Faculty Profiles

Byungchul Cha

Professor, Mathematics & Computer Science
Mathematics, Computer Science & Statistics
484-664-3920

[email protected]

Education

  • Ph.D., mathematics, Johns Hopkins University
  • B.S., mathematics, KAIST, South Korea

Teaching Interests

I teach a variety of math courses at Muhlenberg, ranging from introductory-level statistics and calculus to elective math courses such as number theory.

Research, Scholarship or Creative/Artistic Interests

My research interests lie in number theory. Currently, I study topics related to distribution of prime numbers in the context of function fields and dynamic systems related to arithmetical questions. I enjoy working on cool math problems with undergraduates.

  • Linear Algebra
  • Mathematics Independent Study/Research: Abstract Algebra
  • Mathematics Independent Study/Research: Number Theory
  • Mathematics Independent Study/Research: Binary Quadratic Forms
  • Mathematics Independent Study/Research:Approaching Lagrange Number
  • Statistical Analysis

Donald B. Hoffman Research Professor (AY 2019-2020)

  • B. Cha and D.-H. Kim, "Number Theoretical Properties of Romik’s Dynamical System," Bulletin of the Korean Mathematical Society, (2019).
  • B. Cha, E. Nguyen (’16) and B. Tauber (’16) "Quadratic Forms and Their Berggren Trees," Journal of Number Theory (2018).
  • B. Cha, D. Fiorilli and F. Jouve, "Prime Number Races for Elliptic Curves Over Function Fields,” Annales scientifiques de l'Ecole normale superieure (2016).

List of papers and preprints as of February 2019. (Available upon request.)

  • Lagrange Spectrum of Romik’s Dynamical System, in preparation. (2019). (with Dong Han Kim)
  • The Summatory Function of the Moebius Function in Function Fields, Acta Arithmetica 179 (2017) no. 4, 375-395. (with D. Fiorilli and F. Jouve)
  • Prime Number Races for Elliptic Curves over Function Fields, Annales scientifiques de l’Ecole normale superieure 49 fascicule 5 (2016) (with S. Bae and H. Jung)
  • Moebius Function in Short Intervals for Function Fields, Finite Fields and Their Applications 34 (2015) 235-249. (with B.-H. Im)
  • Chebyshev’s Bias in Galois Extensions of Global Function Fields, Journal of Number Theory 131 (2011) 1875-1886. 
  • Biases in the Prime Number Race of Function Fields, Journal of Number Theory 130 (2010) 1048-1055. (with S. Kim) 
  • Chebyshev’s Bias in Function Fields, Compositio Mathematica 144 (2008) 1351-1374. 
  • Special Units and Ideal Class Groups of Extensions of Imaginary Quadratic Fields, Mathematical Proceedings of the Cambridge Philosophical Society, 143 (2007) 265-270. 
  • Transcendental Functions, Initial Value Problems and a Different Approach to Calculus II, College Math Journal, September (2007) 288-296. 
  • Vanishing of Some Cohomology Groups and Bounds for the Order of Shafarevich-Tate Groups of Elliptic Curves, Journal of Number Theory, 111 (2005) 154-178.

Professional Website

https://sites.google.com/view/byungchulcha/


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