- Assistant Department Chair: Towson University, 08/2023-present
- Professor: Towson University, 08/2016-present
- Acting Associate Dean, FCSM: Towson University, 07/2018-02/2019
- Associate Professor: Towson University, 08/2010-07/2016
- Assistant Professor: Towson University, 08/2005-07/2010
- Postdoc: University of Texas at Austin, 01/2003-07/2005
- Postdoc: University of Toronto, 07/2001-12/2002
- Ph.D. in Mathematics: University of South Carolina, 08/1997-08/2001
- B.S. and M.S. in Mathematics: Plovdiv University, 09/1991-07/1996
- Explicit bounds for large gaps between cubefree integers (with W. McCormick, N. McNew, A. Park, R. Scherr, and W. Ziehr), submitted.
- A framework for discrete bilinear spherical averages and applications to \(\ell^p\)-improving estimates (with T. Anderson and E. Palsson), submitted.
- Short interval results for powerfree polynomials over finite fields (with N. McNew and A. Park), to appear in International Journal of Number Theory.
- Explicit bounds for large gaps between squarefree integers (with W. McCormick, N. McNew, A. Park, R. Scherr, and W. Ziehr). Journal of Number Theory 254 (2024), 336-357.
- Discrete maximal operators for surfaces of higher codimension (with T. Anderson and E. Palsson). (La) Matematica 1 (2022), 442-479.
- The ergodic Waring-Goldbach problem (with T. Anderson, B. Cook and K. Hughes). Journal of Functional Analysis 282 (2022):109334, 39 pp.
- Hilbert transforms and the equidistribution of zeros of polynomials (with E. Carneiro, M. Das, A. Florea, A. Malik, M. Milinovich, C. Turnage-Butterbaugh, and J. Wang). Journal of Functional Analysis 281 (2021):109199, 25 pp.
- On a two-dimensional exponential sum. In “Combinatorial and Additive Number Theory IV” (Proceedings of the CANT Workshops, New York, NY: May 21-24, 2019 and June 1-5, 2020), Springer, Cham, 2021, pp. 371-383.
Recent Seminars and Conference Talks
- May 2023: New versions of old results on gaps between squarefree integers, CANT 2023, New York, NY.
- December 2020: Discrete maximal functions on surfaces of codimension >1, Purdue Analytic Number Theory and Harmonic Analysis Seminar, Purdue University, West Lafayette, IN (virtual).
- June 2020: Discrete maximal functions for surfaces of codimension 3, CANT 2020, New York, NY (virtual).
- March 2020: Diminishing ranges for Diophantine inequalities, MASON IV, Gettysburg, PA.
- Ph.D. Theses, external co-advisor:
- Huafeng Liu (Shandong University, 2017): On the Waring-Goldbach Problem with Almost Equal Summands.
- Taiyu Li (Shandong University, 2012): Additive Problems with Prime Numbers.
- Master’s Projects:
- Felipe Pizarro (2014): A Large-Scale Scheduling Problem Subject to Multiple Constraint Classes
- Amanda Williams (2012): Comparison Between AKS and Other Primality Tests
- Kelly Nulph (2009): An Attack on a Modified KMOV Cryptosystem
- Undergraduate Research Projects:
- REU Group (Summer 2022, jointly with Dr. N. McNew): Gaps Between Powerfree Integers.
- AML Team (2012/2013, jointly with Dr. M. Pemy): Mathematical Modeling of Segregation Patterns in Urban Areas.
- AML Team (2010/2011, jointly with Dr. A. Kolesnikov): Risk Analysis: Toxic Materials Transportation Security.
- Matthew Tiger (2009/2010): Infinite Series.
- at Towson University: College Algebra, Precalculus, Discrete Mathematics, Elementary Linear Algebra, Introduction to Abstract Mathematics, Calculus I, Calculus II, Calculus III, Honors Calculus I, Cryptography, Abstract Algebra I, Real Analysis I, Differential Equations, Linear Algebra, Number Theory, Abstarct Algebra II, Complex Analysis, Senior Seminar: Quadratic Reciprocity, Applied Mathematics Laboratory I; Linear and Nonlinear Programming*, Topics in Applied Operations Research*, Asymptotic and Perturbation Analysis*.
- at the University of Texas: Calculus I, Calculus II, Discrete Mathematics, Elementary Linear Algebra, Probability, Complex Analysis, Topics in Analysis: Distribution of Primes*.
- at the University of Toronto: Calculus, Introduction to PDEs.