EPSRC Reference: 
EP/X038424/1 
Title: 
Classifying spaces, proper actions and stable homotopy theory 
Principal Investigator: 
Patchkoria, Dr I 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematical Sciences 
Organisation: 
University of Aberdeen 
Scheme: 
New Investigator Award 
Starts: 
01 July 2023 
Ends: 
30 June 2026 
Value (£): 
298,276

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
Primary goal of this project is to compute invariants of discrete groups coming from stable homotopy theory. Secondary goal is to explore connections of these computations with number theory.
The project deals with invariants of infinite discrete groups coming from stable homotopy theory, such as Morava Ktheories and Morava Etheories. These invariants generalise the classical Euler characteristic and topological Ktheory. For finite groups they are wellknown and studied by HopkinsKuhnRavenel. For Ktheory these invariants for infinite groups were computed by Lück and coathors. We plan to generalise both these computations.
For Morava Ktheories of infinite groups we expect to obtain a formula for the Morava Ktheoretic Euler characteristic using centralisers. For Morava Etheory we plan to generalise the HopkinsKuhnRavenel character theory from finite to infinite groups.
Finally, we will apply these results to concrete groups. Concrete formulas coming out of these should be of number theoretic nature. Some of them will contain values of Dedekind and Riemann zeta functions.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


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Project URL: 

Further Information: 

Organisation Website: 
http://www.abdn.ac.uk 