Florida analysis

Analysis at UF

The analysis group at UF is involved in contemporary research in a broad range of mathematics with important inter and intra-discipline connections. Below is a brief synopsis of the activities. For more information, follow the links to the left to visit individual faculty and the analysis seminar homepages.

Mathematical Physics

Quantum theory, with an emphasis on algebraic quantum field theory. This involves using operator algebra theory, among other mathematical tools, to address conceptual and mathematical problems in quantum field theory, which itself seeks to describe the fundamental constituents of matter and their laws of interaction.

Complex Analysis and Number Theory

Complex analysis and its applications to special functions including Jacobi elliptic functions, differential equations and number theory.

Measure Theory, Commutative and Noncommutative

Infinite dimensional vector-valued integration and stochastic analysis, including stochastic integration which is the basis for much of financial mathematics. One setting for noncommutative measure theory is within a weak-star closed subalgebra of a C-star algebra, while another setting is provided by a (normal) state on a W-star algebra.

Partial Differential Equations and Image Processing

Harmonic maps on manifolds; theories and methods of non-linear PDEs. The application of PDEs to image processing, particularly medical such as fMRI. On campus collaborating units include the Brain Institute, the medical school, and computer science.

Sympletic Geometry

Representations of the Weyl and Clifford algebras. Symplectic geometry has its origins in the Hamiltonian formulation of classical mechanics. A symplectic manifold is a differentiable manifolds equipped with a closed, nondegenerate 2-form.

Operator Theory and Operator Algebras

Single and several variable operator theory, particularly with connections to analytic functions including interpolation theorems of Pick type which themselves generalize the Schwartz Lemma; composition operators; and index theory. Non-self adjoint operator algebras, and operator systems and spaces. Self-adjoint operator algebras.

Noncommutative semi-algebraic geometry

A large class of engineering problem take the form system of dimensionless matrix inequalities; i.e., polynomial inequalities where the variables are matrices and the only restriction on the sizes of the matrices involved is that the formulas make sense. A theory of noncommutative semi-algebraic parallel to the classical commutative theory is rapidly developing to understand matrix inequalities. That there are very few convex noncommutative semi-algebraic sets is one of the most mathematically striking and practically important differences that has emerged to date.

Probability, Stochastic Analysis, and Financial Mathematics

Martingales, Probabilistic potential theory, numerical stochastic integrations. Stochastic integration and financial mathematics. Applications of probability to image processing.

Faculty

James Brooks
Yunmei Chen
Michael Jury
Scott McCullough
Scott McKinley
Murali Rao
Paul Robinson
Li Shen
Stephen Summers
Lei Zhang

Students

Adam Broschinski
Chen-Xi Chen
Fuhua Chen
Mat Gluck
Xiangqi Li
Meng Liu
Dung Phan
Benjamin Russo
Eric Stetler
Larie Ward
Hao Zhang
Wei Zhang
Jiajie Zhu

 

Former Students

Jung-ha An
Sriram Balasubramanian
Miriam Salome Castillo Gil
Fuhua Chen
Pengwen Chen
Robert Clancey
Andrew Fisher
Martin Florig
Jan Gregus
Weihong Guo
Gudbjort Gylfadottir
Feng Huang
Jin-Seop Lee
Stacey Levine
Kristen Luery
Yuyuan Ouyang
Ilia Posirca
Trevor Richards
Joel Rosenfeld
Ryan Sankarpersad
Anqi Shao
Jiangli Shi
Robert Strich
Pengyi Sun
Sheshadri Thiruvenkadam
Anderew T. Tomerlin
Christopher Tweddle
Richard K. White
Thomas Wunderli
Xiaojing Ye
Qingguo Zeng
Haili Zhang

Seminars

Imaging Seminar

Analysis Seminar