Analysis

Mathematical Analysis initially developed from arguments needed in the infinitesimal study of geometrical objects and physical motions. After the great success of the heroic age of differential and integral calculus, it was realized that, by focusing attention not on a single function in isolation, but rather on an appropriate class of functions, one could obtain a better understanding and an expansion of the classical theories. Thus, Functional Analysis was born about a century ago, with great benefits to several areas of modern mathematics and many remarkable applications to the natural sciences.

The faculty listed by our department as analysts are actually all functional analysts. They like to work in infinite dimensional spaces (of functions, operators, representations, dynamical systems). Among their main objectives are the solution of equations, minimization of functionals, and classification and study of algebras of operators. The numerous applications vary from classical problems of continuum mechanics and information theory to image analysis, knot theory and quantum computing.

Several research seminars devoted to such subjects are organized all year around. They are attended by many of our graduate students and attract many distinguished visitors.

RESEARCH FIELDS
Algebra
Analysis
Applied Math
Geometry
Number Theory
PDE
Topology



Faculty


Charles A. Akemann

PhD:
University of California at Berkeley, 1966
Interests: Functional Analysis
Office
: Room 6706
akemann-A.T-math.ucsb.edu
  Gustavo Ponce

PhD:
The Courant Institute, 1982
Interests: Non-linear PDE's
Office
: Room 6505
ponce-A.T-math.ucsb.edu
         
Mihai Putinar

PhD:
University of Bucharest, 1984
Interests: Complex analysis, operator theory
Office
: Room 6722
mputinar-A.T-math.ucsb.edu
     
         



Visiting Faculty


Julie Rowlett

PhD:
Stanford University, 2006
Interests: Geometric Analysis
Office
: Room 6504
rowlett-A.T-math.ucsb.edu
     
         
Note: Please replace -A.T- with @ in the email addresses above.