报告题目：A q-microscope for supercongruences

摘要：By examining asymptotic behavior of certain infinite basic (q-) hypergeometric sums at roots of unity (that is, at a `q-microscopic' level) we prove polynomial congruences for their truncations. The latter reduce to non-trivial (super)congruences for truncated ordinary hypergeometric sums, which have been observed numerically and proven rarely. A typical example includes derivation, from a q-analogue ofRamanujan's formula

sum_{n=0}^inftyfrac{binom{4n}{2n}{binom{2n}{n}}^2}{2^{8n}3^{2n}},(8n+1)=frac{2sqrt{3}}{pi}, of the two supercongruences S(p-1)equivpbiggl(frac{-3}pbiggr)pmod{p^3} quadtext{and}quad SBigl(frac{p-1}2Bigr) equivpbiggl(frac{-3}pbiggr)pmod{p^3}, valid for all primesp>3, where S(N) denotes the truncation of the infinite sum at the N-th place and bigl(frac{-3}{cdot}bigr) stands for the quadratic character modulo~3.

报告时间：2018年6月1号上午10：30--11：30

报告地点：002cc白菜资讯三楼专家接待室

报告人简介：郭军伟教授现任淮阴师范学院教授、博士生导师。2004年毕业于南开大学组合数学中心,获得博士学位,2004-2006年在法国里昂第一大学Camille Jordan研究所攻读博士后。2006年起在华东师范大学数学系任教，后调入淮阴师范学院。是中国组合数学界杰出的后起之秀，目前已发表SCI论文六十多篇，多次主持国家自然科学基金项目。