Liviu Nicolaescu

Professor, Director of Undergraduate Honors Math Program

Education

B.S. and M. S., University "Al. I. Cuza’’, Iasi, Romania, 1987
Ph.D., Michigan State University, 1994

Research Groups

Analysis and Partial Differential Equations, Differential Geometry, Discrete Math, Operations Research, and Probability, Partial Differential Equations, Topology

Research Area

Topology and Probability

Bio

Research Interests

My research interests belong to the area of mathematics known as global analysis. More specifically, I use analytical tools in the study of shape. Since 1995 I have been almost exclusively interested in the geometric and topologic applications of the Seiberg-Witten equations, a system of nonlinear elliptic equations arising in quantum field theory which turned out to be extremely versatile in detecting subtle properties of 3- and 4-dimensional spaces.

Selected Publications

• Seiberg-Witten invariants and surface singularities, joint with A. Nemethi, Geometry and Topology, 6 (2002), 269-328.
• Notes on Seiberg-Witten Theory, monograph, xii+484p, Graduate Studies in Math., vol. 28, Amer. Math. Soc., 2000.
• Finite energy Seiberg-Witten moduli spaces on 4-manifolds bounding Seifert fibrations, Comm. in Anal. and Geom., 8 (2000), 955-1023.
• Adiabatic limits of the Seiberg-Witten equations on Seifert manifolds, Comm. Anal. and Geom., 6 (1998), 331-392.
• Lectures on the Geometry of Manifolds, monograph, x+450 p, World Scientific Publishing Co., 1996; 2nd Printing 1999.
• Generalized symplectic geometries and the index of families of elliptic problems, Memoirs A.M.S., vol. 128, Number 609, 1997.
• The spectral flow, the Maslov index and decompositions of manifolds, Duke Univ.J, 80 (1995), 485-534.