Research - Current Projects

Quotient singularities and semistable reduction

(DFG priority program SPP1489)

• Computing L-functions and semistable reduction of superelliptic curves, with Irene Bouw, preprint, 2012. To appear in Glasgow Math. J.
• The functional equation for L-functions of hyperelliptic curves, with Irene Bouw und Michel Börner, preprint, 2015, to appear in Experimental Mathematics
• Another proof of the semistable reduction theorem, with Kai Arzdorf, preprint, 2012
• Semistable reduction of curves and computation of bad Euler factors of L-functions, with Irene Bouw, notes for a minicourse at ICERM

The lifting problem

• Cyclic extensions and the local lifting problem, with Andrew Obus. Annals of Math. 180 (2014), no. 1, 233-284
  
• Fiercely ramified cyclic extensions of p-adic fields with imperfect residue field. Manuscripta mathematica 143 (2014), no. 3-4, 445-472
• Wild ramification kinks, with Andrew Obus,  Research in the Mathematical Sciences, (2016), 3:21
  

The nonabelian Chabauty method

• Explicit Chabauty-Kim theory for the thrice punctured line in depth two, with Ishai Dan-Cohen, Proc. London Math. Society 110 (2015), no. 1, 133-171
• Mixed Tate motives and the unit equation, with Ishai Dan-Cohen, preprint, 2013, to appear in Int. Math. Research Notices (Sage code: localanalytic.sage, Lip.sage)
• A nonabelian conjecture of Birch and Swinnerton-Dyer type for hyperbolic curves, with Minhyong Kim, Jennifer Balakrishnan and Ishai Dan-Cohen, preprint, 2012               (some Sage code related to this paper)