### KIAS Number Theory Seminar

 Upcoming seminars Past seminars February 20 (Thu), 2020, 16:00--17:00, Room 1424 Title: On Galois covers of the projective line and their specializations Speaker: Francois Legrand (TU Dresden) Abstract: Studying Galois covers of the projective line and their specializations is a central topic in inverse Galois theory, due to their connection with the inverse Galois problem. In this talk, we shall present two applications to diophantine geometry and the theory of modular forms. Firstly, we shall explain how deriving many curves over $\mathbb{Q}$ failing the Hasse principle, under the abc-conjecture. Secondly, we shall construct infinitely many non-liftable Hecke eigenforms of weight one over $\overline{\mathbb{F}_p}$ with pairwise non-isomorphic projective Galois representations, for $p \in \{3,5,7,11\}$. This talk is based on joint works with Joachim K\"onig, and with Sara Arias-de-Reyna and Gabor Wiese. Please send one of the organizers an email if you are interested in giving a talk. If you want to receive regular email announcement, please send an email with your name/affiliation, in title of "subscribe", to the organizer. The first number theory seminar started March 10th, 2005 and it became a regular seminar since then. For more information on the early history of the number theory seminar, see the article (by Soon-Yi Kang in KIAS News Letter, Fall 2005) and the following archive files.    Archive: 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2005 | Number Theory Group at KIAS Choi, Youn-Seo Choi, Junhwa (jhchoi.math@gmail.com) Haan, Jae-ho Kim, Chan-Ho Lee, Chulhee Yu, Myungjun (mjyu.math@gmail.com)