Stephen Montgomery-Smith

Stephen Montgomery-Smith
Professor and Director of Graduate and Undergraduate Studies
Stephen Montgomery-Smith
222 Mathematical Sciences Building
Phone Number: 
Office Hours: 

Monday and Thursday 11-11:50am

Stephen Montgomery-Smith loved mathematics ever since he was a small child. When he was accepted into Cambridge University to study mathematics, it was like a dream come true. Before entering Cambridge, he had the honor to be part of the team representing the United Kingdom in the International Mathematics Olympiad in 1981. In 1988 he came to the University of Missouri-Columbia as a visiting assistant professor, and has remained there ever since. The first fifteen years of his career were very successful, and he had continuous NSF grant support until 2004.

More recently, Stephen Montgomery-Smith has shifted his research to attempting problems that are too hard for him.  Nevertheless, he still manages to produce a paper once in a while.

  • 1989 Ph.D., Mathematics, Cambridge, UK
Frequently Taught Courses: 
  • MATH 4310/7310 Numerical Linear Algebra
  • MATH 4500/7500 Applied Analysis
  • MATH 4540/7540 Mathematical Modeling
Research Interests: 

His initial research area was applications of probability theory to the local theory of Banach spaces. But he quickly became dissatisfied with the abstract nature of this subject, and wondered around various aspects of analysis until about 2004.  His main contributions during this period were in probability theory, mostly in finding tail distributions of sums of random variables.

In 1995, shortly before obtained tenure, he decided to work on the very hard problem to prove the existence of classical solutions to the three dimensional incompressible Navier-Stokes equation. Since he started working on this, it has become one of the Clay Institute Millennium problems.

While he has not solved this problem, it did lead him to become interested in applied mathematics. He has worked with both engineers and biologists. Some of his recent research includes:

  1. Predicting the orientation of fibers in injection molded plastics.
  2. Looking at robust methods to numerically solve the kinds of equations arising from classical mechanics.
  3. Finding probability distributions that describe the output of the Luria-Delbrück experiment.  The purpose of the original experiment was to determine the type of evolution (Lamarckian or Darwinian) that cause bacteria or yeast to acquire immunity to antibiotics.
Select Publications: 
  • Stephen Montgomery-Smith and Weijun Huang, A numerical method to model dynamic behavior of thin inextensible elastic rods in three dimensions. Journal of Computational and Nonlinear Dynamics, 9,1, (2014).
  • Stephen Montgomery-Smith, Wei He, David Jack and Douglas E. Smith, Exact tensor closures for the three dimensional Jeffery's Equation. Journal of Fluid Mechanics, volume 680, (2011), pp. 321-335.
  • S. Geiss, Stephen Montgomery-Smith and E. Saksman, On singular integral and martingale transforms. Transactions of the American Math Society, 362, (2010), 553-575.
  • Stephen Montgomery-Smith and Frank Schmidt, Statistical methods for estimating complexity from competition experiments between two populations, Journal of Theoretical Biology, Volume 264, Issue 3, June 2010, Pages 1043-1046.
  • Xiaofang Jin, Jessica Rose Newton, Stephen Montgomery-Smith and George P. Smith, A generalized kinetic model for amine modification of proteins with application to phage display, BioTechniques, Volume 46, Issue 3, March 2009, Pages 175-182.
  • Nigel Kalton, Stephen Montgomery-Smith, Krzysztof Oleszkiewicz and Yuri Tomilov, Power-bounded operators and related norm estimates. Journal of London Math. Soc. 70, (2004), 463-478.
  • Paweł Hitczenko and Stephen Montgomery-Smith, Measuring the magnitude of sums of independent random variables. Annals of Probability, 29, (2001), 447-466.
  • Nakhlé Asmar, Stephen Montgomery-Smith and Sadahiro Saeki, Transference in Spaces of Measures. J. Functional Analysis 165, (1999), 1-23.
  • Stephen Montgomery-Smith, Time decay for the bounded mean oscillation of solutions of the Schrödinger and wave equations. Duke Math J. 91 (1998), 393-408.
  • Loukas Grafakos and Stephen Montgomery-Smith, Stephen Best constants for uncentred maximal functions. Bull. London Math. Soc. 29 (1997), no. 1, 60-64.
  • Yuri Latushkin, Stephen Montgomery-Smith and T. Randolph, Evolutionary semigroups and dichotomy of linear skew-product flows on locally compact spaces with Banach fibers.J. Differential Equations (1996), no. 1, 73-116.
  • Stephen Montgomery-Smith and Victor de la Peña, Decoupling inequalities for the tail probabilities of multivariate U-statistics. Ann. Probab. 23 (1995), no. 2, 806-816.
  • Stephen Montgomery-Smith, Comparison of sums of independent identically distributed random vectors. Probab. Math. Statist. 14 (1993), no. 2, 281-285.
  • D.J.H. Garling and Stephen Montgomery-Smith, Complemented subspaces of spaces obtained by interpolation. J. London Math. Soc. (2) 44 (1991), no. 3, 503-513.
  • Raimund Ober and Stephen Montgomery-Smith, Bilinear transformation of infinite-dimensional state-space systems and balanced realizations of nonrational transfer functions. SIAM J. Control Optim. 28 (1990), no. 2, 438-465.
  • Stephen Montgomery-Smith, The distribution of Rademacher sums. Proc. Amer. Math. Soc. 109 (1990), no. 2, 517-522.