The applied analysis research group studies mathematical problems arising from physical, chemical, geophysical, biophysical, and materials sciences. These problems often are described by time-dependent partial, ordinary, or integral differential equations, together with sophisticated boundary conditions, interface conditions, and external forcing. Nonlinear dynamical systems offer a geometrical and topological framework for detecting, understanding, and quantifying complex phenomena of these time-dependent differential equations. Partial differential equation theory allows us to correctly formulate well-posed problems and to examine behaviors of solutions, setting the stage for efficient numerical simulations. Nonlocal equations arise from macroscopic modeling of stochastic dynamical systems with L茅vy noise and from modeling long-range interactions, and consequently give an understanding of anomalous diffusions.
Department of Applied Mathematics
Applied Analysis
Faculty with a Primary or Secondary Interest in Applied Analysis
Sergey Nadtochiy
Professor of Applied Mathematics
Jinqiao (Jeffrey) Duan
Professor Emeritus of Applied Mathematics
Arthur Lubin
Associate Professor of Applied Mathematics
Igor Cialenco
Professor of Applied Mathematics
Xiaofan Li
Professor of Applied Mathematics
Associate Dean, College of Computing
Kiah Wah Ong
Associate Chair and Director of Undergraduate Studies of the Department of Applied Mathematics
Associate Teaching Professor of Applied Mathematics
Fred J. Hickernell
Professor of Applied Mathematics
Vice Provost for Research
Tomasz Bielecki
Director, Master of Mathematical Finance
Professor of Applied Mathematics
Affiliate Professor, Stuart School of Business
Shuwang Li
Professor of Applied Mathematics
Affiliated Faculty
Fred Weening
Associate Teaching Professor of Applied Mathematics
Related Seminars
- Mathematical Finance, Stochastic Analysis, and Machine Learning Seminar
- Stochastic and Multiscale Modeling and Computation Seminar
Recent Research Grants
- NSF DMS- 2309798 (PI S. Li), Collaborative Research: : Mathematical modeling and computation of morphological instabilities in reactive fluids driven out of equilibrium. Start date: 07/01/2023; End date: 06/30/26. $242,677. Shuwang鈥檚 Role: PI.
- NSF DMS- 2244553, REU Site: Summer Undergraduate Research Experience (SURE) at Illinois Tech. Start date: 05/01/2023; End date: 04/30/2026. $404,893. Shuwang鈥檚 Role: Senior personnel (PI: Yuhan Ding).
- NSF DMS-2205751 (PI S. Nadtochiy), 2022鈥2025.NSF CAREER Grant DMS-1855309 (PI S. Nadtochiy), 2017鈥2022.
- NSF (PI X. Li and Co-PI J. Duan): Theoretical and Numerical Studies of Nonlocal Equations Derived from Stochastic Differential Equations with L茅vy Noises, 2016-2020.
- NSF (PI J. Duan and Co-PI X. Li): CBMS Conference: Nonlocal Dynamics 鈥 Theory, Computation and Applications, 2017-2018.
Recent Publications
- Dong, H., Zhao, Z., Li, S. et al. Second Order Convergence of a Modified MAC Scheme for Stokes Interface Problems. J Sci Comput 96, 27 (2023). https://doi.org/10.1007/s10915-023-02239-w
- Tang, X., Li, S., Lowengrub, J.S. et al. Phase field modeling and computation of vesicle growth or shrinkage. J. Math. Biol. 86, 97 (2023). https://doi.org/10.1007/s00285-023-01928-2
- A. Barua, R. Chew, S. Li, et al. Sharp-interface problem of the Ohta-Kawasaki model for symmetric diblock copolymers, Journal of Computational Physics 481, 112032, (2023).https://doi.org/10.1016/j.jcp.2023.112032
- Z. Jin, Y. Cao, S. Li, W. Ying and M. Krishnamurthy. A Kernel-Free Boundary Integral Method for 2-D Magnetostatics Analysis. IEEE Transactions on Magnetics, vol. 59, no. 4, pp. 1-19, April 2023, Art no. 7400319, doi: 10.1109/TMAG.2023.3247444
- H Feng, A Barua, S Li, X Li. Boundary integral simulations of boundary layers in linear viscoelastic flow. Physics of Fluids 35, 023108 ( 2023). https://doi.org/10.1063/5.0138344
- Lu, MJ., Hao, W., Hu, B. et al. Bifurcation analysis of a free boundary model of vascular tumor growth with a necrotic core and chemotaxis. J. Math. Biol. 86, 19 (2023). https://doi.org/10.1007/s00285-022-01862-9
- G. Alonso Alvarez, S. Nadtochiy, and K. Webster 鈥淥ptimal brokerage contracts in Almgren-Chriss model.鈥 To appear in SIAM Journal on Financial Mathematics
- S. Nadtochiy and M. Shkolnikov 鈥淪tefan problem with surface tension: global existence of physical solutions under radial symmetry.鈥 Probability Theory and Related Fields, published online, 2023
- S. Nadtochiy, M. Shkolnikov, and X. Zhang 鈥淪caling limits of external multi-particle DLA on the plane and the supercooled Stefan problem.鈥 To appear in Annales de l鈥橧nstitut Henri Poincare
- J.-F. Chassagneux, S. Nadtochiy, and A. Richou 鈥淩eflected BSDEs in non-convex domains.鈥漃robability Theory and Related Fields, 183:1237-1284, 2022
- S. Nadtochiy 鈥淎 simple microstructural explanation of the concavity of price impact. Mathematical Finance, 32(1):78-113, 2022
- I. Ekren and S. Nadtochiy 鈥淯tility-based hedging and indifference price of contingent claims in Almgren-Chriss model with temporary impact.鈥 Mathematical Finance, 32(1):172-225, 2022
- F. Delarue, S. Nadtochiy and M. Shkolnikov 鈥淕lobal Solution to Super-cooled Stefan Problem with Blow-ups: Regularity and Uniqueness.鈥 Probability and Mathematical Physics, 3(1):171-213, 2022
- S. Nadtochiy and M. Shkolnikov 鈥淢ean Field Systems on Networks, with Singular Interaction through Hitting Times.鈥 Annals of Probability, 48(3):1520鈥1556, 2020
- R. Gayduk and S. Nadtochiy 鈥淐ontrol-Stopping Games for Market Microstructure and Beyond.鈥 Mathematics of Operations Research, 45:1289鈥1317, 2020