Analysis and Applications

Applied mathematics brings together tools from every corner of the field to study scientific problems facing the industry, technology, medicine, and society at large.  Often our goal is to illuminate hidden structures underlying a host of natural phenomena with the use of simplified models, but the resulting insights and new methodologies can also lead to breakthroughs in solving complex real-world problems.  Applied mathematics has a history of encountering deep theoretical obstacles which must be overcome before further progress can be made. Indeed diverse topics such as Fourier analysis, differential operators, generalized functions, differential manifolds, singularity theory, Banach algebras, and random matrix theory all have origins in applications.

Some research includes fundamental topics in Analysis (Harmonic, Complex, and Functional), and their application to the study of Ordinary and Partial Differential Equations arising in Physics, Engineering, and Mathematical Biology.  Our research in dynamical systems employs classical analytic methods as well as numerical methods (sometimes with mathematically rigorous a-posteriori validation) and computational topology in order to analyze qualitative phenomena such as bifurcations, pattern formation, and the onset of chaotic dynamics.  Research in Control Theory is primarily concerned with stabilization of systems of ordinary differential equations and difference equations with delay.  Research taking a probabilistic approach includes stochastic differential equations arising in financial models and topological aspects of random fields.  Further activity in this research group includes inverse problems, free boundary problems, conformal mapping, and analytic combinatorics.


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barry lin   eric jay owl2    

Dr. Barry Booton
Dr. Yuandan Lin Dr. Erik Lundberg Dr. Jason Mireles-James Dr. Francis Motta    
 vince yoram  tomas necibe   yuan  xiao  
Dr. Vincent Naudot Dr. Yoram Sagher Dr. Tomas Schonbek   Dr. Necibe Tuncer Dr. Yuan Wang Dr. Xiao-Dong Zhang  


Grants and Current Projects


nsf Fine Structure in Hamiltonian Systems
PI: Jason Mireles-James
Funding Agency: 
National Science Foundation
Amount Awarded:  $299,717.00





imgProbabilistic and extremal problems of real and complex polynomials
PI: Erik Lundberg
Funding Agency: Simmons Foundation
Amount awarded: $42,000.





nsfModeling the Opioid and HIV Epidemics
Co-Director: Necibe Tuncer
Funding Agency: NSF
Awarded: $99,997





nsfModeling the Opioid and HIV Epidemics
Co-Director: Necibe Tuncer
Funding Agency: NSF
Awarded: $99,997





dukeDeep Chaos
Co-Director: William Kalies
Funding Agency: Duke University/DARPA
Awarded: $26,986



nsf Validated Computational Methods in Global Analysis and Application to Celestial Mechanics, 8/15/18-7/31/21
PI: Jason Mireles-James
Funding Agency: National Science Foundation
Amount Awarded: $131,975





aroA Combinatorial and Topological Framework for Deriving Dynamics from Data
Co-Director: William Kalies
Funding Agency: College of William & Mary/Army Research Office - Awarded: $228,620




dukeAn Adaptive Pipeline from Scientific Data to Models, 9/25/2018 - 7/31/2019
PI: Francis Motta
Funding Agency: Duke University/DARPA SD2
Amount Awarded: $41,230





nsfLinking Within-Host and Between-Host Infectious Disease Dynamics, 9/15/15 - 8/31/19
PI: Necibe Tuncer
Funding Agency: National Science Foundation
Amount Awarded: $92,517 



elDimitry Khavinson and Erik Lundberg:  Linear Holomorphic Partial Differential Equations and Classical Potential Theory. Mathematical Surveys and Monographs Volume: 232; 2018. American Mathematical Society.







elVincent Naudot: Etude locale et globale de champs de vecteurs: sur les variétés 
(Omn.Pres.Franc.) (French Edition) 









vnM. Cwikel, J. Peetre, Y. Sagher and H. Wallin (eds.):  Function Spaces and Applications: Proceedings of the US-Swedish Seminar held in Lund, Sweden, June 15-21, 1986 
(Lecture Notes in Mathematics) 
1988th Edition. 






ysbookMario Milman and Tomas Schonbek (eds.): Harmonic Analysis and Partial Differential Equations.
Contemporary Mathematics, Vol. 107. (Proceedings of a Conference, April 5-5, 1988).
American Mathematical Society.