Curriculum vitae

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Last updated on October 14, 2017

Personal Information
Name:Byungchul Cha
Address:2400 Chew st, Allentown, PA 18104, U.S.A.
Telephone:+1 (484) 664-3920
E-mail:cha@muhlenberg.edu
Homepage:http://mathcs.muhlenberg.edu/~cha/
Employment
2013- Associate Professor of Mathematics, Muhlenberg College, Department of Mathematics and Computer Science, Allentown, Pennsylvania, U.S.A.
2007-2013 Assistant Professor of Mathematics, Muhlenberg College, Department of Mathematics and Computer Science, Allentown, Pennsylvania, U.S.A.
2004-2007 Visiting Assistant Professor, Hendrix College, Department of Mathematics and Computer Science, Conway, Arkansas, U.S.A.
2003-2004 Lecturer, Johns Hopkins University, Department of Mathematics, Baltimore, Maryland, U.S.A.
Education
1997-2003 Ph.D. in Mathematics, Thesis: Vanishing of Some Cohomology Groups and Bounds for the Order of Shafarevich-Tate Groups of Elliptic Curves, Johns Hopkins University, Advisors: V. Kolyvagin and C. Popescu.
1990-1994 B.S. in Mathematics, Korea Advanced Institute of Science and Technology, Daejeon, South Korea.
Research Interests
Algebraic number theory and analytic number theory.
Publications
2017 (with E. Nguyen ('16) and B. Tauber ('16)) "Quadratic Forms and Their Berggren Trees", Journal of Number Theory, (2017) to appear.
2017 "The summatory function of the Moebius function in function fields", Acta Arithmetica 179 (2017) no. 4, 375-395.
2017 (with D. Fiorilli and F. Jouve) "Independence of the zeros of elliptic curve L-functions over function fields", International Mathematics Research Notices, doi: 10.1093/imrn/rnw087.
2016 (with D. Fiorilli and F. Jouve) "Prime number races for elliptic curves over function fields", Annales scientifiques de lEcole normale superieure 49 fascicule 5.
2015 (with S. Bae and H. Jung) "Moebius function in short intervals for function fields", Finite Fields and Their Applications 34 (2015) 235-249.
2011 (with B.-H. Im) "Chebyshev's bias in Galois extensions of global function fields", Journal of Number Theory 131 (2011) 1875-1886.
2010 (with S. Kim) "Biases in the prime number race of function fields", Journal of Number Theory 130 (2010) 1048-1055.
2008 "Chebyshev's bias in function fields", Compositio Mathematica 144 (2008) 1351-1374.
2007"Special units and ideal class groups of extensions of imaginary quadratic fields", Mathematical Proceedings of the Cambridge Philosophical Society, 143 (2007) 265-270.
2007 "Transcendental functions, initial value problems and a different approach to calculus II, College Math Journal, September (2007) 288-296.
2005 "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.
External Grants and Awards
2016-2019REU Site Grant (PI: Eugene Fiorini, Co-PI: Byungchul Cha, NSF-DMS 1560019) Research Challenges of Identifying Integer Sequences Using the OEIS, to support summer mathematics REU programs at Muhlenberg College.
2015-2016Minigrant from The Center for Undergraduate Research in Mathematics (CURM) to support undergraduate research at Muhlenberg.
2005-2006National Project NExT Fellowship (sterling dot).
Mathematics Courses Taught
Muhlenberg Linear algebra, differential equations, number theory, introductory statistics, calculus I and III.
Hendrix Analysis, algebra, linear algebra, differential equations, computational number theory, calculus I and II, precalculus, liberal arts math, and mathematical problem solving seminar.
Hopkins Calculus I, II, III, linear algebra, elliptic curves and cryptography (new course), putnam problem solving seminar, and qualifying exam seminar.
Undergraduate Research Supervised
2017-2018 Daniel DeRemigi (Muhlenberg 2018) and Justin Greenbaum (Muhlenberg 2018), "Pythagorean trees and Romik systems". Independent research project.
2016-2017 Grace Ohanian (Muhlenberg 2017), Eric Jovinelly (Muhlenberg 2017), and Gianna Barres "Searching for new Berggren Trees". Independent research project.
2015-2016 Emily Nguyen (Muhlenberg 2016) and Brandon Tauber (Muhlenberg 2016), "Generalization of Pythagorean trees". Independent research project, funded by CURM.
2014 Jeremy Fus (Muhlenberg 2015), "Parametrizing Pythagorean triples and its generalization". Independent research project.
2014 Benjamin Nassau (Muhlenberg 2015), "Apollonian Circle Packings". Independent research project.
2014 Emily Nguyen (Muhlenberg 2016), "Zaremba's conjecture". Independent research project.
2010 Samantha Unger (Muhlenberg 2010), "Benford's Law and Other Applications in Fraud Detection". Independent research project.
2006 Alex Cameron (Hendrix 2006), "Counting Ring Homomorphisms", published in PME journal Spring 2010, Vol 13, pages 65-67. Awarded Student Presentation Prize at the 2006 Oklahoma-Arkansas MAA meeting.
2005 Douglas Woten (Hendrix 2005), "Reduction Maps on Elliptic Curves", Hendrix College senior thesis.
Selected Presentations
Mar 2016A Tree of Pythagorean Triples and Its Generalization, Philadelphia Area Number Theory Seminar, Bryn Mawr College, Bryn Mawr, PA.
Jul 2015Mobius function in function fields, Philadelphia Area Number Theory Seminar, Bryn Mawr College, Bryn Mawr, PA.
Feb 2015Bias in prime numbers for elliptic curves over function fields, Philadelphia Area Number Theory Seminar, Bryn Mawr College, Bryn Mawr, PA.
Jun 2014Mobius Disjointness in function fields, KIAS Number theory seminar, Korea Institute of Advanced Science, Seoul, Korea.
Jun 2014Thin orbits: Zaremba, Apollonius and Pythagoras, Konkuk University Colloquium, Seoul, Korea.
May 2014Mobius Disjointness in function fields, the 28th Automorphic Forms Workshop, Moab, UT.
Dec 2013Prime number races in function fields, Number Theory Workshop, Busan, Korea.
Jun 2013Analytic Number Theory in function fields, Intensive lecture series, KAIST, Daejeon, Korea.
Mar 2012Prime number race in function fields, Algebra and Representation Theory seminar, University of Oklahoma, Norman, OK.
Nov 2011Prime number race in function fields, Five College Number Theory Seminar, Amherst, MA.
Jun 2011Prime number races in function fields, Number theory and arithmetic geometry, Pohang University of Science and Technology, Pohang, Korea.
Jun 2011Independence of zeta zeros and its applications in analytic number theory, KIAS Number theory seminar, Korea Institute of Advanced Science, Seoul, Korea.
Jun 2011Bounds of partial sum of Moebius function in function fields, Number theory seminar, KAIST, Daejeon, Korea.
Mar 2011Bounds of the summatory function of Moebius function in function fields, the 25th Automorphic Forms Workshop, Oregon State University, Corvallis, OR.
Feb 2011Counting prime numbers, or listening to them, ACM/MAA Lecture Series, Mount St. Mary's University, Emmitsburg, MD.
Oct 2010Bounds of the summatory function of Moebius function in function fields, Algebra and Number Theory Seminar, Penn State University, State College, PA.
Mar 2010Counting prime numbers, or listening to them, Moravian College mathematics colloquium, Bethlehem, PA.
Dec 2009Growth rate of the summatory function of Moebius function in function fields, The 11th Palmetto Number Theory Series, the University of South Carolina, Columbia, SC.
Nov 2009Chebyshev's bias, prime number races and zeros of L-functions, Algebra Seminar, Wesleyan University, Middletown, CT.
Oct 2009Linear independence of zeta zeros in function fields, Number Theory Seminar, University of Illinois at Chicago, IL.
Jun 2009Linear independence of zeros of L-functions, KIAS Number theory seminar, Korea Institute of Advanced Science, Seoul, Korea.
Mar 2008Chebyshev's Bias in Function Fields, AMS Special Session on L-functions and Automorphic Forms, New York, NY.
Services
Referee and review activities
Journals Journal of Number Theory, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Bulletin of the Korean Mathematical Society, The Algorithmic Number Theory Symposium (ANTS), MAA Math Magazine.
Grant NSA Mathematical Sciences Program.
To the math community
2007- Volunteer for indexing Classroom Capsule for MAA journals.
Jan 2007Organized MAA Contributed Paper Session, Use of Technology in Abstract Algebra and Number Theory, The Joint Mathematics Meetings, New Orleans, LA.
2006, 2007Judge for MAA Undergraduate Poster Sessions at the Joint Meetings.
To the institution
2012-Organizer for Annual Muhlenberg High School Math Contest.
2009-Served at various college committees, including Faculty Evaluation Committee, College Committee on Campus Life, Library Committee, Fitness and Athletics Committee, Social Judicial Board, and Multicultural Advisory Board.
2008Served at a faculty search committee for math department, Muhlenberg College.
2008- Maintaining the weekly math problem solving activity Problem of the week in the Muhlenberg community.
Professional Memberships
Mathematical Association of America, American Mathematical Society.