Michael Batanin
- Leading Research Fellow: Faculty of Mathematics
- Michael Batanin has been at HSE University since 2025.
Education and Degrees
Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences
Novosibirsk State University
According to the International Standard Classification of Education (ISCED) 2011, Candidate of Sciences belongs to ISCED level 8 - "doctoral or equivalent", together with PhD, DPhil, D.Lit, D.Sc, LL.D, Doctorate or similar. Candidate of Sciences allows its holders to reach the level of the Associate Professor.
Editorial board membership
Foundational Chied Editor of the online journal "Higher structurues" since 2016.
Publications
1. Mappings of spectral sequences and the generalized homotopy axiom, Siberian Math. Journal, 5, (1987), 22-31.
2. Strong and weak shape equivalences of compact metric spaces, Sibirsk. Mat. Zh., { 31} (1990), 3, 6--10.
3. Coherent categories with respect to monads and coherent prohomotopy theory, Cahiers Topologie Geom. Diff. Cat. XXXIV-4
(1993), 270-304.
4. Categorical strong shape theory, Cahiers Topologie
Geom. Diff. Cat. XXXVIII-1 (1997), 3-66.
5. Homotopy coherent category theory and $A_{\infty}$-structures in monoidal categories, Journal of Pure and Appl. Algebra, 123 (1998), 67-103.
6. Monoidal globular categories as a natural
environment for the theory of weak n-categories, Adv.ances in Math. 136 (1998), pp. 39-103.
7. Computads for finitary monads on globular sets, Contemp. Math. AMS, 230 (1998), 37-58.
8. (joint with R.Street), The universal property of the multitude of trees, Journal of Pure and Appl. Algebra, 154 (2000), 3-13.
9. On Penon method of weakening algebraic structures, Journal of Pure and Appl. Algebra, 172-1 (2002), 1-23.
10. The symmetrisation of $n$-operads and compactification of real configuration spaces}, Advances in Math. { 211} (2007), pp. 684-725.
11. (editor with A,Davydov, M.Johnson, S.Lack, A.Neeman), Categories in Algebra, Geometry and Mathematical Physics, Contemp. Mathematics { 431}(2007).
12. The Eckmann-Hilton argument and higher operads, Advances in Math. { 217}(2008), pp. 334-385.
13. Locally constant $n$-operads as higher braided operads, Journal of Noncommutative Geometry, v.4 , n.2 , 237-265, pp. 2010.
14. (joint with M. Weber M), Algebras of higher operads as enriched categories, Appl. Categorical Structures, v. 19, n.1 pp.93-136, 2011.
15. (joint with J.Kock, A.Joyal, J.-F. Mascari), Polynomial functors and opetopes, Advances in Math., 224 no. 6, 2690-2737 2010.
16 (joint with M.Markl), Crossed interval groups and natural operations on Hochschild cohomology, Journal of Noncommutative Geometry,{v.8}, (n.3), 655--693.{ 2014}
17. (joint with C.Berger), The Lattice Path Operad and Hochschild cochains, Contemporary Math., AMS , vol. 504,, p. 23-52, .2009.
18. (joint with C.Berger and M.Markl), Operads of natural operations I: Lattice paths, braces and Hochschild cochains, { S\'{e}minaire and Congr\`{e}, }, Collection SMF, 26, pp.1-33, 2011.
19. (joint with M.~Markl), Centers and homotopy centers in enriched monoidal categories.
Advances in Math. {230} (2012), 1811--1858.
20. (joint with D.-C. Cisinski and M. Weber),
Multitensor lifting and strictly unital higher category theory, Theory and applications of categories, {28(25)}, pp. 804-856, { 2013.}
21. (joint with M.~Markl), Operadic categories and duoidal Deligne's conjecture,
Advances in Mathematics, 285, 1630--1687, 2015.
22. (joint with J. Kock and M.Weber), Regular patterns, substitudes, Feynman categories and operads, Theory and Application of Categories, vol. 33, 6-7, p.148-192, 2015.
23. (joint with C.~Berger), Homotopy theory for algebras over polynomial monads, Theory and Application of Categories, Vol. 32, No. 6, 148--253, 2017.
24. An operadic proof of the Baez-Dolan stabilisation hypothesis, Proceedings of the AMS 145, 2785--2798, 2017.
25. (joint with F. De Leger), Polynomial monads and delooping of mapping spaces,
Journal of Noncommutative Geometry v.13(4), pp. 1521--1576, 2019.
26. (joint with D.White), Left Bousfield localization and Eilenberg-Moore algebras, Homotopy, Homology and App., vol.23(2), pp.299--323, 2021.
27. (joint with D.White), Homotopy theory of algebras of substitudes and their localisation, Transactions of AMS, v.375(5), pp. 3569--3640, 2022.
28. (joint with A.~Davydov), Cosimplicial monoids and deformation theory of tensor categories, J. Noncommut. Geom. 17, no. 4, pp. 1167--1229, 2023.
29. (joint with M.~Markl), Operadic categories as a natural environment for Koszul duality, Compositionality, Volume 5, 2023.
30. (joint with M.~Markl), Koszul duality for operadic categories,
Compositionality, Volume 5, 2023.
31. (joint with M.~Markl and J.~Obradovi\'c), Minimal models for graphs-related (hyper)operads, Journal of Pure and Applied Algebra, Volume 227, Issue 7, 2023.
32. (joint with D.~White), Left Bousfield localisation without left properness, Journal of Pure and Applied Algebra, Volume 228, Issue 6, 2024.
33. (joint with M.~Markl) Operads, operadic categories and the blob complex, Applied Categorical Structures, (6)32, 2024.
34. (joint with F. De Leger and D. White) Quasi-tame substitudes and the Grothendieck construction, arXiv:2311.07322, accepted for publication in Theory and applications of categories, 2025
35. (joint with F. De Leger and D. White) Model structures on operads and algebras from a global perspective, arXiv:2311.07320, accepted for publication in Tunisian Mathematical Journal, 2025
36. (joint with B.~Shoikhet)\emph{Twisted tensor product of dg categories and Kontsevich's Swiss Cheese conjecture }, arXiv:2412.03239, submitted.