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
- Rose-Hulman Board of Trustees Outstanding Scholar Award Winner, 2022
- 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
- Erdogan, B., and Green, W. "The Lp-continuity of wave operators for higher order Schrödinger operators." Advances in Mathematics Volume 404, Part B, 6 August 2022, 108450.
- Erdogan, B., and Green, W. "On the one dimensional Dirac equation with potential." Journal de Mathématiques Pures et Appliquées Volume 151, July 2021, Pages 132-170.
- Erdogan, B., Green, W. and Toprak, E. "Dispersive estimates for Dirac Operators in dimension three with obstructions at threshold energies," Amer. J. Math., 141, no. 5, 1217-1258.
- Erdogan, B., Goldberg, M., and Green, W. "Limiting absorption principle and Strichartz estimates for Dirac operators in two and higher dimensions," Comm. Math. Phys. 367 (2019), no. 1, 241-263.
- Green, W. and Toprak, E. "On the Fourth order Schrödinger equation in four dimensions: dispersive estimates and zero energy resonances," J. Differential Equations, 267 , (2019), no. 3, 1899-1954.
- Goldberg, M. and Green, W. "The Lp boundedness of wave operators for higher dimensional Schrödinger Operators with threshold singularities," Advances in Mathematics, 303 (2016), 360-389.
Teaching Interests
- Calculus
- Differential equations
- Real and complex analysis
- Linear algebra