报告地点：西南大学25教学楼18楼学术报告厅
报 告 人：蔺友江（重庆工商大学）
报告时间：2020年11月10日上午9:30-10:20
报告题目：Mahler猜想
报告摘要：
对二维的Mahler猜想给出了一个新的证明。我们首先证明了任意的中心对称的多边形能够通过仿射变换为内接于单位圆并且有连续三个顶点在圆周上的多边形，然后我们证明了当中间的顶点在圆周上运动时，对应的Mahler体积是一个凹函数，当中间点运动到与相邻的点重合时，我们得到一个边数变少了的、Mahler体积变小了的多边形。重复这样的过程，最终证明了平行四边形具有最小的Mahler体积。
报 告 人：李明 （重庆理工大学）
报告时间：2020年11月10日上午10:30-11:20
报告题目：Recent progress towards the Unicorn problem
报告摘要：
In this talk, we will give a short survey on the Unicorn problem in the Finsler geometry. We introduce some recent solutions of this problem under extra conditions. Our strategy towards the unicorn problem is establishing equivalence theorems by affine differential geometry method and using nonlinear parallel transports. Partial results are joint work with Huitao Feng and Yuhua Han.
报 告 人：刘克峰（加州洛杉矶大学、重庆理工大学）
报告时间：2020年11月10日下午15:00-15:50
报告题目：Moduli spaces as ball quotients
报告摘要：
I will present a Hodge theoretic criterion for the moduli spaces of certain polarized manifolds to be ball quotients.
报 告 人：郑方阳（美国俄亥俄州立大学、重庆师范大学）
报告时间：2020年11月10日下午16:00-16:50
报告题目：The Kahler-Ricci flow preserves negative anti-bisectional curvature
报告摘要：
The anti-bisectional curvature for tube-domains is related to the MTW tensor in optimal transport. In this joint work with Gabriel Khan of Iowa State University we prove that non-positive anti-bisectional curvature is preserved under normalized Kahler-Ricci flow, and in complex dimension two, non-negative orthogonal anti-bisectional curvature is also preserved under the flow. We provide several applications of these results, both in complex geometry as well as optimal transport.
报 告 人：程新跃（重庆师范大学）
报告时间：2020年11月10日下午17:00-17:50
报告题目：Improved Bochner inequality and its important applications on Finsler manifolds
报告摘要：
In this talk, we will establish some important inequalities under a lower weighted Ricci curvature bound by using improved Bochner inequality and its integrated form. Firstly, we obtain a sharp Poincare-Lichnerowicz inequality. Then we give a new proof for logarithmic Sobolev inequality. Finally, we obtain an estimate of the volume of geodesic balls and a relative volume comparison of Bishop-Gromov type on Finsler manifolds.
