Conference: Workshop on Partial Differential Equations in Geometry and 
Physics

Time: March 9-13, 2015

Venue: Tsinghua Sanya International Mathematics Forum (TSIMF)
http://msc.tsinghua.edu.cn/sanya/Default.aspx

Organizers:
Jurgen Jost， Max Planck Institute for Mathematics in the Sciences, 
Germany 
Qun Chen ， Wuhan University

Synopsis:
PDEs are among the most powerful tools in both geometry and physics. 
Fundamental geo- metric problems like the Poincare conjecture have been 
solved with PDEs, and the basic field equations of physics, like those of 
Maxwell or Einstein, are expressed in terms of PDEs. Usually, those PDEs 
involve some singularities. For instance, the boundary or the underlying 
space could be singular. Or the data or the PDE itself could have 
singularities. Most importantly, how- ever, solutions of nonlinear PDEs can 
by themselves develop singularities. Understanding these singularities then 
is crucial for the underlying geometric or physical problem.
In recent years, substantial advances have been made in understanding 
various PDEs and their singularities in problems from geometry and 
physics. We want to bring together some of the contributors from China 
and abroad to take account of what has been achieved, what methods and 
techniques are available, and most importantly, to set the stage for future 
advances. We therefore intentionally bring people with different knowledge 
and different backgrounds together, ranging from abstract and nonlinear 
analysis to geometry and mathematical physics, in order to explore new 
connections between analysis, geometry, and physics, in particular 
quantum field theory and related fields.
Many (but not all) of the PDEs that are important in geometry and physics 
arise from variation- al problems. One can therefore try to solve them 
either by minimizing or saddle point methods or by studying the 
corresponding heat flow. Comparing these approaches often yields 
additional insight.
More specifically, we shall address key topics of geometric analysis, like 
minimal hypersurfaces and submanifolds, harmonic maps or geometric 
optimization, study variational problems motivated by QFT, and also 
discuss specific types of singular behavior at the boundary or in the 
interior. A problem session towards the end of the workshop will not only 
take stock of the known problems in the field, but also try to identify new 
problems that emerge from the discussions during the workshop. We 
believe that the scheme of our workshop will be particularly beneficial for 
young mathematicians that want to get an overview of the state of the art, 
concerning both methods and topics, and learn about new research 
directions and challenging open problems.
Much of this will build upon successful cooperation between 
mathematicians from China and Germany, but it is important for us to also 
bring the different groups together and to involve some talented graduate 
students and postdocs. In particular, it is an explicit aim of the workshop to 
stimulate new collaborations.
See the website for more detail：
http://msc.tsinghua.edu.cn/sanya/2015/WPDEGP2015/synopsis_and_organi
zers.aspx


 

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