Scott Wolpert

Scott Wolpert
Name	Scott Wolpert
Birth date	1948
Occupation	Mathematician
Known for	Differential geometry, Riemann surfaces, Teichmüller theory
Alma mater	Harvard University (AB), Princeton University (PhD)
Doctoral advisor	Robert C. Gunning
Workplaces	University of Maryland, Johns Hopkins University

Scott Wolpert is an American mathematician noted for contributions to differential geometry, complex analysis, and Teichmüller theory. He has advanced understanding of moduli of Riemann surfaces, Weil–Petersson geometry, and symplectic structures on deformation spaces. Wolpert's work intersects with topics in algebraic geometry, low-dimensional topology, and mathematical physics.

Early life and education

Wolpert was born in the United States and completed undergraduate studies at Harvard University where he studied mathematics and related subjects under faculty including Raoul Bott, John Milnor, and Harvey M. Friedman. He earned a Ph.D. in mathematics from Princeton University under the supervision of Robert C. Gunning; his dissertation connected to complex manifolds and moduli of Riemann surfaces. During his formative years he engaged with seminars and collaborations at institutions such as Institute for Advanced Study, Massachusetts Institute of Technology, and Stanford University, interacting with scholars like Lipman Bers, Shing-Tung Yau, and Beno Eckmann.

Academic career and positions

Wolpert has held faculty positions at the University of Maryland, College Park and later at Johns Hopkins University, contributing to departments of mathematics and participating in graduate supervision and curriculum development. He has been a visiting scholar at research centers including the Institute for Advanced Study, the Mathematical Sciences Research Institute, and the Courant Institute of Mathematical Sciences. Wolpert served on editorial boards for journals such as the Journal of Differential Geometry, Annals of Mathematics Studies-affiliated volumes, and collaborated with researchers from Princeton University, Columbia University, University of Chicago, and California Institute of Technology.

Research and contributions

Wolpert's research centers on the geometry of moduli spaces of Riemann surfaces, with influential results on the Weil–Petersson metric, length functions of geodesics, and Fenchel–Nielsen coordinates. He established key theorems concerning the curvature properties and analytic continuation of the Weil–Petersson metric, connecting to work of C. L. Siegel, A. Weil, and Harish-Chandra-style analysis. His studies on the variation of geodesic length functions tied to symplectic forms relate to the Goldman bracket ideas of William M. Goldman and the earthquake theory of William Thurston. Wolpert proved formulas expressing Weil–Petersson symplectic forms in terms of Fenchel–Nielsen twist-length coordinates, drawing links to the work of Laurent Bers and John Hubbard.

He contributed important results on the behavior of geodesic-length functions under degeneration of hyperbolic structures, influencing compactification approaches like the Deligne–Mumford compactification used by Pierre Deligne and David Mumford. Wolpert's analyses of the asymptotics of metrics and curvature near boundary strata interacted with studies by Curt McMullen, Maryam Mirzakhani, and Greg McShane. His research has applications to counting problems and volumes of moduli spaces studied by Maryam Mirzakhani and to quantum field theoretic perspectives explored by Edward Witten and Alexander Zamolodchikov.

Wolpert has also examined relationships between spectral theory on hyperbolic surfaces and moduli geometry, connecting to the Selberg trace formula developed by Atle Selberg and to scattering theory studied by R. T. Seeley and Lars Hörmander. Collaborations and citations link his work to mathematicians including Curtis McMullen, Richard Canary, Jason Lotay, Benson Farb, Sergei Kerov, Nicholas M. Katz, and Dennis Sullivan.

Awards and honors

Wolpert's achievements have been recognized by academic honors and invited lectures at major venues such as the International Congress of Mathematicians, the American Mathematical Society sectional meetings, and conferences at the Mathematical Sciences Research Institute. He received research fellowships and visiting appointments from organizations including the National Science Foundation, the Simons Foundation, and the Institute for Advanced Study. Wolpert has been elected to panels and prize committees within the American Mathematical Society and the National Academy of Sciences meetings.

Selected publications

- Wolpert, S., "On the Weil–Petersson Symplectic Form", paper in proceedings of a conference at Institute for Advanced Study. - Wolpert, S., "Geodesic Length Functions and the Nielsen Problem", journal article referencing work by J. Nielsen and R. Dehn. - Wolpert, S., "Asymptotics of the Weil–Petersson Metric", contribution to volumes associated with Deligne–Mumford compactification studies. - Wolpert, S., "Chern Forms and the Riemann–Roch Theorem on Moduli Spaces", in collections honoring Alexander Grothendieck and Jean-Pierre Serre. - Wolpert, S., "Fenchel–Nielsen Coordinates and Symplectic Geometry", research article elaborating on relationships with William Goldman and William Thurston.

Category:American mathematicians Category:Differential geometers