Current Research Projects
- I have some representation theoretic results which give a list of computable invariants which determine the isomorphism class of an arbitrary -lattices when G has cyclic Sylow p-subgroup. My results combine with existing work of Yakovlev with regulator constants. A report on this work is available here.
- In some cases the above results can be applied relatively easily to lattices arising in number theory from unit groups of rings of integers or Mordell-Weil groups of abelian varieties. Hopefully some details of this will appear soon. This uses existing results of Bartel, Dokchitser-Dokchitser and Burns-Macias Castillo-Wuthrich.
- More recently, I have been thinking about lifting decompositions of various cohomology theories to motives in the setting of universal abelian schemes over Shimura varieties.
Publications and Preprints
- Regulator constants of integral representations of finite groups, Alex Torzewski, 41 pages, preprint.
- Nottingham - Number Theory Seminar - Mar. 2017
- Cambridge - Number Theory Seminar - Feb. 2017
- Oxford - Junior Number Theory - Jan. 2017
- Bristol - Linfoot Seminar - Dec. 2016
- Hopf Galois Theory and Galois Module Structures Conference - Exeter - Jun. 2015
Previously, I was in
- 2013-2014 - Cambridge - Part III (Distinction)
- 2010-2013 - Warwick - BSc (1st (Hons))
For more details, see my CV.