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Last updated on October 16, 2018
Personal Information | |
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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 | |
2018 | (with E. Nguyen '16 and B. Tauber '16) "Quadratic Forms and Their Berggren Trees", Journal of Number Theory, 185 (2018) 218-256. |
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 | |
2016-2019 | REU 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. |
2015-2016 | Minigrant from The Center for Undergraduate Research in Mathematics (CURM) to support undergraduate research at Muhlenberg. |
2005-2006 | National 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 2019) and Justin Greenbaum (Muhlenberg 2019), "Pythagorean trees and Romik systems". Independent research project. |
2016-2017 | Grace Ohanian (Muhlenberg 2018), Eric Jovinelly (Muhlenberg 2018), and Gianna Barres (Muhlenberg 2018) "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 | |
Jul 2018 | Lagrange spectrum for Romik's dynamical system, Philadelphia Area Number Theory Seminar, Bryn Mawr College, Bryn Mawr, PA. |
Jan 2018 | Berggren trees, Romik system and Lagrange Theorem, Joint Mathematics Meetings, Contributed Paper Session, San Diego, CA. |
Mar 2016 | A Tree of Pythagorean Triples and Its Generalization, AMS Sectional Meeting, Stony Brook, NY. |
Mar 2016 | A Tree of Pythagorean Triples and Its Generalization, Philadelphia Area Number Theory Seminar, Bryn Mawr College, Bryn Mawr, PA. |
Jul 2015 | Mobius function in function fields, Philadelphia Area Number Theory Seminar, Bryn Mawr College, Bryn Mawr, PA. |
Feb 2015 | Bias in prime numbers for elliptic curves over function fields, Philadelphia Area Number Theory Seminar, Bryn Mawr College, Bryn Mawr, PA. |
Jun 2014 | Mobius Disjointness in function fields, KIAS Number theory seminar, Korea Institute of Advanced Science, Seoul, Korea. |
Jun 2014 | Thin orbits: Zaremba, Apollonius and Pythagoras, Konkuk University Colloquium, Seoul, Korea. |
May 2014 | Mobius Disjointness in function fields, the 28th Automorphic Forms Workshop, Moab, UT. |
Dec 2013 | Prime number races in function fields, Number Theory Workshop, Busan, Korea. |
Jun 2013 | Analytic Number Theory in function fields, Intensive lecture series, KAIST, Daejeon, Korea. |
Mar 2012 | Prime number race in function fields, Algebra and Representation Theory seminar, University of Oklahoma, Norman, OK. |
Nov 2011 | Prime number race in function fields, Five College Number Theory Seminar, Amherst, MA. |
Jun 2011 | Prime number races in function fields, Number theory and arithmetic geometry, Pohang University of Science and Technology, Pohang, Korea. |
Jun 2011 | Independence of zeta zeros and its applications in analytic number theory, KIAS Number theory seminar, Korea Institute of Advanced Science, Seoul, Korea. |
Jun 2011 | Bounds of partial sum of Moebius function in function fields, Number theory seminar, KAIST, Daejeon, Korea. |
Mar 2011 | Bounds of the summatory function of Moebius function in function fields, the 25th Automorphic Forms Workshop, Oregon State University, Corvallis, OR. |
Feb 2011 | Counting prime numbers, or listening to them, ACM/MAA Lecture Series, Mount St. Mary's University, Emmitsburg, MD. |
Oct 2010 | Bounds of the summatory function of Moebius function in function fields, Algebra and Number Theory Seminar, Penn State University, State College, PA. |
Mar 2010 | Counting prime numbers, or listening to them, Moravian College mathematics colloquium, Bethlehem, PA. |
Dec 2009 | Growth 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 2009 | Chebyshev's bias, prime number races and zeros of L-functions, Algebra Seminar, Wesleyan University, Middletown, CT. |
Oct 2009 | Linear independence of zeta zeros in function fields, Number Theory Seminar, University of Illinois at Chicago, IL. |
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 2007 | Organized MAA Contributed Paper Session, Use of Technology in Abstract Algebra and Number Theory, The Joint Mathematics Meetings, New Orleans, LA. |
2006, 2007 | Judge 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. |
2008 | Served 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. |