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| Wolpert, Scott A. | |
|---|---|
| Name | Scott A. Wolpert |
| Birth date | 1948 |
| Birth place | United States |
| Nationality | United States |
| Fields | Mathematics |
| Institutions | University of Maryland, College Park, University of Michigan, Stanford University |
| Alma mater | University of California, Berkeley, Harvard University |
| Doctoral advisor | Andrew M. Gleason |
Wolpert, Scott A. Scott A. Wolpert is an American mathematician noted for contributions to Teichmüller theory, hyperbolic geometry, and the geometry of moduli spaces. He has held faculty positions at major research universities and collaborated with leading figures in complex analysis, algebraic geometry, and low-dimensional topology. His work connects classical problems treated by researchers such as Henri Poincaré, Bernhard Riemann, and William Thurston to modern developments influenced by Maxim Kontsevich and Edward Witten.
Wolpert was born in the United States and raised with early exposure to mathematics through regional science programs and summer seminars associated with institutions like Massachusetts Institute of Technology and Stanford University. He completed undergraduate studies at Harvard University where he encountered faculty including Andrew M. Gleason and peers who later joined faculties at Princeton University and California Institute of Technology. Wolpert earned his doctorate at University of California, Berkeley under the supervision of Andrew M. Gleason, situating him in a lineage connected to the challenges of Riemann surfaces and classical complex function theory developed by figures such as Bernhard Riemann and Ludwig Bieberbach.
Wolpert's early appointments included postdoctoral and faculty positions at institutions including Stanford University and University of Michigan before a long-term professorship at University of Maryland, College Park. He taught courses that intersected the curricula of Princeton University and University of Chicago style programs, supervising graduate students who later joined faculties at Columbia University and Yale University. His collaborations span mathematicians affiliated with Institute for Advanced Study, Courant Institute of Mathematical Sciences, and international centers such as Mathematical Sciences Research Institute and Institut des Hautes Études Scientifiques. Wolpert developed research programs combining techniques from Riemannian geometry, symplectic geometry, and analysis on moduli spaces of Riemann surfaces influenced by work of Shing-Tung Yau, Michael Atiyah, and Graeme Segal.
Wolpert is best known for rigorous results on the Weil–Petersson metric on Teichmüller space and the geometry of the moduli space of curves. He proved foundational theorems about curvature, geodesics, and metric completion that relate to conjectures proposed by William Thurston and later refined by Maryam Mirzakhani. His results on asymptotics and analytic torsion connect to studies by Dennis Sullivan and Richard Wentworth, while his formulae for volumes of moduli spaces echo approaches used by Maxim Kontsevich and Eduard Witten in intersection theory. Wolpert introduced and analyzed important identities—often cited as "Wolpert formulas"—that express variations of length functions for closed geodesics on hyperbolic surfaces; these identities underpin techniques shared with researchers such as Curt McMullen, Howard Masur, and Yair Minsky.
His work on Fenchel–Nielsen coordinates formalized how twist parameters interact with the Weil–Petersson symplectic form, influencing computational methods used in conjunction with theories developed by John Hubbard and Lipman Bers. Wolpert contributed to the understanding of earthquake maps originally studied by William Thurston and later extended in contexts considered by Marcelo Viana and Amie Wilkinson. He also produced influential papers on the determinant of the Laplacian and analytic torsion relating to investigations by S.-T. Yau, Daniel Bump, and Peter Sarnak.
Wolpert's achievements have been recognized by election to learned societies and by awards from national academies associated with mathematical research. He has received fellowships and invited addresses at institutions such as International Congress of Mathematicians, Institute for Advanced Study, and the Mathematical Sciences Research Institute. His invited lectures include series at Clay Mathematics Institute programs and named lectureships hosted by universities like Princeton University and University of California, Berkeley. Wolpert has been cited in prize committees alongside recipients of the Fields Medal, Abel Prize, and Clay Research Award for work that advanced the geometry of moduli spaces.
Wolpert's mentorship influenced a generation of geometers and analysts who went on to positions at Stanford University, Harvard University, Princeton University, and international centers including Université Paris-Sud and University of Bonn. His collected papers and lecture notes are held in archives used by scholars at Mathematical Sciences Research Institute and have been included in graduate curricula at University of Chicago and Columbia University. Wolpert's theoretical innovations continue to inform active research areas involving collaborators and successors such as Maryam Mirzakhani (posthumously), Curt McMullen, and Richard Penner. His legacy endures in the techniques now standard in the study of Teichmüller theory, hyperbolic 3-manifolds as considered by Thurston, and the wider program connecting geometry, topology, and mathematical physics developed by figures like Edward Witten and Maxim Kontsevich.