Dr. William Green's areas of expertise include partial differential equations, harmonic analysis, and mathematical physics. He has several publications and presentations to his credit that cover his research activities in the analysis of dispersive partial differential equations, with particular focus on Schrodinger's equation. Dr. Green organizes the Rose-Hulman Mathematics Seminar, which features presentations by faculty, visiting professionals and professors, and students. He earned Albion College's Young Alumni Award. Check out his personal web page.
Academic Degrees
- PhD, University of Illinois, 2010
- MSc, University of Illinois, 2006
- BA, Albion College, 2005
Awards & Honors
- Simons Collaboration Grant, 2017-2022
- Simons Travel Grant, American Mathematical Society, 2012-15
- Young Alumni Award, Albion College, 2014
- Brahana TA Instructional Award, University of Illinois at Urbana-Champaign, 2009
Research Interests
- Analysis of dispersive partial differential equations
- Partial differential equations
- Time-decay estimates for wave, Schrödinger and Dirac equations
- Functional analysis
- Wave operators for Schrödinger equations
- Mathematical physics
Select Publications & Presentations
- Green, W. and Goldberg, M., “The Lp Boundedness of Wave Operators for Schrödinger Operators with Threshold Singularities,” Advances in Mathematics, 303, 360-389, 2016
- “Time Decay Estimates for the Wave Equation with Potential in Dimension Two,” Journal of Differential Equations, 257, 868-919, 2014
- Green, W. and Erdogan, M. B., “A Weighted Dispersive Estimate for Two-Dimensional Schrödinger Operators,” Communications in Mathematical Physics, 319, 791-811, 2013
- Green, W. and Erdogan, M. B., “Dispersive Estimates for the Schrödinger Equation with C(n-3)/2 Potentials in Odd Dimensions,” International Mathematics Research Notices, 13, 2532-2565, 2013
- Green, W., Erdogan, M. B., and Goldberg, M., “Dispersive Estimates for Four Dimensional Schrödinger and Wave Equations with Obstructions at Zero Energy,” Communications in Partial Differential Equations, 39, 10, 1936-1965
Teaching Interests
- Calculus
- Differential equations
- Real and complex analysis
- Linear algebra