William Beckner

Department of Mathematics
University of Texas at Austin
2515 Speedway Stop C1200
Austin, Texas 78712-1202

Phone:

Department: 512-471-7711
Fax: 512-471-9038

E-Mail:

beckner@math.utexas.edu

Research:

to examine how the interplay of symmetry, smoothness and uncertainty can
characterize structure for geometric manifolds and model dynamical processes

to develop a new paradigm for fundamental inequalities, information encoding
structures, and invariants for analysis on geometric manifolds

principal themes in my research -- symmetry, inequalities, analysis on manifolds

• Fourier Analysis
  
• Geometric Inequalities
  
• Lie Groups & Differential Geometry
  
• Mathematical Physics
  
• Partial Differential Equations
  
• Probability
  

Teaching:

to foster creative tension between research & teaching -- to teach students how to decipher
mathematical ideas and develop intellectual skills to meet the scientific challeges of the 21st century
-- the basic question: what do you see & what does it mean

Purpose -- to engage students on the cutting edge of curiosity and provide the analytical tools to decode
and explain the universe, investigate new and difficult things, create novel concepts that didn't exist before,
recognize beauty in mathematics and nature
[with lines borrowed from Isaac Newton and friends]

To those who do not know mathematics, it is difficult to get across a real feeling as to the beauty,
the deepest beauty, of nature. If you want to learn about nature, to appreciate nature, it is necessary
to understand the language that she speaks in. [Richard Feynman]

It behooves us to place the foundations of knowledge in mathematics. [Roger Bacon]

Creativity takes courage [Henri Matisse]

Symmetry seems to be absolutely fascinating to the human mind. [Richard Feynman]

the fact that Mathematics does such a good job of describing the Universe is a mystery that we don't understand [Lord Kelvin];
and it is probable that that there is some secret here which remains to be discovered [C.S. Pierce];
one should look for interesting mathematics [Paul Dirac];
the unreasonable effectiveness of Mathematics [Eugene Wigner]

what's important and interesting are the pattern and structure -- the emerging complexity [Marin Rees]

Mathematics guided by curiosity, inspiration and rigorous reasoning, state no hypothesis but compute,
search for patterns of symmetry, innovation occurs on the boundary, goal is analytical insight!
[thoughts on reading and writing in Arroyo Seco]

Decoding the universe with rigor -- computation & geometric imagination are essential -- symmetry is the key --
the objective is to frame a new paradigm
[thoughts on writing in Princeton]

On writing a paper, there must be a calculation
[thoughts on writing in Manarola]

To look for an invariant way to describe analysis on a geometric manifold with negative curvature,
and to find hidden principles that bring order to the chaos of information -- more precisely, to determine
patterns of knowledge and principles of symmetry that characterize mathematical understanding
[thoughts on writing in Austin]

Writing is the most important step -- because it leads to new ideas
[thoughts on writing in Azenhas do Mar]

Writing should be succinct -- look for the "right way" to explain ideas
[thoughts on writing in Austin]

• Complex Analysis (361) [Fall 13, Fall 17]
• Honors Vector Calculus (427L-H) [Fall 18-21]
• Honors Differential Equations (427J-H) [Spring 20-22]
• Fourier Analysis (391C) [Spring 22]
• Stein Seminar
• Methods of Real Analysis (365D) [Spring 14-16, Spring 18-21]
• Math Club Talk: All Things Fourier [November 20, 2013]

Current Reading:

• If Then -- How the Simulmatics Corporation Invented the Future (Jill Lepore)
  
• Sirens of Mars -- Searching for Life on Another World (Sarah Stewart Johnson
  

Recommended Books:

• Birth of a Theorem (Cedric Villani)
  
• Princeton Lectures in Analysis (Elias M. Stein & Rami Shakarchi)
  
• Lectures on Partial Differential Equations (Vladimir I. Arnold)
  
• Mathematics and Computation (Avi Wigderson)
  
• The Cosmic Cocktail-Three Parts Dark Matter (Katie Freese)
  

Favorite Movies:

• Les enfants du paradis
  
• La grande illusion
  
• The Seventh Seal
  
• Chimes at Midnight
  

Interesting Movies:

• El abrazo de la serpiente (Embrace of the Serpent)
  
• Patterson (2016)
  

Education:

• BS in Physics, University of Missouri (Columbia); Adviser - Bernard Goodman
  
• PhD in Mathematics, Princeton University; Adviser - Elias M. Stein
  
• Post-doctoral study, University of Chicago; Adviser - A.P. Calderon

Honors:

• Prix Salem 1975
• Sloan Research Fellow 1977
• ICM Invited Lecture -- Helsinki, 1978
• Fellow, American Mathematical Society

Administrative Positions:

• Managing Editor, Transactions of the American Mathematical Society, 2000-05
• Chair, Department of Mathematics, 2007-11
• Assistant Director, Institute for Computational Engineering and Sciences, 2006-
• Advisory Board, Institute for Computational Engineering and Sciences, 2003-
• Undergraduate Studies Advisory Committee, School of Undergraduate Studies, 2013-2016
• Chair, UT Faculty Council, 2014-15

Photos from Summer 2015:

West Lake, Hangzhou -- June 2017

Antartic Peninsula, January 2019

With Amalia in Houston

Oden Institute, 2019

With Eli Stein