# Forschung

Publikationen:

 Tame covers of curves: p-ranks and fundamental groups PhD thesis. The p-rank of ramified covers of curves Comp. Math. 126(2001), no. 3, 295--322. The p-rank of curves and covers of curves Courbes semi-stables et groupe fondamental en géométrie algébrique (Luminy, 1998), 267--277, Progr. Math., 187, Birkhäuser, Basel, 2000. Reduction of covers and Hurwitz spaces.  Mit Stefan Wewers. Crelle J. 574 (2004), 1--49. Rigidity, Reduction, and Ramification. Mit Rachel Pries. Math. Ann 326 (2003), 803--824. Stable reduction of modular curves. Mit Stefan Wewers. math.AG/0210363. Modular curves and abelian varieties, Progress in Math. 224 (2004), 1--22, Birkhäuser. Reduction of the Hurwitz space of metacyclic covers. Duke Math. J. 121 (2004), 75--111. Ordinary elliptic curves of high rank over $\bar F_p(x)$ with constant j-invariant. Mit Claus Diem und Jasper Scholten. Manuscripta Math. 114 (2004), 487--501 Alternating groups as monodromy groups in positive characteristic. Mit Stefan Wewers. Pacific J. Math. 222 (2005), 185-?? Asymptotically good towers and differential equations. Mit Peter Beelen. Compositio Math. 141 (2005), 1405--1424. The local lifting problem for dihedral groups. Mit Stefan Wewers. Duke Math J. 134 (2006), 412--452. Rational functions with given monodromy on generic curves. Mit Stefan Wewers. problems from the workshop on "automorphisms of curves" (Leiden 2004). Rend. Sem. Math. Univ. Padova. 113 (2005), 129--177. Invariants of ternary quadratic forms. Asterique 312, 2007. Pseudo-elliptic bundles, deformation data, and the reduction of Galois covers Habilitation thesis. Indigenous bundles with nilpotent p-curvature. Mit Stefan Wewers. Internat. Math. Res. Notices (2006), 1-37. Teichmueller curves, triangle groups, and Lyapunov exponents. Mit Martin Moeller. Annals of Math. 172 (2010). The accessory parameter problem in positive characteristic. Preprint Construction of covers in positive characteristic via degeneration. Proc. A.M.S. 137 (2009), 3169--3176. Differential equations associated with nonarithmetic Fuchsian groupsMit Martin Moeller Journal of the London Math. Soc. 81 (2010), 65--90. Deformation data, Belyi maps, and the local lifting problem, mit Stefan Wewers und Leonardo Zapponi. Trans. AMS. 362 (2009), 6645--6659. Some 4-point Hurwitz numbers in positive characteristic, mit Brian Osserman. Trans. AMS.303, 2011, 6685–6711. Covers of the affine line in positive characteristic with prescribed ramification In WIN, Fields Institute Communications 60, 193-200, 2011. Syndrom decoding for Hermite codes with a Sugiyama algorithmmit Sabine Kampf Advances of math Communications 6, 2012, 419-442. Existence of covers with fixed ramification in positive characteristicmit Leonardo Zapponi IJNT 9(2013), 1475-1489, arXiv:1206.1262 Computing L-functions and semistable reduction of superelliptic curves, with Stefan Wewers Glasgow math J. 59,  77-108, 2017.arXiv:1211.4459 Bad reduction of genus-3 curves with complex multiplication, with Jenny Cooley, Kristin Lauter, Elisa Lorenzo Garcia, Michelle Manes, Rachel Newton, Ekin Ozman. in: Women in numbers - Europe, research directions in number theory, AWM series Vol. 2, Bertin  et al (eds), 109-151, Springer,  2015.arXiv:1407.3589 Zeta functions of a class of Artin-Schreier curves with many automorphisms, with Wei Ho, Beth Malmskog, Renate Scheidler, Padma Srinivasan, and Christelle Vincent. in: Directions in Number Theory. Proceedings of the 2014 WIN Workshop. AWM series Vol. 3, Eischen et al (eds), 87-124, Springer, 2016.arXiv:1410.7031 The functional equation for L-functions of hyperelliptic curves, with Michel Börner and Stefan Wewers. To appear in: Experimental Math.arXiv:1504.00508 Picard curves with small conductor, with Michel Börner and Stefan Wewers. arXiv:1701.01986 Improved power decoding of one-point Hermitian codes, with Sven Puchinger and Johan Rosenkilde né Nielsen. arXiv:1703.07982 Dynamical Belyi Maps, with Jacqueline Anderson, Özlem Ejder, Neslihan Girgin, Valentijn Karemakers, and Michelle Manes. arXiv:1703.08563