报告一
题目：On the algebraicity of Thue-Morse and period-doubling continued fractions
摘要：We put forward several general conjectures concerning the algebraicity or transcendence of continued fractions and Stieltjes continued fractions defined by the Thue-Morse and period-doubling sequences in characteristic $2$. We present our Guess'n'Prove method, in which we exploit the structure of automata, for proving some of our conjectures in the general case.
报告人：胡怡宁博士（2011毕业于中国科技大学物理系，同年到巴黎六大，2017年获巴黎六大数学博士，现在华中科技大学数学学院工作。工作领域主要集中在有限自动机的数学理论、组合和数论）。
时间：2020年12月2日（星期三）14:00 --15:00
地点：理科楼数学系A-404
邀请人：文志英
报告二
题目: Big images of Galois representations associated to Hida families
摘要: We study the images of Galois representations associated to Hida families. In 2015, Hida and Jacyln Lang have proved that the image of Ga-lois representation associated to a non-CM family of ordinary classical modular forms contains a congruence subgroup of Iwasawa algebra of weights and also of a nite extension of this algebra, which is called the self-twist ring. Hida and Jacques Tilouine have generalized the results about the existence of nontrivial congruence subgroups contained in the image of the Galois representation to the case of a Hida family of "general" Siegel modular forms of genus 2. Under some technical hypothesis, we have proved the same result for general reductive groups, when the associated Galois representation exists. In this talk, I will explain the results and show the main steps of the proof. This is a joint work with Jacques Tilouine.
报告人：陈欢博士（清华大学数学系2007级本科，2010年考入巴黎高师，2017年于巴黎13大获数学博士，现在华中科技大数学学院工作。工作领域集中在代数几何和表示论）。
时间：2020年12月2日（星期三）15:00 --16:00
地点：理科楼数学系A-404
邀请人：瞿燕辉
