Burton Rodin

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Burton Rodin
Alma mater University of California, Los Angeles
Known for Thurston conjecture for circle packings
Awards Fellow of the American Mathematical Society (2012)
Scientific career
Fields Mathematics
Institutions University of California, San Diego
Thesis Reproducing Formulas on Riemann Surfaces (1961)
Doctoral advisor Leo Sario

Burton Rodin is an American mathematician known for his research in conformal mappings and Riemann surfaces. He is a professor emeritus at the University of California, San Diego.

Contents

Education

Rodin received a Ph.D. at the University of California, Los Angeles in 1961. His thesis, titled Reproducing Formulas on Riemann Surfaces, was written under the supervision of Leo Sario. [1]

Career

He was a professor at the University of California, San Diego from 1970 to 1994. He was chair of the Mathematics Department from 1977 to 1981, and became professor emeritus in June 1994.[ citation needed ]

Research

Rodin's 1968 work on extremal length of Riemann surfaces, together with an observation of Mikhail Katz, yielded the first systolic geometry inequality for surfaces independent of their genus. [2] [3]

In 1980, Rodin and Stefan E. Warschawski solved the Visser–Ostrowski problem for derivatives of conformal mappings at the boundary. [4] In 1987 he proved the Thurston conjecture for circle packings, jointly with Dennis Sullivan. [5]

Awards and honors

In 2012, Rodin was elected fellow of the American Mathematical Society. [6]

Selected books

Related Research Articles

Riemann mapping theorem

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Conformal map Mathematical function which preserves angles

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Lars Ahlfors Finnish mathematician

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Riemann surface One-dimensional complex manifold

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In mathematics, the uniformization theorem says that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere. The theorem is a generalization of the Riemann mapping theorem from simply connected open subsets of the plane to arbitrary simply connected Riemann surfaces.

Dennis Sullivan American mathematician (born 1941)

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In mathematics, the Schwarz alternating method or alternating process is an iterative method introduced in 1869–1870 by Hermann Schwarz in the theory of conformal mapping. Given two overlapping regions in the complex plane in each of which the Dirichlet problem could be solved, Schwarz described an iterative method for solving the Dirichlet problem in their union, provided their intersection was suitably well behaved. This was one of several constructive techniques of conformal mapping developed by Schwarz as a contribution to the problem of uniformization, posed by Riemann in the 1850s and first resolved rigorously by Koebe and Poincaré in 1907. It furnished a scheme for uniformizing the union of two regions knowing how to uniformize each of them separately, provided their intersection was topologically a disk or an annulus. From 1870 onwards Carl Neumann also contributed to this theory.

Circle packing theorem Describes the possible tangency relations between circles with disjoint interiors

The circle packing theorem describes the possible tangency relations between circles in the plane whose interiors are disjoint. A circle packing is a connected collection of circles whose interiors are disjoint. The intersection graph of a circle packing is the graph having a vertex for each circle, and an edge for every pair of circles that are tangent. If the circle packing is on the plane, or, equivalently, on the sphere, then its intersection graph is called a coin graph; more generally, intersection graphs of interior-disjoint geometric objects are called tangency graphs or contact graphs. Coin graphs are always connected, simple, and planar. The circle packing theorem states that these are the only requirements for a graph to be a coin graph:

Stefan Emanuel "Steve" Warschawski was a mathematician, a professor and department chair at the University of Minnesota and the founder of the mathematics department at the University of California, San Diego.

Theodore Frankel was a mathematician who introduced the Andreotti–Frankel theorem and the Frankel conjecture.

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Paul C. Yang is a Taiwanese-American mathematician specializing in differential geometry, partial differential equations and CR manifolds. He is best known for his work in Conformal geometry for his study of extremal metrics and his research on scalar curvature and Q-curvature. In CR Geometry he is known for his work on the CR embedding problem, the CR Paneitz operator and for introducing the Q' curvature in CR Geometry.

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Introduction to Circle Packing: The Theory of Discrete Analytic Functions is a mathematical monograph concerning systems of tangent circles and the circle packing theorem. It was written by Kenneth Stephenson and published in 2005 by the Cambridge University Press.

Ring lemma

In the geometry of circle packings in the Euclidean plane, the ring lemma gives a lower bound on the sizes of adjacent circles in a circle packing.

References

  1. "Burton Rodin - The Mathematics Genealogy Project". www.genealogy.ams.org.
  2. "Website for systolic geometry and topology". www.cs.biu.ac.il.
  3. The method of extremal length: invited hour address presented at the 705th meeting of the American Mathematical Society. Bull. Amer. Math. Soc. 80, 1974, 587606
  4. B. Rodin and S. E. Warschawski, “On the derivative of the Riemann mapping function near a boundary point and the Visser-Ostrowski problem”, Mathematische Annalen, 248, (1980), 125137.
  5. B. Rodin and D. Sullivan, “The convergence of circle packings to the Riemann mapping”, Journal of Differential Geometry, 26 (1987), 349360.
  6. List of Fellows of the American Mathematical Society, retrieved 2013-01-27.