# Alex Torzewski

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.
• 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.
• 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

### Past

Previously, I was in

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

For more details, see my CV.