William R. Green

William R. Green is a Professor and Associate Department Head in the Department of Mathematics at Rose-Hulman Institute of Technology, where he has been on the faculty since 2012. He earned his PhD in Mathematics from the University of Illinois at Urbana-Champaign in 2010 under the supervision of Burak Erdogan. Prior to joining Rose-Hulman, he served as an Assistant Professor at Eastern Illinois University from 2010-2012.

His educational background includes:

• PhD in Mathematics, University of Illinois at Urbana-Champaign (2010)
• MS in Mathematics, University of Illinois at Urbana-Champaign (2006)
• BA in Mathematics and Physics with Chemistry minor, Albion College (2005)

Dr. Green's research focuses on the intersection of harmonic analysis, partial differential equations, and mathematical physics. He specializes in the analysis of dispersive partial differential equations, with particular emphasis on Schrödinger's equation, wave equations, and Dirac equations. His work often involves studying oscillatory and singular integrals, wave operators, and time-decay estimates for various dispersive PDEs. A significant portion of his research examines how obstructions at threshold energies affect dispersive estimates, particularly in different dimensions. Since September 2017, his work has been partially supported by the Simons Foundation under grant #511825.

His recent publications (2021-2025) demonstrate a consistent focus on extending dispersive estimates to fractional order Schrödinger operators, higher dimensional settings, and exploring the behavior of wave operators in various contexts. A notable trend is his work with collaborators (particularly M.B. Erdogan and M.J. Goldberg) on understanding threshold obstructions across different dimensional settings for Dirac and Schrödinger equations. His research spans both theoretical developments and practical applications in mathematical physics.

Dr. Green has received several prestigious awards and recognitions:

• Rose-Hulman Board of Trustees Outstanding Scholar Award Winner (2022)
• Simons Collaboration Grant (2017-2022)
• Simons Travel Grant from the American Mathematical Society (2012-2015)
• Young Alumni Award from Albion College (2014)
• Brahana TA Instructional Award from University of Illinois (2009)

Dr. Green actively mentors undergraduate researchers, having supervised several students including Casey Garner (2018-19), and more recently Connor Lane, Benjamin Lyons, Shyam Ravishankar, and Aden Shaw (2023-24) who co-authored a paper published in the Journal of Differential Equations. He organizes the Rose-Hulman Mathematics Seminar, which features presentations by faculty, visiting professionals, and students. His research has been consistently supported by external funding, most notably the Simons Foundation grant that has enabled his continued work in dispersive PDEs.

While specific laboratory information isn't provided in the materials, Dr. Green appears to lead a research group focused on mathematical analysis of dispersive equations, collaborating extensively with colleagues at the University of Illinois and other institutions. His work bridges pure mathematical analysis with applications in quantum mechanics and mathematical physics.