PhD from UFPE, Recife, Brazil (2000); held postdoc positions in Stockholm, Nice and Montréal; professor titular at the UAB since 2009. In his thesis (2000) he used gravitational quantum cohomology à la Witten to solve the characteristic number problem for rational curves in projective space. With Toën (2005) he proved a non-linear version of the Deligne conjecture in homotopical algebra, and with Joyal (2007) he proved Simpson’s conjecture in dimension 3, connecting homotopy theory with higher category theory.

He pioneered the theory of polynomial functors (2013) and the theory of decomposition spaces (2018), so far culminating with the unification of algebraic and geometric semantics of Petri nets (2022). He is currently developing the field of homotopy combinatorics.

Category Theory, Homotopy Theory, Algebraic Geometry, Combinatorics

• J. Kock. Whole-grain Petri nets and processes. J. ACM 70 (2022), 1-58.
• D. Gepner, J. Kock, R. Haugseng. Infinity-operads as analytic monads. Int. Math. Res. Notices 2022, 12516-12624.
• K. Ebrahimi-Fard, L. Foissy, J. Kock, F. Patras. Operads of (noncrossing) partitions, interacting bialgebras, and moment-cumulant relations. Adv. Math. 369 (2020), 107170.
• I. Gálvez-Carrillo, J. Kock, A. Tonks. Decomposition spaces, incidence algebras and Möbius inversion I: basic theory. Adv. Math. 331 (2018), 952-1015.
• J. Kock. Polynomial functors and combinatorial Dyson-Schwinger equations; J. Math. Phys. 58 (2017), 041703.
• J. Kock, W. Pitsch. Hochster duality in derived categories and point-free reconstruction of schemes. Trans. Amer. Math. Soc. 369 (2017), 223-261.