Biography
Knut Sølna is a Professor in the Department of Mathematics at the University of California, Irvine. He earned his Ph.D. in Scientific Computing and Computational Mathematics from Stanford University in 1997, where he also obtained his M.S. in Statistics in 1996. Sølna received an M.Sc. in Engineering Economic Systems from Stanford University in 1989 and an M.Sc. in Engineering Cybernetics from the Norwegian Institute of Technology in 1987. After completing his Ph.D., he served as a Wylie Instructor at the University of Utah from 1997 to 2000.
Sølna’s research interests include wave propagation in random media, stochastic volatility models, and imaging in complex environments. He has published extensively in peer-reviewed journals, contributing significantly to the understanding of wave dynamics and financial mathematics. His work has been supported by multiple grants from organizations such as the National Science Foundation (NSF) and the Air Force Office of Scientific Research (AFOSR). Some of his notable projects include "Deep Wave Probing and Imaging of Heavy Tailed Fabric" funded by the NSF and "Propagation of Electromagnetic Beams with Applications" supported by the AFOSR.
At UC Irvine, Sølna is responsible for teaching both undergraduate and graduate courses in applied mathematics and statistical methods. He has advised numerous doctoral and postdoctoral students, many of whom have gone on to successful academic and industry careers. Sølna has also been actively involved in the broader mathematical community, serving as an associate editor for journals such as the SIAM Journal on Multiscale Modeling and Simulation. Additionally, he has co-organized various conferences and workshops, contributing to the advancement of research in mathematics and its applications.
Return to topDegrees
- PhD in Scientific Computing and Computational Mathematics, Stanford University, 1997
- M.S. in Statistics, Stanford University, 1996
- M.S. in Engineering Economic Systems, Stanford University, 1989
- M.Sc. in Engineering Cybernetics, The Norwegian Institue of Technology
Distinctions
- Sloan Fellowship Award, 2004
- NSF grant on “Deep Wave Probing and Imaging of Heavy Tailed Fabric”, 2023
- AFOSR grant on “Propagation of Electromagnetic Beams with Applications”, 2022
- NSF grant on “Novel Approaches to Wave Propagation in Random Media”, 2020
- AFOSR grant on “Deep Electromagnetic Probing and Imaging Through Complex Media”, 2018
- NSF grant on “Complex Media Optics and Imaging”, 2016
- AFOSR grant on “Electromagnetic Probing in Complex Media”, 2014
- AFOSR grant on “Research Topics on Cluttered Environments Interrogation and Propagation”, 2011
- NSF grant on “Propagation and Application of Waves in Complex Media”, 2007
- ONR grant for research work on imaging and time-reversal methods, 2001
Areas of Expertise
- Mathematical Imaging
- Wave Propagation
- Stochastic Volatility
- Inverse Problems
- Random Media Analysis
- Electromagnetic Wave Propagation
- Time Reversal Methods
- Financial Mathematics
- Acoustic Pulse Spreading
- Scattering Theory
Recent Publications
- Hoop M.V.D.E., Garnier J., Sølna K., “THREE-DIMENSIONAL RANDOM WAVE COUPLING ALONG A BOUNDARY AND AN ASSOCIATED INVERSE PROBLEM*”, Multiscale Modeling and Simulation, vol. 22, pp. 39-65, 2024.
- Annio G., Holm S., Mangin G., Penney J., Bacquët R., Mustapha R., Darwish O., Wittgenstein A.S., Schregel K., Vilgrain V., Paradis V., Sølna K., Nordsletten D.A., Sinkus R., “Making sense of scattering: Seeing microstructure through shear waves”, Science Advances, vol. 10, 2024.
- Garnier J., Sølna K., “SHOWER CURTAIN EFFECT AND SOURCE IMAGING”, Inverse Problems and Imaging, vol. 18, pp. 993-1023, 2024.
- Baldassari L., Siahkoohi A., Garnier J., Sølna K., de Hoop M.V., “Conditional score-based diffusion models for Bayesian inference in infinite dimensions”, Advances in Neural Information Processing Systems, vol. 36, 2023.
- Garnier J., Sølna K., “SPECKLE MEMORY EFFECT IN THE FREQUENCY DOMAIN AND STABILITY IN TIME-REVERSAL EXPERIMENTS”, Multiscale Modeling and Simulation, vol. 21, pp. 80-118, 2023.
- Borcea L., Garnier J., Sølna K., “PARAXIAL WAVE PROPAGATION IN RANDOM MEDIA WITH LONG-RANGE CORRELATIONS”, SIAM Journal on Applied Mathematics, vol. 83, pp. 25-51, 2023.
- de Hoop M.V., Garnier J., Sølna K., “System of radiative transfer equations for coupled surface and body waves”, Zeitschrift fur Angewandte Mathematik und Physik, vol. 73, 2022.
- Garnier J., Sølna K., “Scintillation of partially coherent light in time-varying complex media”, Journal of the Optical Society of America A: Optics and Image Science, and Vision, vol. 39, pp. 1309-1322, 2022.
- Garnier J., Solna K., “Enhanced backscattering of a partially coherent field from an anisotropic random lossy medium”, Discrete and Continuous Dynamical Systems - Series B, vol. 26, pp. 1171-1195, 2021.
- Borcea L., Garnier J., Sølna K., “Multimode communication through the turbulent atmosphere”, Journal of the Optical Society of America A: Optics and Image Science, and Vision, vol. 37, pp. 720-730, 2020.
- Garnier J., Sølna K., “Optimal Hedging under Fast-Varying Stochastic Volatility”, SIAM Journal on Financial Mathematics, vol. 11, pp. 274-325, 2020.
- Garnier J., Sølna K., “Implied Volatility Structure in Turbulent and Long-Memory Markets”, Frontiers in Applied Mathematics and Statistics, vol. 6, 2020.
Most Cited Publications
- J.P. Fouque, G. Papanicolaou, R. Sircar, K. Sølna, “Multiscale Stochastic Volatility for Equity, Interest-Rate and Credit Derivatives”, Cambridge University Press, 2011.
- Fouque J.P., Papanicolaou G., Sircar R., Solna K., “Multiscale stochastic volatility asymptotics”, Multiscale Modeling and Simulation, vol. 2, pp. 22-42, 2004.
- Ammari H., Garnier J., Kang H., Park W.K., Sølna K., “Imaging schemes for perfectly conducting cracks”, SIAM Journal on Applied Mathematics, vol. 71, pp. 68-91, 2011.
- Fouque J.P., Papanicolaou G., Sircar R., Solna K., “Singular perturbations in option pricing”, SIAM Journal on Applied Mathematics, vol. 63, pp. 1648-1665, 2003.
- Hou S., Solna K., Zhao H., “A direct imaging algorithm for extended targets”, Inverse Problems, vol. 22, pp. 1151-1178, 2006.
- Papanicolaou G., Ryzhik L., Sølna K., “Statistical stability in time reversal”, SIAM Journal on Applied Mathematics, vol. 64, pp. 1133-1155, 2004.
- Ammari H., Garnier J., Kang H., Lim M., Sølna K., “Multistatic Imaging of Extended Targets”, SIAM Journal on Imaging Sciences, vol. 5, pp. 564-600, 2012.
- Hou S., Solna K., Zhao H., “Imaging of location and geometry for extended targets using the response matrix”, Journal of Computational Physics, vol. 199, pp. 317-338, 2004.
- Fouque J.P., Sircar R., Sølna K., “Stochastic volatility effects on defaultable bonds”, Applied Mathematical Finance, vol. 13, pp. 215-244, 2006.
- Garnier J., Sølna K., “Coupled paraxial wave equations in random media in the white-noise regime”, Annals of Applied Probability, vol. 19, pp. 318-346, 2009.
Contact Information
Website: http://www.math.uci.edu/~ksolna
Email: ksolna@uci.edu
Address: Department of Mathematics, University of California at Irvine
Return to topThis profile was last updated on 2/7/2025.