User:Harer52/sandbox

''' John L. Harer, born November 29, 1952, is an American mathematician, working in Topology and Computational Biology. He is known for his work on the Homology of the Mapping Class Group and in Computational Topology. He is professor of Mathematics, Computer Science and Electrical and Computer Engineering at Duke University and Founder-CEO of Geometric Data Analytics.

Life
Harer graduated from Lexington High School (Lexington, Virginia) in 1970 and from Haverford College (Haverford, Pennsylvania) in 1974. He received his Ph.D. in Mathematics from the University of California, Berkeley in 1979, working with Robion Kirby. He has been a Ritt Assistant Professor at Columbia University (1979-1983), and Professor at the University of Maryland (1983-85), the University of Michigan (1985-1991), Washington and Lee University (1991-1992) and Duke University (1992–present). He has been a Visiting Professor at Stanford University, the University of Rome, and the Curie Institute. He held a Sloan Foundation Research Fellowship (1986-87).

Work
Harer's work has focused in three areas.

Homology of the Mapping Class Group and the Moduli Space of Curves
Harer computed the Second Homology Group of the Mapping Class Group of an Orientable Surface, which provided a proof of a conjecture of Mumford that the Picard group of the Moduli Space of Curves has rank 1. Later he proved that the homology of the Mapping Class Group was stable, showed that it is a virtual duality group, computed its virtual cohomological dimension, and in joint work with Don Zagier computed its virtual Euler characteristic. This work formed the foundation for a number of advances in the study of moduli spaces, including the later proof by Madsen and co-authors of the Mumford Conjecture.

Computational Topology
Persistent Homology was invented by Edelsbruner, Letscher and Zomorodian in 2002, creating the field of Computational Topology. Harer was one of the first mathematicians to work on computational topology and has been active in its growth and application for over 10 years. Methodologies from the field are being used in his company Geometric Data Analytics.

Computational Biology
Harer also studies the cellular networks that regulate gene expression. He focuses on how periodic processes such as circadian rhythms and the cell division cycle are controlled, how these processes couple and how they relate to disease.