Workshop on Geometry and Physics
Workshop on Geometry and Physics will be held on Jan 3- 4, 2020, in east campus of USTC (University of Science and Technology of China). This workshop is supported by the institute of Geometry and Physics (IGP).
Organizing Committee
Bing Wang (USTC)
Bin Xu (USTC)
About IGP
The mission of the Institute of Geometry and Physics (IGP) is to advance the understanding of geometry and its interface with theoretical physics, to nurture the next generation of original mathematicians and ultimately to build a top notch institution for the subject area. We thus endeavor to provide a quiet, comfortable and inspiring environment, where talented researchers in geometry and related fields from all over the world are invited to visit, be it short term or long, to work and to thrive; and where academic freedom, diligence and originality are promoted and valued. The center provides strong funding for our faculty research including support for doctoral students and postdoctoral researchers.
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Shibing Chen (USTC)
Xuezhang Chen (Nanjing University)
Qi Ding (Fudan University)
Song Shao (USTC)
Guoyi Xu (Tsinghua University)
Di Yang (USTC)
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Schedule
Jan 3, 2020 Registration
Jan 4, 2020 Conference Schedule (Room 1418, management and research building)
| Time | Speaker | Title | Abstract |
| 8:40-8:50 | Opening Remarks | ||
| 8:50-9:40 | Qi Ding | Liouville Theorems and Hessian Estimates for Special Lagrangian Equations |
We will first review history on the classification of entire special Lagrangian graphs in Euclidean space, then talk about our Liouville type theorem for solutions to special Lagrangian equations under a general 'convexity' condition. Moreover, we will discuss interior Hessian estimates in terms of the gradient of the solutions. |
| 9:40-9:55 | Tea Break | ||
| 9:55-10:45 | Shibing Chen | $L_p$-Brunn-MInkowski inequality for $p<1.$ |
The Brunn-Minkowski inequality is one of the most important inequalities in geometry. Many efforts are devoted to strengthen the inequality. In particular, one of the most attractive extension of the classical BM inequality is the so called $L_p$-BM inequality for $0<p<1.$ This family of inequalities become stronger when $p$ decreases. In this talk I will discuss some progress towarding this direction. This is based on a joint work with Yong Huang, Qirui Li and Jiakun Liu. |
| 10:55-11:45 | Guoyi Xu | The growth rate of harmonic functions |
Since Cheng-Yau proved the gradient estimate of harmonic functions in 1975, their method played important role in geometric analysis. Yau proposed the study of harmonic functions with polynomial growth in 1980’s. In this talk, we will firstly review the history of harmonic functions with restricted growth rate, following Li-Tam, Colding-Minicozzi and others. Especially, we will reveal relationship between the growth rate estimate and the existence problem, and present our results in this direction. Some open questions will be posed in `accessible disguise’, basic PDE and Riemannian geometry is enough to understand most part of the talk |
| 14:30-15:20 | Xuezhang Chen | Conformal curvature flows on compact manifolds |
Using various negative gradient flows of scalar curvature problem on the sphere/Kazan-Warner problem as models, we intend to show basic techniques in proving the asymptotic convergence of these flows through ruling out the occurrence of bubbles in the blow up analysis. Such flows can be naturally applied to compact manifolds in order to handle the boundary Yamabe problems, and even Han-Li conjecture. We will mention the scalar curvature and mean curvature flows on compact manifolds, including my finished projects and ongoing ones. |
| 15:20-15:35 | Tea Break | ||
| 15:35-16:25 | Song Shao | Nilpotent systems in topological and ergodic dynamics |
In this talk we will discuss nilsystems both in ergodic theory and topological dynamics, and its connections with combinatorial number theory. This talk is based on the work with Wen Huang and Xiangdong Ye etc. |
| 16:35-17:25 | Di Yang | On Hodge-GUE correspondence |
The Hodge-GUE correspondence gives an explicit relationship between certain special cubic Hodge integrals on the Deligne—Mumford moduli space and the enumeration of ribbon graphs. We prove this correspondence by deriving the Virasoro constraints for their generating series. I will then explain some recent progress on its generalization. The talk is based on a series of joint works with Boris Dubrovin, Si-Qi Liu, Youjin Zhang and Chunhui Zhou. |
Accommodation: All invited speakers will be arranged to live at Guest House (USTC).
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Contact Us
Xin Wang: xinw09@ustc.edu.cn
University of Science and Technology of China
96 Jinzhai Road, Hefei, 230026, Anhui, P.R. China