Dr. Anudeep Kumar Arora

   Assistant Professor of Mathematics

   Office: Science & Technology Building 425

   Phone: (910) 672-2072

   Email: fanudeepkumar@uncfsu.edu

   Personal Homepage: https://sites.google.com/view/a-k-a/home

BIOGRAPHY

An engineer-turned-mathematician, Dr. Anudeep Kumar Arora is an Assistant Professor of Mathematics at Fayetteville State University. He earned his Ph.D. in Applied Mathematics from Florida International University, where his research focused on nonlinear partial differential equations with nonlocal terms. Before joining Fayetteville State University, he held postdoctoral positions at the University of Illinois at Chicago, working on variational methods, and at the University of Rochester.

Before entering academia, Dr. Arora worked as a Project Engineer in industry and earned his Bachelor's degree in Mechanical Engineering. His current research interests include nonlinear PDEs, variational methods, and applied analysis.

Beyond mathematics, he values creativity, and culture as sources of inspiration that enrich both his teaching and research.

Fun Fact: When not working on equations, he enjoys listening to music and hopes to learn a musical instrument someday.

TEACHING

MATH 130 Pre-calculus Mathematics II  
MATH 412 Advanced Calculus

RESEARCH INTERESTS

Nonlinear PDEs
Variational Methods
Applied Analysis
Mathematical Physics

RECENT PUBLICATIONS

Self-bound vortex states in nonlinear Schrödinger equations with LHY correction (with C. Sparber). Nonlinear Differ. Equ. Appl., 30, (2022), Article No. 14.

Global behavior of solutions to the focusing generalized Hartree equation (with S. Roudenko). Michigan Math. J., 71(3), (2022), 619-672.

Scattering below the ground state for the 2d radial nonlinear Schrödinger equation (with B. Dodson and J. Murphy). Proc. Amer. Math. Soc., 148(4), (2020), 1653-1663.

Well-posedness and blow-up properties for the generalized Hartree equation (with S. Roudenko). J. Hyperbolic Differ. Equ., 17(4), (2020), 727-763.

On the focusing generalized Hartree equations (with S. Roudenko and K. Yang). Math. in Appl. Sci. and Eng., 1(4), (2020), 383-402.

Scattering of radial data in the focusing NLS and generalized Hartree equation. Discrete Contin. Dyn. Syst. Series-A, 39 (2019), 6643-6668.

Exponential bases on two dimensional trapezoids (with L. De Carli), Proc. Amer. Math. Soc. 143(7), (2015), 2893-2903.