Professor Grigory Garkusha

Professor

Mathematics

+44 (0) 1792 602761

g.garkusha@swansea.ac.uk

Office - 342
Third Floor
Computational Foundry
Bay Campus

Available For Postgraduate Supervision

Research Links

https://orcid.org/0000-0001-9836-0714

ResearchGate

Google Scholar

About

I am a mathematician working in the field of motivic homotopy theory, algebraic K-theory, algebraic geometry and topology. I am mostly interested in the interplay between Algebra, Topology and Category theory.

My most recent works are dedicated to investigating various motives of algebraic varieties, stable motivic homotopy theory, algebraic Kasparov K-theory and enriched category theory.

Please visit my personal page https://ggarkusha.github.io

Areas Of Expertise

Motivic homotopy theory
Algebraic K-theory
Algebraic geometry and topology
Category theory
Rings and modules theory

Career Highlights

Award Highlights

Principal Investigator, EPSRC Award, EP/W012030/1.
Principal Investigator, EPSRC Award, EP/J013064/1.
Principal Investigator, EPSRC Award, EP/H021566/1.
Fellow of the Higher Education Academy

Publications

Research Highlights

Garkusha, G. (n.d.) The Ziegler spectrum for enriched ringoids and schemes. In ECM Satellite Conference "Functor and Tensor Categories, Models and Systems"Springer.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa69532
Garkusha, G. (2023). Correspondences and stable homotopy theory. Transactions of the London Mathematical Society, 10(1), 124-155.
https://doi.org/10.1112/tlm3.12056, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa64111
http://dx.doi.org/10.1112/tlm3.12056
Garkusha, G. & Neshitov, A. (2023). Fibrant resolutions for motivic Thom spectra. Annals of K-theory, 8(3), 421-488.
https://doi.org/10.2140/akt.2023.8.421, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa64028
Garkusha, G. (2023). Semilocal Milnor K-Theory. International Mathematics Research Notices, 2023(24), 22069-22095.
https://doi.org/10.1093/imrn/rnac343, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa61996
Garkusha, G., Panin, I., & Ostvaer, P. (2023). Framed motivic Gamma-spaces. Izvestiya: Mathematics, 87(1), 1-28.
https://doi.org/10.4213/im9246e, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa60277
https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=9246&option_lang=eng
Garkusha, G. (2024). Group schemes and motivic spectra. Israel Journal of Mathematics, 259, 727-758.
https://doi.org/10.1007/s11856-023-2492-x, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa59418
http://dx.doi.org/10.1007/s11856-023-2492-x
Garkusha, G. & Jones, D. (2022). Recollements for derived categories of enriched functors and triangulated categories of motives. Journal of Algebra, 589, 238-272.
https://doi.org/10.1016/j.jalgebra.2021.09.020, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa58283
Ananyevskiy, A., Garkusha, G., & Panin, I. (2021). Cancellation theorem for framed motives of algebraic varieties. Advances in Mathematics, 383, 107681
https://doi.org/10.1016/j.aim.2021.107681, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa56475
Garkusha, G., Neshitov, A., & Panin, I. (2021). Framed motives of relative motivic spheres. Transactions of the American Mathematical Society, 374(7), 5131-5161.
https://doi.org/10.1090/tran/8386, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa56370
Garkusha, G. & Panin, I. (2021). Framed motives of algebraic varieties (after V. Voevodsky). Journal of the American Mathematical Society, 34(1), 261-313.
https://doi.org/10.1090/jams/958, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa54023
https://www.ams.org/journals/jams/0000-000-00/S0894-0347-2020-00958-4/

All Research

Journal Articles

Garkusha, G. (2024). Group schemes and motivic spectra. Israel Journal of Mathematics, 259, 727-758.
https://doi.org/10.1007/s11856-023-2492-x, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa59418
http://dx.doi.org/10.1007/s11856-023-2492-x
Garkusha, G. (2023). Semilocal Milnor K-Theory. International Mathematics Research Notices, 2023(24), 22069-22095.
https://doi.org/10.1093/imrn/rnac343, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa61996
Garkusha, G. (2023). Correspondences and stable homotopy theory. Transactions of the London Mathematical Society, 10(1), 124-155.
https://doi.org/10.1112/tlm3.12056, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa64111
http://dx.doi.org/10.1112/tlm3.12056
Garkusha, G. & Neshitov, A. (2023). Fibrant resolutions for motivic Thom spectra. Annals of K-theory, 8(3), 421-488.
https://doi.org/10.2140/akt.2023.8.421, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa64028
Garkusha, G., Panin, I., & Ostvaer, P. (2023). Framed motivic Gamma-spaces. Izvestiya: Mathematics, 87(1), 1-28.
https://doi.org/10.4213/im9246e, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa60277
https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=im&paperid=9246&option_lang=eng
Garkusha, G. & Jones, D. (2022). Recollements for derived categories of enriched functors and triangulated categories of motives. Journal of Algebra, 589, 238-272.
https://doi.org/10.1016/j.jalgebra.2021.09.020, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa58283
Ananyevskiy, A., Garkusha, G., & Panin, I. (2021). Cancellation theorem for framed motives of algebraic varieties. Advances in Mathematics, 383, 107681
https://doi.org/10.1016/j.aim.2021.107681, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa56475
Garkusha, G., Neshitov, A., & Panin, I. (2021). Framed motives of relative motivic spheres. Transactions of the American Mathematical Society, 374(7), 5131-5161.
https://doi.org/10.1090/tran/8386, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa56370
Garkusha, G. & Panin, I. (2021). Framed motives of algebraic varieties (after V. Voevodsky). Journal of the American Mathematical Society, 34(1), 261-313.
https://doi.org/10.1090/jams/958, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa54023
https://www.ams.org/journals/jams/0000-000-00/S0894-0347-2020-00958-4/
Garkusha, G. & Panin, I. (2020). Homotopy invariant presheaves with framed transfers. Cambridge Journal of Mathematics, 8(1), 1-94.
https://doi.org/10.4310/cjm.2020.v8.n1.a1, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa52799
Garkusha, G. (2019). Reconstructing rational stable motivic homotopy theory. Compositio Mathematica, 155(7), 1424-1443.
https://doi.org/10.1112/S0010437X19007425, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa50767
https://www.cambridge.org/core/journals/compositio-mathematica/article/reconstructing-rational-stable-motivic-homotopy-theory/82617A1E778DAEB69789827B05B9DC31
Garkusha, G. (2018). Comparing motives of smooth algebraic varieties. C. R. Math. Acad. Sci. Paris, 356(11), 1100-1105.
https://doi.org/10.1016/j.crma.2018.11.006, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa45920
Garkusha, G. & Panin, I. (2018). On The Motivic Spectral Sequence. Journal of the Institute of Mathematics of Jussieu, 17(1), 137-170.
https://doi.org/10.1017/s1474748015000419, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa24748
http://dx.doi.org/10.1017/s1474748015000419
Garkusha, G. (2016). Algebraic Kasparov K-theory, II. Annals of K-Theory, 1(3), 275-316.
https://doi.org/10.2140/akt.2016.1.275, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa28417
http://msp.org/scripts/coming.php?jpath=akt
Al Hwaeer, H. & Garkusha, G. (2016). Grothendieck categories of enriched functors. Journal of Algebra, 450, 204-241.
https://doi.org/10.1016/j.jalgebra.2015.09.052, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa24965
Garkusha, G. (2014). Algebraic Kasparov K-theory. I. Documenta Mathematica, 19, 1207-1269.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa19687
Garkusha, G. & Panin, I. (2014). The triangulated category of K-motives DK_(k). Journal of K-theory, 14(01), 103-137.
https://doi.org/10.1017/is014004013jkt263, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa18164
Garkusha, G. (2013). Universal bivariant algebraic K-theories. Journal of Homotopy and Related Structures, 8(1), 67-116.
https://doi.org/10.1007/s40062-012-0013-4, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13021
Garkusha, G. & Panin, I. (2012). K-motives of algebraic varieties. Homology, Homotopy and Applications, 14(2), 211-264.
https://doi.org/10.4310/HHA.2012.v14.n2.a13, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13023
http://www.intlpress.com/HHA/v14/n2/a13/
Garkusha, G. (2010). R-SUPPORTS IN TENSOR TRIANGULATED CATEGORIES. Journal of Algebra and Its Applications, 09(06), 1001-1014.
https://doi.org/10.1142/S0219498810004361, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa7740
http://www.worldscientific.com/doi/abs/10.1142/S0219498810004361
Garkusha, G. & Prest, M. (2008). Classifying Serre subcategories of finitely presented modules. Proc. Amer. Math. Soc., 136(3), 761-770.
https://doi.org/10.1090/S0002-9939-07-08844-2, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1059
http://www.ams.org/journals/proc/2008-136-03/S0002-9939-07-08844-2/
Garkusha, G. & Prest, M. (2008). Reconstructing projective schemes from Serre subcategories. Journal of Algebra, 319(3), 1132-1153.
https://doi.org/10.1016/j.jalgebra.2007.10.034, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1060
http://www.sciencedirect.com/science/article/pii/S0021869307006035
Garkusha, G. (2007). Homotopy theory of associative rings. Advances in Mathematics, 213(2), 553
https://doi.org/10.1016/j.aim.2006.12.013, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1648
Garkusha, G. (2007). Systems of diagram categories and $K$-theory. I. St. Petersburg Mathematical Journal, 18(06), 957
https://doi.org/10.1090/S1061-0022-07-00978-8, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1647
Garkusha, G. (2005). Systems of diagram categories and K-theory. II. Mathematische Zeitschrift, 249(3), 641
https://doi.org/10.1007/s00209-004-0726-0, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1646
Garkusha, G. & Prest, M. (2005). Triangulated Categories and the Ziegler Spectrum. Algebras and Representation Theory, 8(4), 499-523.
https://doi.org/10.1007/s10468-005-8147-2, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa50921
Garkusha, G. (2004). Relative Homological Algebra for the Proper Class ωf. Communications in Algebra, 32(10), 4043
https://doi.org/10.1081/AGB-200028236, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1645

Book Chapters

Garkusha, G. & Jones, D. (2019). Derived categories for Grothendieck categories of enriched functors. In Alberto Facchini, Lorna Gregory, Sonia L’Innocente, Marcus Tressl (Ed.), Model Theory of Modules, Algebras and Categories (pp. 23-45). American Mathematical Society
https://doi.org/10.1090/conm/730/14708, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa50768

Conference Contributions

Garkusha, G. & Prest, M. (2008). Torsion classes of finite type and spectra. In K-theory and Noncommutative Geometry. Proceedings of the ICM2006 Satellite Conference held in Valladolid (pp. 393-412). European Mathematical Society Publishing House.
https://doi.org/10.4171/060-1/12, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1058
http://www.ems-ph.org/books/show_abstract.php?proj_nr=89&vol=1&rank=12
Garkusha, G. (n.d.) The Ziegler spectrum for enriched ringoids and schemes. In ECM Satellite Conference "Functor and Tensor Categories, Models and Systems"Springer.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa69532

Supervision

Enriched motives and transfers (current)

PhD

Other supervisor: Dr Nelly Villamizar
Nijenhuis Operators on Trusses and Lie Affgebras (current)

PhD

Other supervisor: Prof Tomasz Brzezinski
Rational enriched motivic spaces (awarded 2023)

PhD

Other supervisor: Dr Edwin Beggs
A GENERAL FRAMEWORK FOR TROPICAL DIFFERENTIAL EQUATIONS (awarded 2022)

PhD

Other supervisor: Prof Jeffrey Giansiracusa

Other supervisor: Prof Tomasz Brzezinski

Taught Modules

MA-112 Introductory Linear Algebra

An introduction to combinatorics, vectors, matrices and abstract vector spaces.
MA-211 Vector Spaces

This module covers the abstract theory of vector spaces and inner product spaces together with the theory of linear transformations.
MA-300 Project

This module provides the opportunity to explore a mathematical topic and learn new subjects without instruction, but under the supervision of a member of staff.
MA-350 Dissertation in the Mathematics of Finance

This module provides the opportunity to explore a topic within the mathematics of finance and independently learn new subjects with the guidance of a member of staff.
MA-360 Dissertation in Mathematics and Computer Science

This module provides the opportunity to explore a topic within Mathematics and Computer Science and independently learn new subjects with the guidance of a member of staff.
MA-M00 Project

This module provides the opportunity to explore a mathematical topic and learn new subjects without instruction, but under the supervision of a member of staff.
MAW112 Cyflwyniad i Algebra Llinol

Cyflwyniad i rifau cymhlyg, fectorau, matricsau a gofodau fector haniaethol.
MAW211 Gofodau Fector

Mae'r modiwl hwn yn ystyried theori haniaethol o ofodau fector a gofodau lluosymiau mewnol ynghyd a'r theori o drawsffurfiadu llinol.
MAW300 Prosiect

This module provides the opportunity to explore a mathematical topic and learn new subjects without instruction, but under the supervision of a member of staff

Professor Grigory Garkusha

Telephone number

Email address

Research Links

About

Areas Of Expertise

Career Highlights

Publications

Research Highlights

All Research

Journal Articles

Book Chapters

Conference Contributions

Supervision

Enriched motives and transfers (current)

Nijenhuis Operators on Trusses and Lie Affgebras (current)

Rational enriched motivic spaces (awarded 2023)

A GENERAL FRAMEWORK FOR TROPICAL DIFFERENTIAL EQUATIONS (awarded 2022)

Taught Modules

MA-112 Introductory Linear Algebra

MA-211 Vector Spaces

MA-300 Project

MA-350 Dissertation in the Mathematics of Finance

MA-360 Dissertation in Mathematics and Computer Science

MA-M00 Project

MAW112 Cyflwyniad i Algebra Llinol

MAW211 Gofodau Fector

MAW300 Prosiect