# Liviu Nicolaescu

Professor, Director of Undergraduate Honors Math Program

B.S. and M. S., University "Al. I. Cuza’’, Iasi, Romania, 1987

Ph.D., Michigan State University, 1994

Email: Liviu.Nicolaescu.1@nd.edu

Office: 224 Hayes-Healy

Phone: (574) 631-3370

Fax: (574) 631-6579

For additional information see Liviu Nicolaescu’s Personal Page.

**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.

Please direct questions and comments to: Liviu.Nicolaescu.1@nd.edu