Angel V. Kumchev, Ph.D.

Professor & Assistant Chair

Dr. Angel V. Kumchev

Contact Info

Phone:
410-704-2983
Office:
7800 York Road, Room 323
Email:
akumchev@towson.edu

Education

Ph.D., Mathematics, University of South Carolina, 2001
M.S. & B.S., Mathematics, Plovdiv University, 1996

Areas of Expertise

Analytic number theory
Harmonic analysis
Optimization

Biography

Dr. Angel Kumchev, a native of Bulgaria, received an undergraduate degree in Mathematics from Plovdiv University (Bulgaria) and a Ph.D. in Mathematics from the University of South Carolina. He joined Towson University in the Fall of 2005, after holding postdoctoral positions at the University of Toronto (Canada) and the University of Texas at Austin. His mathematical research is focused primarily on the distribution of prime numbers and on additive prime number theory (i.e., problems of the Waring-Goldbach type) and on the interface between number theory and harmonic analysis. Indeed, all but a handful of his almost 50 research papers fall in at least one of those categories, and many belong to both. He has done also work on exponential sums and their applications to various questions in analytic number theory and on the occasional odd problem in other areas of mathematics (analysis, algebra) that leads to questions of number theoretic nature.  

Dr. Kumchev's teaching at Towson stretches from lower-level college mathematics, through upper-level mathematics courses, to applied mathematics courses in our APIM graduate program. In the past, he has been involved in revisions of our Calculus III course and our senior seminar and in the maintenance of the Mathematica labs for the calculus sequence at TU. Presently, he is part of the efforts to revise our “transition-to-proofs” course and to coordinate our calculus sequence. Through his work for TU’s Applied Mathematics Laboratory (AML), Dr. Kumchev has also been a contributor to the departmental push to engage students in undergraduate research in mathematics. He served as faculty supervisor of two AML teams (2010-2011 and 2012-2013) as well as the Lab’s director for five years (2013-2018).

Recent Publications

  • Explicit boudns for large gaps between cubefree integers (with W. McCormick, N. McNew, A. Park, R. Scherr, and W. Ziehr). To appear in “Combinatorial and Additive Number Theory VI” (Proceedings of the CANT Workshops, New York, NY: May 24-27, 2022 and May 23-26, 2023), Springer, Cham; 2024,
  • A framework for discrete bilinear spherical averages and applications to -improving estimates (with T. Anderson and E. Palsson). Colloquium Mathematicum 175 (2024), 55–76.
  • Short interval results for powerfree polynomials over finite fields (with N. McNew, and A. Park). International Journal of Number Theory 20 (2024), 867–892.
  • Explicit boudns 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), Paper 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), Paper 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, 371-383; 2021.