Nick Anderson
I am an assistant professor at BYU. From 2016 to 2019 I was an assistant adjunct professor (postdoc) at UCLA. During the Spring semester 2017 I was a postdoctoral research associate at MSRI in the Analytic Number Theory program. I received my PhD in 2016 from UIUC under the direction of Scott Ahlgren. I completed my BS in mathematics with a minor in physics in 2011 at BYU.
My research interests are in number theory. I am particularly interested in arithmetic aspects of automorphic forms and their relation to (in no particular order) invariants of quadratic number fields, hyperbolic geodesics, class numbers, L-functions, and additive number theory.
Here is my CV.
Contact:
nick [at] math [dot] byu [dot] edu
Office 328 TMCB
Selected Papers
- Asymptotic distribution of traces of singular moduli (with W. Duke)
submitted. [arxiv] - Zeros of GL2 L-functions on the critical line (with J. Thorner)
Forum Math., to appear. [arxiv] - On a theorem of Davenport and Schmidt (with W. Duke)
Acta Arith., to appear. [arxiv] - The Minkowski Chain and Diophantine approximation (with W. Duke)
J. Theor. Nombres Bordeaux, to appear. [arxiv] - Modular invariants for real quadratic fields and Kloosterman sums (with W. Duke)
Algebra & Number Theory, to appear. [arxiv] - Markov spectra for modular billiards (with W. Duke)
Math. Annalen 373 (2019), no. 3-4, 1151-1175. [arxiv] [journal] - Level reciprocity in the twisted second moment of Rankin-Selberg L-functions (with E. M. Kiral)
Mathematika 64 (2018), no. 3, 770-784. [arxiv] [journal] - Shifted polyharmonic Maass forms for PSL(2,Z) (with J. Lagarias and R. Rhoades)
Acta Arith. 185 (2018), 39-79. [arxiv] [journal] - A polyharmonic Maass form of depth 3/2 for SL2(Z) (with S. Ahlgren and D. Samart)
J. Math. Anal. Appl. 468 (2018), no. 2, 1018-1042. [arxiv] [journal] - Vector-valued modular forms and the mock theta conjectures
Res. Number Theory (2016) 2:32. [arxiv] [journal] - Kloosterman sums and Maass cusp forms of half integral weight for the modular group (with S. Ahlgren)
Int. Math. Res. Notices, rnw234 (2016), 1-79. [arxiv] [journal] - Algebraic and transcendental formulas for the smallest parts function (with S. Ahlgren)
Adv. Math. 289 (2016) 411-437. [arxiv] [journal] - Singular invariants and coefficients of weak harmonic Maass forms of weight 5/2
Forum Math. 29 (2017), no. 1, 7-29. [arxiv] [journal] - Periods of the j-function along infinite geodesics and mock modular forms
Bull. Lond. Math. Soc. 47 (2015), 407-415. [arxiv] [journal] - Classification of congruences for mock theta functions and weakly holomorphic modular forms
Q. J. Math. (2014) 65 (3): 781-805. [arxiv] [journal]
You can find a complete list of papers here.
Teaching
In Winter 2020 I am teaching Math 290: Fundamentals of Mathematics and Math 371: Introduction to Abstract Algebra. I am also supervising a Python programming lab [Fall Labs] [Winter Labs] See the teaching page for my previous teaching.
Papers
- Non-convex geometry of numbers and continued fractions
with W. Duke, Z. Hacking, and A. Woodall, submitted. [arxiv] - Asymptotic distribution of traces of singular moduli
with W. Duke, submitted. [arxiv] - Odd, spoof perfect factorizations
with the BYU Computational Number Theory Group, J. Number Theory, to appear. [arxiv] - Zeros of GL2 L-functions on the critical line
with J. Thorner, Forum Math., to appear. [arxiv] - On a theorem of Davenport and Schmidt
with W. Duke, Acta Arith., to appear. [arxiv] - The Minkowski chain and Diophantine approximation
with W. Duke, J. Theor. Nombres Bordeaux, to appear. [arxiv] - Modular invariants for real quadratic fields and Kloosterman sums
with W. Duke, Algebra & Number Theory, to appear. [arxiv] - Markov spectra for modular billiards
with W. Duke, Math. Annalen 373 (2019), no. 3-4, 1151-1175. [arxiv] [journal] - Level reciprocity in the twisted second moment of Rankin-Selberg L-functions
with E. M. Kiral, Mathematika 64 (2018), no. 3, 770-784. [arxiv] [journal] - Shifted polyharmonic Maass forms for PSL(2,Z)
with J. Lagarias and R. Rhoades, Acta Arith. 185 (2018), 39-79. [arxiv] [journal] - A polyharmonic Maass form of depth 3/2 for SL2(Z)
with S. Ahlgren and D. Samart, J. Math. Anal. Appl. 468 (2018), no. 2, 1018-1042. [arxiv] [journal] - Images of Maass-Poincare series in the lower half-plane
with K. Bringmann and L. Rolen, L-functions and automorphic forms, Contrib. in Math. and Comp. Science 10, Springer 2017. [arxiv] [book] - Vector-valued modular forms and the seventh order mock theta functions
Analytic number theory, modular forms and q-hypergeometric series, 11-23, Springer Proc. Math. Stat., 221, Springer, Cham, 2017. [pdf] [book] - Vector-valued modular forms and the mock theta conjectures
Res. Number Theory (2016) 2:32. [arxiv] [journal] - Kloosterman sums and Maass cusp forms of half integral weight for the modular group
with S. Ahlgren, Int. Math. Res. Notices, rnw234 (2016), 1-79. [arxiv] [journal] - Algebraic and transcendental formulas for the smallest parts function
with S. Ahlgren, Adv. Math. 289 (2016) 411-437. [arxiv] [journal] - Singular invariants and coefficients of weak harmonic Maass forms of weight 5/2
Forum Math. 29 (2017), no. 1, 7-29. [arxiv] [journal] - Periods of the j-function along infinite geodesics and mock modular forms
Bull. Lond. Math. Soc. 47 (2015), 407-415. [arxiv] [journal] - Euler-like recurrences for smallest parts functions
with S. Ahlgren, Ramanujan J. 36 (2015), special issue in memory of Basil Gordon, 237-248. [arxiv] [journal] - Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function
with S. Ahlgren, Res. Number Theory (2015) 1:10. [arxiv] [journal] - Classification of congruences for mock theta functions and weakly holomorphic modular forms
Q. J. Math. (2014) 65 (3): 781-805. [arxiv] [journal] - Hecke grids and congruences for weakly holomorphic modular forms
with S. Ahlgren, Contemp. Math. 627 (2014). [arxiv] [book] - Effective congruences for mock theta functions
with H. Friedlander, J. Fuller, H. Goodson, Mathematics (2013), 1, 100-110. [arxiv] - Hecke-type congruences for two smallest parts functions
Int. J. Number Theory, 09, 713-728 (2013). [arxiv] [journal] - Divisibility properties of coefficients of level p modular functions for genus zero primes
with P. Jenkins, Proc. Amer. Math. Soc. 141 (2013), 41-53. [arxiv] [journal]
If you would like to see my thesis, here it is, but I recommend that you look at the individual papers instead (8, 9, 11, and 12 above).
Awards and Honors
- National Science Foundation Grant, 2017-2021, DMS-1701638 (co-PI with W. Duke)
- Plenary speaker at PANTS XXVIII (2017)
- Plenary speaker at TORA VII (2016)
- 2016 Bateman Prize (excellence in number theory research)
- Dissertation Completion Fellowship (2015-2016)
- 2015 Bateman Fellowship (excellence in number theory research)
- 2014-2016 Illinois ARCS Scholar (research grant)
Current Teaching
Winter 2021: Math 487 (Number Theory) and Math 371 (Introduction to Abstract Algebra)UIUC TA teaching awards committee (2015-2016)
Previous Teaching
Fall 2020 (UCLA): Math 290 (Fundamentals of Mathematics) and Math 113 (Calculus II)
Winter 2020 (UCLA): Math 290 (Fundamentals of Mathematics) and Math 371 (Introduction to Abstract Algebra)
Fall 2019 (UCLA): Math 290 (Fundamentals of Mathematics)
Spring 2019 (UCLA): Math 32B (Multivariable Calculus) and Math 33A (Linear Algebra)
Fall 2018 (UCLA): Math 205A (Analytic Number Theory) and Math 31B (Integration and Infinite Series)
Summer 2018 (UCLA): Boot Camp: Linear Algebra for incoming graduate students
Spring 2018 (UCLA): Math 132 (Complex Analysis) and Math 32A (Multivariable Calculus)
Winter 2018 (UCLA): Math 3B (Calculus for Life Sciences)
Fall 2017 (UCLA): Math 131A (Real Analysis) and Math 33B (Differential Equations)
Fall 2016 (UCLA): Math 31B (Integration and Infinite Series)
Fall 2014 (UIUC): Math 220 (Calculus I) - full instructor
Spring 2013 (UIUC): Math 220 (Merit Calculus I) - TA
Fall 2012 (UIUC): Math 241 (Merit Calculus III) - TA
Spring 2012 (UIUC): Math 241 (Merit Calculus III) - TA
Fall 2011 (UIUC): Math 221 (Calculus I) - TA
Awards and Honors
- UCLA Distinguished Teaching Award (2018)
- UIUC Campus Award for Excellence in Undergraduate Teaching (2016)
- UIUC College of LAS Award for Excellence in Undergraduate Teaching (2016)
- UIUC Mathematics Departmental TA Instructional Award (2015)
- UIUC List of teachers ranked as excellent by their students (every semester in which I taught)
