Brian Van Koten

I am an Assistant Professor in the Department of Mathematics and Statistics at the University of Massachusetts, Amherst.

Contact Info

• Office: LGRT 1428
• Office Hours: See my directory page.
• email: vankoten@math.umass.edu

Teaching

This semester I will be teaching Math 652, a course in numerical analysis. Topics will include numerical solution of partial differential equations and optimization methods for machine learning. Please find the syllabus and homework assignments here.

Talks

On 6/28/2019, I presented some work on computing rare event probabilities using stratification at the Institute for Computational and Experimental Research in Mathematics (ICERM). Video and slides are available here.

On 10/19/2017, I presented some recent work on the string method for finding saddle points at the Institute for Pure and Applied Mathematics (IPAM). Video and slides are available here.

Research Interests

• Applied probability and numerical analysis
• Computer simulation of molecular systems and applications in biology, chemistry, and materials science
• Variance reduction for Markov chain Monte Carlo methods and applications in statistics and computational statistical physics
• Sampling rare events
• Numerical methods for finding saddle points and applications to the computation of reaction rates
• Atomistic/continuum couplings for the simulation of defects in crystalline materials

CV

Publications

• B. Van Koten and M. Luskin. Stability and convergence of the string method for computing minimum energy paths. arXiv:1807.06094
• A. R. Dinner, E. H. Thiede, B. Van Koten, and J. Weare. Stratification of Markov chain Monte Carlo. arXiv:1705.08445
• D. Olson, X. H. Li, C. Ortner, and B. Van Koten. Force-Based Atomistic/Continuum Blending for Multilattices. arXiv:1611.05935
• J. O. B. Tempkin, B. Van Koten, J. C. Mattingly, A. R. Dinner, and J. Weare. Trajectory stratification for stochastic dynamics. to appear in SIAM Review. arXiv:1610.09426
• X. H. Li, C. Ortner, A. V. Shapeev, and B. Van Koten. Analysis of blended atomistic/continuum hybrid methods. Numerische Mathematik, 134(2):275--326, 2016. arXiv:1404.4878
• E. H. Thiede, B. Van Koten, J. Weare, and A. R. Dinner. Eigenvector method for umbrella sampling enables error analysis. The Journal of Chemical Physics, 145(8), 084115, 2016. arXiv:1603.04505
• E. Thiede, B. Van Koten, and J. Weare. Sharp entrywise perturbation bounds for Markov chains. SIAM Journal on Matrix Analysis and Applications, 36(3):917--941, 2015. arXiv:1410.1431
• B. Van Koten and C. Ortner. Symmetries of 2-lattices and second order accuracy of the Cauchy--Born model. Multiscale Modeling and Simulation, 11(2):615--634, 2013. arXiv:1203.5854
• M. Luskin, C. Ortner, and B. Van Koten. Formulation and optimization of the energy-based blended quasicontinuum method. Computer Methods in Applied Mechanics and Engineering, 253:160--168, 2013. arXiv:1112.2377
• B. Van Koten, X. H. Li, M. Luskin, and C. Ortner, A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods. Numerical Analysis of Multiscale Problems, volume 83 of Lect. Notes Compu. Sci. Eng. Springer, 2012. arXiv:1012.6031
• B. Van Koten and M. Luskin, Analysis of energy-based blended quasi-continuum approximations. SIAM Journal on Numerical Analysis, 49(5):2182--2209, 2011. arXiv:1008.2138
• R. Held, I. Stavrov, and B. VanKoten. (Semi-)Riemannian geometry of (para-)octonionic projective planes. Differential Geometry and its Applications, 27(4):464--481, 2009. arXiv:0702631
• J. Hardin, A. Mitani, L. Hicks, and B. VanKoten. A robust measure of correlation between two genes on a microarray. BMC Bioinformatics, 8(1):220, 2007.