Senior Lecturer
- 51cg
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- Email Address
- irakli.patchkoria@abdn.ac.uk
- Telephone Number
- +44 (0)1224 272749
- Office Address
Department of Mathematics
51cg
Fraser Noble Building
Office 161
- School/Department
- School of Natural and Computing Sciences
- Research
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Research Overview
Algebraic Topology, K-theory, Group theory, Homological Algebra,
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:
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 and :
Funding and Grants
EPSRC Grant:
- 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 1 Results 1 to 25 of 25
Adams spectral sequences and Franke's algebraicity conjecture
American Mathematical Society, Providence, Rhode Island. 140 pagesBooks and Reports: Books- [ONLINE]
Comparison of equivariant cohomological dimensions
Israel Journal of MathematicsContributions to Journals: Articles- [ONLINE] DOI:
On the Farrell–Tate K-theory of Out(𝐹𝑛)
Forum of Mathematics, Sigma, vol. 14, e107Contributions to Journals: Articles- [ONLINE] DOI:
- [OPEN ACCESS]
On the cyclic homology of certain universal differential graded algebras
Homology, Homotopy and Applications, vol. 27, no. 2, pp. 25-51Contributions to Journals: Articles- [ONLINE] DOI:
- [OPEN ACCESS]
Witt vectors with coefficients and TR
Proceedings of the London Mathematical Society, vol. 130, no. 5, e70047Contributions to Journals: Articles- [ONLINE] DOI:
- [OPEN ACCESS]
On the geometric fixed-points of real topological cyclic homology
Journal of the London Mathematical Society, vol. 109, no. 2, e12862Contributions to Journals: Articles- [ONLINE] DOI:
- [OPEN ACCESS]
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On the cyclic homology of certain universal differential graded algebras
Working Papers: Preprint Papers- [ONLINE] DOI:
Proper Equivariant Stable Homotopy Theory
Vol. 288, American Mathematical SocietyBooks and Reports: Books- [ONLINE] DOI:
- [OPEN ACCESS]
Comparison of equivariant cohomological dimensions
Working Papers: Preprint Papers- [ONLINE] DOI:
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Equivariant dimensions of groups with operators
Groups, Geometry and Dynamics, vol. 16, no. 3Contributions to Journals: Articles- [ONLINE]
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- [OPEN ACCESS]
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On the de Rham-Witt complex over perfectoid rings
International Mathematics Research Notices, vol. 2022, no. 18, pp. 13897-13983Contributions to Journals: Articles- [ONLINE] DOI:
- [OPEN ACCESS]
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Witt vectors with coefficients and characteristic polynomials over non-commutative rings
Compositio Mathematica , vol. 158, no. 2, pp. 366-408Contributions to Journals: Articles- [ONLINE] DOI:
- [OPEN ACCESS]
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The spectrum of derived Mackey functors
Transactions of the American Mathematical Society, vol. 375, pp. 4057-4105Contributions to Journals: Articles- [ONLINE] DOI:
- [OPEN ACCESS]
Witt Vectors, Polynomial Maps, and Real Topological Hochschild Homology
Annales Scientifiques de l'École Normale Supérieure, vol. 55, no. 2, pp. 473-535Contributions to Journals: Articles- [ONLINE] DOI:
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Real topological Hochschild homology
Journal of the European Mathematical Society, vol. 23, no. 1, pp. 63-152Contributions to Journals: Articles- [ONLINE] DOI:
- [OPEN ACCESS]
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Rigidity and exotic models for v1-local G-equivariant stable homotopy
Mathematische Zeitschrift, vol. 295, pp. 839-875Contributions to Journals: Articles- [ONLINE] DOI:
- [OPEN ACCESS]
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Equivariant dimensions of groups with operators
Working Papers: Working Papers- [ONLINE]
- [OPEN ACCESS]
Comparing cyclotomic structures on different models for topological Hochschild homology
Journal of Topology, vol. 12, no. 4, pp. 1146-1173Contributions to Journals: Articles- [ONLINE] DOI:
- [OPEN ACCESS]
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On exotic equivalences and a theorem of Franke
Bulletin of the London Mathematical Society, vol. 49, no. 6, pp. 1085-1099Contributions to Journals: Articles- [ONLINE]
Stable finiteness properties of infinite discrete groups
Journal of Topology, vol. 10, no. 4, pp. 1169-1196Contributions to Journals: Articles- [ONLINE] DOI:
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The derived category of complex periodic K-theory localized at an odd prime
Advances in Mathematics, vol. 309, pp. 392-435Contributions to Journals: Articles- [ONLINE]
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Rigidity in equivariant stable homotopy theory
Algebraic & Geometric Topology, vol. 16, no. 4, pp. 2159-2227Contributions to Journals: Articles- [ONLINE]
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Topological Hochschild homology and the cyclic bar construction in symmetric spectra
Proceedings of the American Mathematical Society, vol. 144, pp. 4099-4106Contributions to Journals: Articles- [ONLINE] DOI:
Cubical approach to derived functors
Homology, Homotopy and Applications, vol. 14, no. 1, pp. 133-158Contributions to Journals: Articles- [ONLINE]
On the algebraic classification of module spectra
Algebraic & Geometric Topology, vol. 12, pp. 2329-2388Contributions to Journals: Articles- [ONLINE]