Analysis and Partial Differential Equations
Analysis is broadly concerned with problems and techniques that involve estimation, approximation and limiting processes. Many specific areas of math fall entirely or largely under the analysis umbrella. These include riemannian geometry, complex analysis, dynamical systems, probability and many aspects of mathematical physics. Differential equations, which aims to understand functions from relationships among their derivatives, plays a particularly important role in most of these areas and as a subfield of analysis in its own right.
Faculty 

Jeffrey Diller  Complex Analysis and Geometry, Dynamical Systems 
Karsten Grove  Differential Geometry and Topology 
Matthew Gursky  Differential Geometry and Partial Differential Equations 
Brian C. Hall  Mathematical Physics and Complex Analysis 
Qing Han  Partial Differential Equations and Differential Geometry 
Richard K. Hind  Differential Geometry 
Gerard Misiolek  Global Analysis, Partial Differential Equations 
Liviu Nicolaescu  Topology and Probability 
Marco Radeschi  Differential Geometry 
MeiChi Shaw  Complex Analysis and Partial Differential Geometry 
Brian B. Smyth  Emeritus  
Dennis Snow  Complex Geometry 
Nancy Stanton  Partial Differential Equations and Complex Geometry 
Gabor Szekelyhidi  Complex and Partial Differential Geometry 
Frederico J. Xavier  Emeritus  
Current Visiting Faculty 

Greg Edwards  
Harrison Pugh  
Priyanka Rajan  
Behrouz Taji  
Activities 

Felix Klein Seminar  
PDE, Complex Analysis and Differential Geometry Seminar 