Research in Analysis

Mathematical Analysis Group

Name Rank Office Extension
Guihua Gong Full Professor NCN II C-115 88261
Valentin Keyantuo Full Professor NCN II C-124 88255
Liangqing Li Full Professor NCN II C-117 88263
Lin Shan Associate Professor NCN II C-171 88268
Mahamadi Warma Full Professor NCN II C-112 88258

Research in Mathematical Analysis

Mathematical Analysis is the part of mathematics that originated with calculus and has strong connections with geometry. Modern analysis developed from the theory of integration and differentiation and took off with Banach’s work on linear operations after the groundwork has been laid with topology, algebra and Lebesgue’s theory of integration and integral equations. Von Neumann’s work on operator theory, motivated by quantum mechanics, gave a strong impetus. Mathematical Analysis has applications to many other areas of mathematics, science and technology and on the other hand, several problems from these areas have led to important developments in analysis. The research in analysis in the Mathematics Department involves two main subareas.

Gong, Li and Pasnicu work on C∗-algebras and noncommutative geometry. A commutative C∗ -algebra corresponds to a locally compact Hausdorff space. But many geometrical ob jects such as foliations, dynamical systems, give rise to noncommutative C∗-algebras. The researches have been successful in obtaining results concerning classification and structure for many important classes of C∗-algebras as well as interesting results in some geometry problems by using C ∗ -algebras. Their publications have appeared on Journals such as Annals of Math, Invent. Math., Duke Math. Journal, J. Reine Angew. Math. (Crelle’s Journal), Mem. Amer. Math. Soc., Ameri- can J. Math., GAFA and J. Funct. Analysis.

The research of Keyantuo and Warma centers around functional analytic methods for partial differential equations. Semigroups of operators and their generalizations combined with tools from vector-valued harmonic analysis and potential theory are used to study well-posedness and maximal regularity for of initial and boundary-value problems. The theory of differential equations is at the origin of much of modern analysis and has connections with differential geometry, dynamical systems and mathematical physics. Results have been published in such journals as the Journal of Differential Equations, Potential Analysis and Mathematische Annalen.