# Alex Torzewski

I am a 3rd PhD student in number theory under the supervision of Alex Bartel. My interests include arithmetic geometry, representation theory and Galois representations.

### Current Research Projects

• I have some representation theoretic results which give a list of computable invariants which determine the isomorphism class of an arbitrary $\mathbb{Z}_{(p)}[G]$-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.

### Recent talks

• 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

### Past

Previously, I was in

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

For more details, see my CV.