2015) “Toward formalizing ologs: Linguistic structures, instantiations, and
mappings”. Submitted. Available online: http://arxiv.org/abs/1503.08326
David I. Spivak
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Spivak, D.I.; Schultz, P.; Wisnesky, R. (2015) “A Purely Equational Formalism for Functorial Data
Migration”. Available online: http://arxiv.org/abs/1503.03571
Spivak, D.I. (2015) “Nesting of dynamic systems and mode-dependent networks”. Submitted. Available
online: http://arxiv.org/abs/1502.07380
Spivak, D.I. (2014) “Categories as mathematical models”. To appear in Categories for the Working Philosopher. Available online http://arxiv.org/abs/1409.6067
Rupel, D.; Spivak, D.I. (2013) “The operad of temporal wiring diagrams: formalizing a graphical
language for discrete-time processes”. Submitted. Available online http://arxiv.org/abs/1307.6894
Spivak, D.I. (2013) “The operad of wiring diagrams: Formalizing a graphical language for databases,
recursion, and plug-and-play circuits.” Available online: http://arxiv.org/abs/1305.0297
Spivak, D.I. (2012) “Kleisli database instances”. Available online: http://arxiv.org/abs/1209.1011
Spivak, D.I.. (2010) “Table manipulation in simplicial databases”. Available online: http://arxiv.org/abs/1003.2682
Spivak, D.I. (2009) “Simplicial databases.” Available online: http://arxiv.org/abs/0904.2012
Invited Talks
Applied category theory:
U. Mass. Boston (Mathematics colloquium) 2015/10/14;
NIST (Computational category theory workshop) 2015/09/28;
University of Oslo (Department of Informatics) 2015/09/21;
ÉPFL (8 hour mini-course) 2015/09/14 – 2015/09/18;
MIT (LIDS lunch seminar) 2015/06/26;
NIST 2015/06/16;
NIST 2015/06/18;
Foundational Methods in Computer Science 2015/06/06;
Categorical Foundations of Network Theory workshop (ISI Turin) 2015/05/28;
U. Pennsylvania (Complex systems seminar) 2015/04/03;
Pennsylvania State U. (Applied algebra and network theory seminar) 2015/03/18;
MINES ParisTech (International workshop on Design Theory) 2015/01/26;
MIT (Programming languages seminar) 2014/04/15;
IAS (Bar talk) 2014/03/20;
PARC 2014/03/03;
Amgen 2014/03/04;
Oracle 2014/02/28;
UIUC (Topology seminar) 2014/02/25;
Harvard (PL seminar) 2014/02/19;
Carnegie Mellon U. (POP seminar) 2014/01/23;
NIST 2013/06/12;
Courant Institute 2012/12/03;
U. Oregon 2012/11/12;
Brown U. 2012/09/19;
Mathfest (Madison, WI) 2012/08/04;
Stanford Center for Biomedical Informatics Research (Colloquium) 2012/07/27;
Office of Naval Research 2012/06/13;
U. Texas (Special geometry seminar) 2012/01/31;
Amgen Inc. 2012/01/24–25;
Carnegie Mellon U. (POP seminar) 2012/01/18;
UIUC (MSS Colloquium) 2011/11/29;
Agent-based complex systems conference (IPAM) 2009/10/13;
David I. Spivak
Johns Hopkins (Topology seminar) 2011/11/21
Amgen Inc. 2011/02/17–18;
Boston Haskell 2011/01/20;
Harvard U. 2010/11/03 (EECS seminar);
Galois Inc. 2010/10/22 (Tech talk);
MIT 2010/09/20 (Topology seminar);
MIT 2010/09/16 (CSAIL seminar);
MIT 2010/09/15 (Linguistics – semantics reading group);
Foundational methods in computer science conference (U. Calgary) 2010/06/12;
Galois Inc. 2010/06/03 (Tech talk);
U. Chicago 2010/05/11 (Topology seminar);
Reed College (colloquium) 2010/03/25;
Amgen Inc. 2010/03/15-16
Carnegie Mellon U. 2009/11/13;
Agent-based complex systems conference (IPAM) 2009/10/13. McGill U. 2009/05/19
U. California, Riverside (colloquium) 2009/04/29;
Algebraic Topological Methods in Computer Science (U. Paris 7) 2008/07/07;
U. Oregon (Topology Seminar) 2008/05/06;
U. Oregon Computer Science Department (colloquium) 2008/02/07.
Derived Manifolds:
U. Toronto (4 hour mini-course) 2010/02/22-26;
Derived Algebraic Geometry conference (U. Salamanca, Spain) 2009/06/04;
U. Quebec at Montreal 2009/05/22;
MIT 2009/05/04;
U. California, Riverside 2009/04/30;
Stanford U. 2009/02/03;
Cascade Topology Conference (Portland State U.) 2008/11/08;
UIUC 2008/10/04;
AMS Sectional (U. British Columbia) 2008/10/04;
CATS3 conference (Pisa, Italy) 2008/09/03.
Mapping spaces in Quasi-categories:
U. Illinois Chicago 2009/12/09;
U. Pennsylvania 2009/11/18;
Novemberfest Category theory conference (Carnegie Mellon U.) 2009/11/15;
AMS sectional (U. California, Riverside) 2009/11/08.
Teaching Experience
Graduate classes at MIT:
Category theory for scientists (18-S996) – Spring 2013.
Undergraduate classes at MIT:
Differential equations (18.03) – Spring 2012.
Graduate classes at U. Oregon:
Characteristic classes – Fall 2008
Categorical Informatics – Winter 2010.
Undergraduate classes at U. Oregon:
Integral calculus – Fall 2008
Calculus III (sequences and series) – Winter 2009
Differential equations – Winter 2009, Fall 2007
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David I. Spivak
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Linear algebra – Spring 2010, Winter 2008
Discrete Mathematics – Fall 2007.
Undergraduate classes at U. California, Berkeley
Precalculus (large lecture, managing TAs leading sections) – Spring 2005, Fall 2004
Other undergraduate classes, akin to those above at U. Oregon (as a TA) – Fall 2001 to Spring 2007.
Related Professional Experience
I have supervised three postdocs, Dr. Ryan Wisnesky (2014/02 – 2015/08), Dr. Patrick Schultz (2014/08
– present), and Dr. Marco Pérez (2014/07–2015/07), working on mathematical foundations or information and communication. Funded by the above grants, their work includes some papers on which I
am not an author:
Malecha and Wisnesky, “Using Dependent Types and Tactics to Enable Semantic-optimization of
Language-integrated Queries” (DBPL 2015).
Schultz, “Regular and exact (virtual) double categories”. http://arxiv.org/abs/1505.00712.
I have supervised thirteen undergraduates doing a total of eighteen UROPs (Undergraduate research
opportunity program) at MIT between 2011 and 2015, each involving research in Categorical Information Theory. I also joint-mentored a Research Science Institute high-school student, who did a project
combining materials science and mathematics in 2013, which ended in an article published in 2015.
In 2015 I was the PI on an NSF micro-grant called an I-Corps site program award through MIT’s Venture
Mentoring Service (grant #1347267), which funded market research for a categorical database company.
I gave a four-day mini-course on applied category theory in Switzerland, at the École Polynechnique
Fédéral Lausanne in September 2015. I had about 20 students, half of whom were mathematicians and
half of whom were from other sciences.
I was on the organizing committee for the ”Agent-based complex systems” conference at the Institute
of Pure and Applied Math, October 12 – 14, 2009. I was also on the organizing committee for a
workshop at the PSB 2016 conference.
I’ve hired four graduate students to implement my work on applied category theory: two from University of Oregon (2009 – 2010), and two from Harvard (2012 – 2014).
I led two seminars on in the Computer and Information Science department at the University of
Oregon. They were called ”Category theory in computer science” (Spring 2008) and ”Mathematical
methods in computer science” (Fall 2008).
I gave two talks (2010 and 2012) at the Boston Math Circle (a group for mathematically advanced teens)
about various aspects of category theory, and I gave an “IAP Math Lecture” in January 2014 and again
in January 2015 at MIT on various applied categorical subjects.