题目：Toric periods and non-tiling numbers

报告人：潘锦钊，北京雁栖湖应用数学研究院

时间：2020年12月11日（星期五）14:30-15:30

https://meeting.tencent.com/s/6jDAr9D35M9N 

腾讯会议：160 799 281

摘要：This is a joint work with Ye Tian.A positive integer n is called a tiling number if the equilateral triangle can be dissected into nk^2 congruent triangles for some positive integer k. Let n>3 be a square-free integer. Assume n is congruent to 7 mod 24 whose prime factors are congruent to 1 mod 3, or n is congruent to 3 mod 24. Also assume that Q(\sqrt{-n}) has no ideal classes of order 4. Then we show that n is not a tiling number and the 2-part of BSD conjecture hold for corresponding elliptic curves. As a corollary, non-tiling numbers have positive density. In this talk I will introduce its relations to toric periods, the idea of proof and some further topics.