报告题目：Enlarging the modular torus and trace polynomials for closed curves

报告简介：The modular torus is a once-cusped hyperbolic torus with the maximal order of symmetry. The traces of the simple closed geodesics on the modular torus give the geometric version of the classical Markoff numbers. We study trace polynomials for the closed curves on the enlarged modular torus, with the single variable the enlargement factor. We obtain partial ordering of the polynomials for certain simple closed curves, and positivity of the polynomials for all closed curves. We have observed log-concavity for these polynomials and confirmed log-concavity of the polynomials for the simple closed curves. We also discuss the problem to enlarge an arbitrary complete one-holed hyperbolic torus. This is joint work with Xiangfei Li.

报告人：张影，苏州大学数学科学学院教授、博士生导师、中国数学会常务理事，从事几何拓扑学领域的研究，研究工作涉及双曲曲面上的测地线、曲面特征簇上的几何拓扑、McShane恒等式的推广、四维双曲空间的三角学、Markoff数的性质等，在Adv. in Math., Amer. J. Math., J. Diff. Geom., Math. Res. Letters等国际数学杂志发表学术论文，先后主持国家自然科学基金面上项目四项。

报告时间：2023年3月23日（星期四）下午4:00-5:00

报告地点：扬州大学瘦西湖校区数学科学学院204报告厅

主办单位：扬州大学数学科学学院

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