John D'Angelo

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John D'Angelo
BornMarch 5. 1951
Philadelphia, Pa. USA
Alma mater Univ. of Pennsylvania (BA) Princeton University (PhD )
Known forResearch in
Functions of several complex variables,
D'Angelo Type,
Rational Sphere Maps
Awards Fellow of the American Mathematical Society (2014)
Stefan Bergman Prize (1999)
Scientific career
Fields Functions of several complex variables
Institutions Massachusetts Institute of Technology
University of Illinois, Champaign-Urbana
Doctoral advisor Joseph J. Kohn
Doctoral students Dusty Grundmeier,
Daniel Lichtblau

John D'Angelo is an American mathematician. He is currently Professor Emeritus in the Department of Mathematics at the University of Illinois at Champaign-Urbana.

Contents

Education

D'Angelo received his PhD from Princeton University in 1976, under the direction of J.J. Kohn. [1] He was then a C.L.E. Moore Instructor at MIT from 1976 to 1978, becoming an Assistant Professor at University of Illinois in 1978, and was promoted to Full Professor in 1987. He became an emeritus professor in 2018. [2]

Awards and honors

D'Angelo was the recipient of the Stefan Bergman Prize in 1999 for "remarkable geometric insight that has led him to make several spectacular contributions to complex analysis". [3] In 2014 he became a fellow of the American Mathematical Society: "For contributions to several complex variables and Cauchy-Riemann geometry, and for his inspiration of students". [4]

Research

D'Angelo's early work involved the study of order of contact between analytic subvarieties and boundaries of weakly pseudoconvex domains, which resulted in the definition and analysis of what are now known as points of D'Angelo finite type. [5] The D'Angelo type provides a quantitative measure of the order contact between the boundary of the domain and analytic subvarieties. D'Angelo's work uses analysis and commutative algebra. A domain all of whose boundary points have finite D'Angelo type has analytic properties, with respect to holomorphic functions, that are quite similar to strictly pseudoconvex domains. David Catlin was able to prove regularity estimates for the -Neumann problem, the Bergman projection, and related operators for domains all of whose boundary points satisfy a condition closely related to finite D'Angelo type. [6]

Since 1990 D'Angelo's work has been focused on problems connected to the existence of proper holomorphic mappings between balls of different dimensions. [7] That work led him to a study of complex variables analogues of Hilbert’s 17th problem [8] and to various combinatorial and algebraic properties of Rational Sphere Maps. [7]

Books

References

  1. ↑ "John D'Angelo - The Mathematics Genealogy Project". www.mathgenealogy.org. Retrieved 2025-12-09.
  2. ↑ "CV for John P. D'Angelo – John P. D'Angelo". 2023-07-05. Retrieved 2025-12-09.
  3. ↑ "Mathematics People" (PDF). Notices of the American Mathematical Society. 46 (5). 1990.
  4. ↑ "2014 Class of the Fellows of the AMS". Notices of the American Mathematical Society. 61 (4): 420–421. April 2014 – via AMS.
  5. ↑ D'Angelo, John P. (1982). "Real Hypersurfaces, Orders of Contact, and Applications". Annals of Mathematics. 115 (3): 615–637. doi:10.2307/2007015. ISSN   0003-486X.
  6. ↑ Catlin, David (July 1987). "Subelliptic Estimates for the $\overline \partial$-Neumann Problem on Pseudoconvex Domains". The Annals of Mathematics. 126 (1): 131. doi:10.2307/1971347.
  7. 1 2 D'Angelo, John P. (2021). Rational Sphere Maps. Progress in Mathematics Ser. Cham: Springer International Publishing AG. ISBN   978-3-030-75808-0.
  8. ↑ D'Angelo, John P. (2013). Hermitian analysis: from Fourier series to Cauchy-Riemann geometry. Cornerstones. New York: Birkhauser/Springer. ISBN   978-1-4614-8525-4.
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