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 
Areas of Research 

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 Lie Groups  
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  
Dennis Snow  Complex Geometry  
Gabor Szekelyhidi  Complex and Partial Differential Geometry  
Current Visiting Faculty 

Greg Edwards  Geometric Analysis, Complex Geometry  
Harrison Pugh  
Priyanka Rajan  
Behrouz Taji  Complex Geometry and Algebraic Geometry  
Emeritus Faculty 

Brian B. Smyth  Differential Geometry  
Nancy Stanton  Complex Geometry, Several Complex Variables and Partial Differential Equations  
Frederico J. Xavier  Differential Geometry and Geometric Analysis  
Activities 

Felix Klein Seminar  
PDE, Complex Analysis and Differential Geometry Seminar 