题 目：chen-yang’s volume conjecture for twist knots with rational dehn surgeries
主讲人：葛化彬 教授
单 位：中国人民大学
时 间：2024年8月16日 16:30
地 点：学院二楼会议室
摘 要：the volume conjecture of kashaev-murakami-murakami predicts a precise relation between the asymptotics of the n-colored jones polynomials of a knot l in s^3 and the hyperbolic volume of its complement. several years ago, chen-yang proposed a new “volume conjecture” for hyperbolic 3-manifolds, which gives a deep relation between the quantum su(2) invariant (the reshetikhin–turaev invariant), the hyperbolic volume and chern-simons invariant of the manifolds. their conjecture was later refined to include the adjoint twisted reidemeister torsion in the asymptotic expansion of the invariants. recently, chen-yang’s volume conjectures have been proved for many examples by various groups.
in this report, we will show our progress on chen-yang’s volume conjecture for hyperbolic 3-manifolds obtained by rational surgeries along the twist knot. to be precise, let s be the twist number of the twist knot k_s, and let (p,q) be the coefficients of the dehn-filling. there exists a constant m such that when the absolute values of p, q, and s are greater than m, the chen-yang’s volume conjecture holds true. this development provides important clues for understanding the general validity of the chen-yang’s volume conjecture. this is joint work with yunpeng meng, chuwen wang and yuxuan yang.
简 介：葛化彬，北京大学数学科学学院博士、北京国际数学研究中心博士后，现为中国人民大学数学学院教授，博士生导师。主要研究方向为几何拓扑，推广了柯西刚性定理和thurston圆堆积理论，部分解决thurston的“几何理想剖分”猜想、完全解决cheeger-tian、林芳华的正则性猜想，相关论文分别发表在geom. topol., geom. funct. anal., amer. j. math., adv. math.等著名数学期刊。