Invited by Prof.Heping Zhang and Prof. Shoujun Xu of the School of Mathematics and Statistics,Dr.Qianqian Yangfrom University of Science and Technology of China will visit our school and give a series of lectures from December 12th to December 13th in 2019.

Title:The integrability of integral lattices generated by vectors of norm 3

Time：17:00p.m.,December13th,2019

Location：Room911,QiyunBuilding

Abstract:In this talk I will give an overview of the classification of the Q-polynomial distance-regular graphs. Also I will present some recent results.Given a positive integer s, an integral lattice is s-integrable if it can be embedded in the lattice for $\frac{1}{\sqrt{s}^{Z^t}}$ some $l$. Assume that Λ is an integral lattice.

• If Λ is generated by vectors of norm 1, then it is a standard lattice. Thus it is s-integrable for all s.

• If Λ is generated by vectors of norm 2, Witt in 1941 showed that it is the direct sum of some root lattices. As each root lattice is s-integrable for all s ≥ 2, which is proved by Conway and Sloane in 1989, this implies that Λ is s-integrable for all s ≥ 2.

In this talk, I will show that if Λ is generated by vectors of norm 3 which satisfy

certain conditions, then Λ is also s-integrable for all s ≥ 2.

Curriculum Vitae

Qianqian Yang, from September 2009 to June 2013, studied in the base class of the School of Mathematics and Statistics, Lanzhou University. From September 2013 to November 2019,She studied continuously at the School of Mathematical Sciences, University of Science and Technology of China, her tutorisProfessor Koolen. Beginning in December 2019,she will be a postdoc in the School of Mathematical Sciences, University of Science and Technology of China. During Dr. Yang Qianqian's PhD, the research theme was "graphs with a minimum eigenvalue not less than -3". A total of 7 papers have been published on this topic in international journals, including one on Advances in Mathematics.

Welcome to attend!

Provincial Key Laboratory of Applied Mathematics and Complex Systems,

Gansu Province

School of mathematics and statistics

CuiyingHonors College

December 11th, 2019