Applied mathematics, applied probablility, stochastic differential equations, mathematical finance, waves in random media
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.
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.
L. Borcea, J. Garnier and K. Solna, Onset of energy equipartition among surface and body waves,
Proceedings of the Royal Society, A477, 2246, 2021.
J. Garnier and K. Solna, Correction to Black-Scholes formula due to fractional stochastic volatility,
SIAM J. Finan. Math., 8:1, pp. 560–588, 2017.
J. Garnier and K. Solna, Fourth-moment Analysis for Wave Propagation in the White-Noise Paraxial Regime,
Arch. Rat. Mech. Anal., 220, 37-81, 2016.
H. Ammari, J. Garnier, H. Kang, M. Lim and K. Solna, Multistatic imaging of extended targets,
SIAM J. Imaging Science, 5:2, 564-600, 2012.
R. Marty and K. Solna, A general framework for waves in random media with long-range correlations,
Ann. Applied Probability, 21, 115-139, 2011.
J. Garnier and K. Sølna, 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. Sølna, Multiname and Multiscale Default Modeling,
SIAM J. on Multiscale Modeling and Simulation, 7, 1956-1978, 2009.
A.C. Fannjiang and K. Solna, Propagation and time-reversal of wave beams in atmospheric turbulence,
SIAM Journal on Multiscale Modeling and Simulation, 3(3), 522-558, 2005.
G. Papanicolaou, L. Ryzhik and K. Solna, Statistical stability in time reversal,
SIAM Journal on Applied Mathematics, 64, 1133-1155, 2003.
K. Solna and G. Milton, Can mixing materials make electromagnetic signals travel faster?,
SIAM Journal on Applied Mathematics, 62(6), 2064-2091, 2002.
G. Golub, K. Solna and P. Van Dooren, Computing the SVD of a general matrix product/quotient,
SIAM Journal on Matrix Analysis and Applications, 22, 1(1), 1-19, 2001.
National Science Foundation (NSF),
SIAM, Society for Industrial and Applied Mathematics.
AMS, American Mathemaical Society.