nLab Jack Morava

Jack Johnson Morava (1944-2025)

• institute page

• Johns Hopkins obituary

• Wikipedia entry

• GoogleScholar page

• Michael Hopkins: Talk on Jack Morava’s work at Jack’s 60th birthday conference (2004) [webpage (archived)]

• reminiscences on the AlgTop mailing list (starting 1st Aug 2025): thread

Selected writings

Early seminar notes on what was to become chromatic homotopy theory:

• Jack Morava (scan by Haynes Miller): “Bording School” notes, Princeton (~1973) [pdf, pdf]

On prequantized (and polarized) symplectic manifolds in the context of cobordism rings and Thom spectra:

• Jack Morava, Cobordism of symplectic manifolds and asymptotic expansions, talk at the conference in honor of S.P. Novikov’s 60th birthday [arXiv:9908070]

On prime spectra of symmetric monoidal stable (∞,1)-categories:

• Jack Morava, Toward a fundamental groupoid for the stable homotopy category [arXiv:math/0509001]

On cobordism cohomology theory, algebraic topology and chromatic homotopy theory:

• Jack Morava, Complex cobordism and algebraic topology [arXiv:0707.3216]

On stable cohomotopy as the algebraic K-theory of FinSet:

• Jack Morava: Some background on Manin’s theorem $K(\mathbb{F}_1) \sim \mathbb{S}$ [pdf, pdf]

Comments on the analogy between power operations in homotopy theory and Lambda ring structure in Borger's absolute geometry:

• Jack Morava, Rakha Santhanam: Power operations and Absolute geometry (2012) [pdf]

On configuration spaces of points and a possible Galois group over the sphere spectrum:

• Jack Morava, Jonathan Beardsley, Toward a Galois theory of the integers over the sphere spectrum, Journal of Geometry and Physics Volume 131, September 2018, Pages 41-51 (arXiv:1710.05992, doi:10.1016/j.geomphys.2018.04.011)

On the cosmic Galois group:

• Jack Morava, The motivic Thom isomorphism (web, pdf)

• Jack Morava, The Cosmic Galois group as Koszul dual to Waldhausen’s A(pt) [arXiv:1108.4627]

• Nitu Kitchloo, Jack Morava: The Grothendieck–Teichmüller group and the stable symplectic category (2012) [arxiv:1212.6905]

On orbifolds in mathematical physics and in particular string theory:

• Alejandro Adem, Jack Morava, Yongbin Ruan: Orbifolds in Mathematics and Physics, Contemporary Mathematics 310, American Mathematical Society (2002) [ISBN:978-0-8218-2990-5]

On the “canonical formula of myth”:

• Jack Morava, On the Canonical Formula of C. Lévi-Strauss [arXiv:math/0306174]

• Jack Morava, Une interprétation mathématique de la formule canonique de Claude Lévi-Strauss , Cahiers de L’Herne 88 (2004) 216-218.

• Jack Morava, From Lévi-Strauss to Chaos and Complexity , in Mosko, Damon (eds.), On the Order of Chaos , Berghahn Oxford (2005)

On the Weinstein symplectic category:

• Nitu Kitchloo, Jack Morava, The Grothendieck–Teichmüller group and the stable symplectic category, 2012. (arxiv:1212.6905)

On quotient stacks:

• Theories of anything [arXiv:1202.0684]

On the Burau braid representation in relation to configuration spaces of points, group completion and topological quantum field theory:

• Jack Morava, Dale Rolfsen: Toward the group completion of the Burau representation, Trans. Amer. Math. Soc. 376 (2023) 1845-1865 [arXiv:1809.01994, doi:10.1090/tran/8796]

and related discussion revolving around the loop space of the 2-sphere regarded as a classifying space:

• Jack Morava: A homotopy-theoretic context for CKM/Birkhoff renormalization [arXiv:2307.10148, spire:2678618]

• Jack Morava: Some very low-dimensional algebraic topology [arXiv:2411.15885]

See also:

• Jack Morava: Boundary framings for locally conformally symplectic four-manifolds [arXiv:2502.05983]

Related entries

• Morava K-theory

• Morava E-theory

category: people