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Alex Torzewski

About Me

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I am a 4th year PhD student in number theory under the supervision of Alex Bartel. My interests include arithmetic geometry, representation theory and Galois representations.

p-divisible Groups Study Group

Summer 2017: Chris Birkbeck and I are organising the number theory study group on p-divisible groups. The webpage and schedule is available here.

Current Research Projects

  • I have been working on some representation theoretic results which give a list of computable invariants which determine the isomorphism class of an arbitrary \mathbb{Z}_{(p)}[G]-lattices for certain G. This requires studying regulator constants as invariants of lattices and also builds on existing work of Yaklovlev. A preprint is available here(PDF Document).
  • In some cases the above results can be applied relatively easily to lattices arising in number theory. In work to appear in my thesis I did this for unit groups of rings of integers and am hoping to look at Mordell-Weil groups of abelian varieties in the near future. This makes use of existing results of Bartel, Dokchitser-Dokchitser and Burns-Macias Castillo-Wuthrich.
  • More recently, I have been looking at lifting decompositions of various cohomology theories to motives in the setting of universal abelian schemes over Shimura varieties. A preliminary version of this is available here.

Publications and Preprints

  • Regulator constants of integral representations of finite groups, Alex Torzewski, 41 pages, preprint(PDF Document).
  • Functoriality of Ancona lifting, Alex Torzewski, 19 pages, preliminary version.

Selected Talks

  • Exeter - Pure Mathematics Seminar - Feb. 2018
  • Glasgow - Algebra Seminar - Nov. 2017
  • Journées Arithmétiques - Caen - July 2017
  • 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

Contact

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Past

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Previously, I was in

  • 2013-2014 - Cambridge - Part III (Distinction)
  • 2010-2013 - Warwick - BSc (1st (Hons))

For more details, see my CV(PDF Document).