Knut Solna

Professor, Mathematics
School of Physical Sciences

Ph.D., Stanford University, 1997, Applied Math

Phone: (949) 824-3154

University of California, Irvine
Mathematics Department
340 Rowland Hall
Mail Code: 3875
Irvine, CA 92697
Research Interests
Applied mathematics, applied probablility, stochastic differential equations, mathematical finance, waves in random media
Academic Distinctions
Sloan Fellowship 2004-2006
Instructorship award at the University of Utah 1998.
Fulbright Award 1990
Wylie Instructor, Department of Mathematics, University of Utah, 1997-2000.
Research Abstract
Modeling and analysis of problems described by partial differential equations
with heterogeneous and random coefficients. Analysis of waves propagating
through multiscale and heterogeneous media with applications to seismology,
remote sensing and communication through the turbulent atmosphere.
Applications to pricing theory for financial instruments in volatile
and multiscale markets.
H. Ammari, J. Garnier and K. Solna,
Resolution and stability analysis in full-aperture linearized conductivity and wave imaging,
Proceedings of the AMS, 141, 3431--3446, 2013.
J. Garnier and K. Solna,
Coupled Wideangle Wave Approximations,
SIAM Multiscale Model. Simul.,
10:1, 217-244, 2012.
H. Ammari, J. Garnier and K. Solna,
A statistical approach to target detection and localization in the presence of noise,
Waves in Random and Complex Media, 2011.
J. Garnier and K. Solna,
Effective fractional acoustic wave equations in random multiscale media,
J. Acoust. Soc. Am., 127, 67-72, 2010.
J. Garnier and K. Solna,
Coupled paraxial wave equations in random media in the white-noise regime,
Ann. Applied Probability, 19, 318-346, 2009.
J.P. Fouque, R. Sircar and K. Solna,
Multiname and Multiscale Default Modeling,
SIAM J. on Multiscale Modeling and Simulation,
7, 1956-1978, 2009.
S. Hou, K. Solna and H. Zhao,
A direct imaging method using far-field data,
Inverse Problems, 23, 1533-1546, 2007.
G. Papanicolaou, L. Ryzhik and K. Solna, Statistical stability in time reversal, SIAM Journal on Applied Mathematics, 2003.
J.P. Fouque, G. Papanicolaou, K. R. Sircar and K. Solna, Multiscale Stochastic Volatility Asymptotics, SIAM Journal on Multiscale Modeling and Simulation, 2003.
K. Solna and G. Milton, Can mixing materials make electromagnetic signals travel faster?, SIAM Journal on Applied Mathematics, V 62, 6, 2064-2091, 2002.
G.C. Papanicolaou and K. Solna, Wavelet based estimation of Kolmogorov turbulence, In: Long-range Dependence: Theory and Applications, P. Doukhan, G. Oppenmeim and M.S. Taqqu, editors, Birkhauser, 2002.
National Science Foundation (NSF),
Professional Societies
SIAM, Society for Industrial and Applied Mathematics.
AMS, American Mathemaical Society.
Last updated