Senior Lecturer
- About
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- Email Address
- irakli.patchkoria@abdn.ac.uk
- Telephone Number
- +44 (0)1224 272749
- Office Address
Department of Mathematics
University of Aberdeen
Fraser Noble Building
Office 161
- School/Department
- School of Natural and Computing Sciences
Biography
I am a keen tennis player. Here is my British Tennis profile with the recent statistics and results.
- Research
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Current Research
Invariants of infinite groups coming from stable homotopy theory, Farrell-Tate cohomology, Morava K-theory of classifying spaces, tt-geometry in (proper) equivariant stable homotopy theory.
Here are some talks I have given recently:
On the K(n)-local duality for infinite groups
Chromatic congruences and Bernoulli numbers
Morava K-theory of infinite groups and Euler characteristic
Classification of module spectra and Franke's algebraicity conjecture
Knowledge Exchange
I was previously responsible for public outreach of our Department. Here is a popular science talk about my research area Topology organised by Aberdeen Science Centre and Maths Week Scotland:
Funding and Grants
EPSRC Grant: Classifying spaces, proper actions and stable homotopy theory
- Teaching
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Teaching Responsibilities
Spring term 2026: MX3535 Analysis IV, SMSTC graduate course: Stable Homotopy Theory, Exercises on MA1510 Combinatorics
Winter term 2025: MX3036 Metric and Topological spaces, SMSTC graduate course: Homotopy Theory
Spring term 2025: MX3535 Analysis IV
Winter term 2024: MX3036 Metric and Topological spaces
Spring term 2024: MX3536 Differential Equations
Winter term 2023: MX3036 Metric and Topological spaces
Spring term 2023: MA1510 Combinatorics, MX3536 Differential Equations
Winter term 2022: MX3036 Metric and Topological spaces
Spring term 2022: MA1510 Combinatorics, MX3536 Differential Equations
Winter term 2021: MX3036 Metric and Topological spaces
Spring term 2021: MA1510 Combinatorics, MX3536 Differential Equations
Winter term 2020: MX3036 Metric and Topological spaces, Exercises for MA2010 Probability
Spring term 2020: MA1510 Combinatorics
Winter term 2019: MX3036 Metric and Topological spaces
Spring term 2019: MA1510 Combinatorics
- Publications
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Page 1 of 3 Results 1 to 10 of 25
On the Farrell--Tate $K$-theory of $\Out(F_n)$
Forum of Mathematics, SigmaContributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.1017/fms.2026.10239
Comparison of equivariant cohomological dimensions
Israel Journal of MathematicsContributions to Journals: Articles- [ONLINE] DOI: https://doi.org/10.1007/s11856-026-2910-y
On the cyclic homology of certain universal differential graded algebras
Homology, Homotopy and Applications, vol. 27, no. 2, pp. 25-51Contributions to Journals: ArticlesAdams spectral sequences and Franke's algebraicity conjecture
American Mathematical SocietyBooks and Reports: BooksWitt vectors with coefficients and TR
Proceedings of the London Mathematical Society, vol. 130, no. 5, e70047Contributions to Journals: ArticlesOn the geometric fixed-points of real topological cyclic homology
Journal of the London Mathematical Society, vol. 109, no. 2, e12862Contributions to Journals: ArticlesOn the cyclic homology of certain universal differential graded algebras
Working Papers: Preprint Papers- [ONLINE] DOI: https://doi.org/10.48550/arXiv.2308.12369
Proper Equivariant Stable Homotopy Theory
Vol. 288, American Mathematical SocietyBooks and Reports: Books- [ONLINE] DOI: https://doi.org/10.1090/MEMO/1432
- [OPEN ACCESS] http://aura.abdn.ac.uk/bitstreams/303b371c-a65c-45d5-930f-8bd63120e775/download
Comparison of equivariant cohomological dimensions
Working Papers: Preprint Papers- [ONLINE] DOI: https://doi.org/10.48550/arXiv.2302.08574
- [ONLINE] BIMSA- Advances in Homotopy Theory IV Workshop
Equivariant dimensions of groups with operators
Groups, Geometry and Dynamics, vol. 16, no. 3Contributions to Journals: Articles