Caroline Turnage-Butterbaugh

Education & Professional History

Wofford College, BA; Wake Forest University, MA; University of Mississippi, PhD

Previous Appointments

William W. Elliott Assistant Research Professor, Duke University, 2015-2018
Postdoctoral Fellow, Mathematical Sciences Research Institute, Spring 2017
Postdoctoral Research Fellow, North Dakota State University, 2014-2015
Postdoctoral Undergraduate Research Mentor, Williams College, Summer 2014

At Carleton since 2018.

Highlights & Recent Activity

NSF DMS-1902193 (2019-2023, PI)
NSF DMS-1854398 FRG (2019-2022, Senior Scientist Consultant)

Organizations & Scholarly Affiliations

American Mathematical Society
Association for Women in Mathematics
Mathematical Association of America
Math Alliance
National Association of Mathematicians

Current Courses

Fall 2022
MATH 232: Linear Algebra
MATH 282: Elementary Theory of Numbers
MATH 400: Integrative Exercise
Winter 2023
MATH 210: Calculus 3
MATH 236: Mathematical Structures
MATH 400: Integrative Exercise
Spring 2023
MATH 395: Introduction to Analytic Number Theory

Research Interests

My research interests lie in the field of analytic number theory. In particular, I study properties of L-functions (such as the Riemann zeta-function, Dedekind zeta-functions, Artin L-functions, and automorphic L-functions), their zeros, and class groups of number fields.

NSF DMS-1902193 (2019-2023, PI), and NSF DMS-1854398 FRG (2019-2022, Senior Scientist Consultant)

Research Related Travel & Talks

2023

Dynamics and Asymptotics in Algebra and Number Theory (invited speaker)
September 11-15, 2023
Bielefeld University
Bielefeld, Germany

Arithmetic, Algebra, and Algorithms (invited participant)
April 10-14, 2023
International Centre for Mathematical Sciences
Edinburgh, Scotland

Algebra/Number Theory Seminar
March 15, 2023
University of Rochester
Rochester, NY

2022

Number Theory Seminar
December 7 , 2022
Duke University
Durham, NC

Number Theory Days (invited speaker)
September 30 – October 1, 2022
École Polytechnique Fédérale de Lausanne
Lausanne, Switzerland

Duke University (research visit)
September 2, 2022
Durham, NC

American Institute of Mathematics (FRG research visit)
August 8-12, 2022
San Jose, California

ANTeater ’22 (invited speaker)
August 1-4, 2022
University of California – Irvine
Irvine, California

PIMS CRG Workshop on Moments of L-functions
July 25-29, 2022
University of Northern British Columbia
Prince George, BC, Canada (Virtual)

50 Years of Number Theory & Random Matrix Theory Conference
June 21-24, 2022
Institute for Advanced Study
Princeton, New Jersey

AWM Research Symposium Special Session: Number Theory (co-organizer)
June 16-19, 2022
The Institute for Mathematics and its Applications, University of Minnesota
Minneapolis, Minnesota

47th Annual New York Regional Graduate Mathematics Conference (plenary speaker)
April 2-3, 2022
Syracuse University
Syracuse, New York

American Institute of Mathematics (FRG research visit)
February 3 – March 25, 2022
San Jose, California

~~AMS Special Session: Number Theory at Non-PhD Granting Institutions II~~ (session cancelled)
TBD (was January 7, 2022)
Joint Mathematics Meetings (Conference Postponed)
Seattle, Washington

2021

Algebraic Geometry and Number Theory Seminar
October 20, 2021
Chalmers University of Technology / University of Gothenburg (Virtual)

Focused Research Group (FRG) Graduate Seminar
October 4, 2021
American Institute of Mathematics (Virtual)

American Institute of Mathematics (FRG research visit)
August 18 – 31, 2021
San Jose, California

Wofford College Summer Research Seminar
June 28, 2021
Spartanburg, South Carolina

Vanderbilt Number Theory Seminar
May 5, 2021
Vanderbilt University (Virtual)

Quebec-Vermont Number Theory Seminar
April 29, 2021
Université de Montréal (Virtual)

UVA Number Theory Seminar
April 23, 2021
University of Virginia (Virtual)

Purdue Analytic Number Theory and Harmonic Analysis seminar (PANTHA) (invited speaker)
March 31, 2021
Purdue University (Virtual)

KSU Number Theory Seminar
March 8, 2021
Kansas State University (Virtual)

Virtual Brazilian Number Theory Seminar (ViBraNT)
February 25, 2021
Universidade Federal de Minas Gerais, Brazil (Virtual)

UM Algebra and Number Theory Seminar
February 4, 2021
University of Mississippi (Virtual)

2020

Automorphic Forms and Arithmetic
August 30 – September 5, 2020
Mathematisches Forschungsinstitut Oberwolfach, Germany (Virtual)

MathFest (Project NExT Fellow)
July 28 – August 1, 2020
Philadelphia, PA (Virtual)

VaNTAGe Seminar
Tuesday, February 18, 2020
Broadcasting live from Northfield, MN!

Joint Mathematics Meetings (invited speaker and Project NExT fellow)
January 15-18, 2020
Denver, CO

2019

Duke University (research visit)
December 11-20, 2019
Durham, NC

Analytic Number Theory
November 3 – 9, 2019
Mathematisches Forschungsinstitut Oberwolfach, Germany

American Institute of Mathematics (FRG research visit)
August 27 – September 4, 2020
San Jose, CA

MathFest (Project NExT Fellow)
July 31 – August 3, 2019
Cincinnati, Ohio

NSF-CBMS Conference: L-functions and Multiplicative Number Theory (invited speaker)
University of Mississippi, May 20-24, 2019
Oxford, Mississippi

Analytic Aspects of Automorphic Forms (invited speaker)
Université de Lille, April 3-5, 2019
Lille, France

Value Distribution of Zeta and L-functions and Related Topics (invited speaker)
RIKEN Institute March 21 – 27, 2019
Wako, Japan

2018

CMS 2018 Winter Meeting (invited speaker)
Special Session: Distributions in Analytic Number Theory
Vancouver, Canada
December 7 – 10, 2018

University of Minnesota – Number Theory Seminar (invited speaker)
Minneapolis, MN
December 3, 2018

LMS-CMI Research School: New Trends in Analytic Number Theory (invited speaker)
Exeter, United Kingdom
August 13 – 17, 2018
slides

Max Planck Institute for Mathematics (research visit)
Bonn, Germany
July 1 – 31, 2018
• Number Theory Lunch Seminar (July 18, 2018)
• PLeaSANT Seminar (July 25, 2018)
Number Theory Seminar
Mathematical Institute, University of Cologne
Cologne, Germany
July 10, 2018
HCM School: L-functions: Open Problems and Current Methods (course lecturer)
Bonn, Germany
June 25 – 29, 2018
Perspectives on the Riemann Hypothesis
Bristol, United Kingdom
June 4 – 7, 2018
Institute for Advanced Study (research visit)
Princeton, New Jersey
May 7 -10, 2018
Number Theory Seminar
University of New South Wales Sydney
Sydney, Australia
March 13, 2018
Pure Maths Seminar
University of New South Wales Sydney
Sydney, Australia
March 13, 2018
Department Colloquium
University of New South Wales Canberra
Canberra, Australia
March 8, 2018
Joint Mathematics Meetings
San Diego, CA
January 10 – 13, 2018

2017

Department Colloquium
Oberlin College, Oberlin, OH
November 29, 2017
Algebra, Geometry, and Number Theory Seminar
Tufts University, Boston, MA
November 16, 2017
Mathematics & Statistics Department Colloquium
Elon University, Elon, NC
October 18, 2017
WIN4
Banff International Research Station, Canada
August 14 – 18, 2017
MCA 2017
Special Session Advances in algebraic and analytic number theory (co-organizer)
Montréal, Canada
July 24 – 28, 2017
SWIM 2017 (course lecturer)
Duke University, Durham, NC
July 20 – 30, 2017
Careers in Academia
AIM, San Jose, California
June 6 – 9, 2017
re:boot number theory 2017 (co-organizer)
Duke University, Durham, NC
June 1 – 3, 2017
AMS Spring Western Sectional Meeting
Special Session Analytic number theory and automorphic forms (invited speaker)
Washington State University
April 22 – 23, 2017
Algebraic Geometry and Number Theory Seminar
Rice University
April 11, 2017
MSRI Analytic Number Theory Semester Program
Connections for Women (invited speaker)
Program Member (postdoc)
MSRI, Berkeley, CA
January 17 – May 26, 2017
Joint Mathematics Meetings
AMS Special Session Analytic number theory and arithmetic (invited speaker)
MAA Invited Paper Session L-functions and other animals (co-organizer)
Atlanta, Georgia
January 4 – 7, 2016

2016

Number Theory Seminar
University of South Carolina
November 17, 2016
Harkness Table Series
Spartanburg Day School
October 21, 2016
Moments of zeta and correlations of divisor sums
AIM, San Jose, California
August 29 – September 2, 2016
WADE Into Research (invited speaker)
Wake Forest University, Winston-Salem, NC
June 24, 2016
SWIM (invited speaker)
Duke University, Durham, NC
June 21, 2016
Winthrop University REU (invited speaker)
Winthrop University, Rock Hill, SC
June 17, 2016
Number Theory Seminar
University of Illinois Urbana-Champaign
April 21, 2016
Department Colloquium
Wake Forest University, Winston-Salem, NC
April 6, 2016
Department Colloquium
Winthrop University, Rock Hill, SC
April 1, 2016
re:boot Number Theory 2016 (co-organizer)
Duke University, Durham, NC
March 17-20, 2016
30th Automorphic Forms Workshop
Wake Forest University, Winston-Salem, NC
March 7-10, 2016

2015

Computational Aspects of the Langlands Program (invited speaker)
ICERM, Providence, Rhode Island
November 8-21, 2015
Elementary, analytic, and algorithmic number theory: Research inspired by the mathematics of Carl Pomerance (invited speaker)
University of Georgia, Athens, GA
June 9-11, 2015
Analytic Methods in Elementary Number Theory (invited speaker)
AMS Special Session Southeastern Sectional
University of Alabama, Huntsville, AL
March 27-29, 2015
Department Colloquium
Williams College, Williamstown, MA
January 23, 2015
UNC-Duke Number Theory Seminar
Duke University, Durham, NC
January 21, 2015
2015 Joint Mathematics Meetings
San Antonio, TX
January 10-13, 2015

2014

New Approaches in Probabilistic and Multiplicative Number Theory
CRM, Montréal, Canada
December 8-12, 2014
Bounded Gaps Between Primes
AIM, Palo Alto, CA
November 17-21, 2014
Young Mathematicians Conference
Ohio State University, Columbus, Ohio
August 22-24, 2014
ENFANT & ELEFANT
Hausdorff Center, Bonn, Germany
July 11-18, 2014

Letters of Recommendation – Please read this note if you would like me to write you a letter of recommendation.

Current Courses

Fall 2022
MATH 232: Linear Algebra
MATH 282: Elementary Theory of Numbers
MATH 400: Integrative Exercise
Winter 2023
MATH 210: Calculus 3
MATH 236: Mathematical Structures
MATH 400: Integrative Exercise
Spring 2023
MATH 395: Introduction to Analytic Number Theory

Preprints

Twisted 2k-th moments of primitive Dirichlet L-functions: beyond the diagonal, with S. Baluyot, submitted, preprint available at https://arxiv.org/abs/2205.00641
On the Montgomery-Odlyzko method regarding gaps between zeros of the zeta-function, with D. A. Goldston and T. S. Trudgian, submitted, preprint available at https://arxiv.org/abs/2201.10676

Publications

Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function, with T. Trudgian and A. Simonič, Transactions of the American Mathematical Society, 375, no. 3 (2022), 3239-3265. [preprint] [journal]
Hilbert transforms and the equidistribution of zeros of polynomials, with E. Carneiro, M. K. Das, A. Florea, A. V. Kumchev, A. Malik, M. B. Milinovich, and J. Wang, Journal of Functional Analysis, 281 (2021), no. 9, Paper No. 109199, 25 pp. [preprint] [journal]
On a conjecture for l-torsion in class groups of number fields: from the perspective of moments, with L. B. Pierce and M. Matchett Wood, Mathematical Research Letters, 28, no. 2 (2021), pp. 575-621. [preprint] [journal]
An effective Chebotarev density theorem for families of number fields with an application to l-torsion in class groups, with L. B. Pierce and M. Matchett Wood, Inventiones Mathematicae, 219 (2020), no. 2, 701-778. [preprint] [journal]
Extremal primes of elliptic curves without complex multiplication, with C. David, A. Gafni, A. Malik, and N. Prabhu, Proceedings of the American Mathematical Society, 148 (2020), no. 3, 929-943. [preprint] [journal]
On r-gaps between zeros of the Riemann zeta-function, with J. B. Conrey, Bulletin of the London Mathematical Society, 50 (2018) no. 2, 349-356. [preprint] [journal]
Gaps between zeros of Dedekind zeta-functions of quadratic number fields. II, with H.M. Bui and W.P. Heap, Quarterly Journal of Mathematics, 67 (2016) no. 3, 467-482. [preprint] [journal]
Consecutive primes in tuples, with W. D. Banks and T. M. Freiberg, Acta Arithmetica, 167 (2015), 261-266. [preprint] [journal]
Gaps between zeros of Dedekind zeta-functions of quadratic number fields, Journal of Mathematical Analysis and Applications, 418 (2014), no. 1, 100-107. [journal]
Moments of products of automorphic L-functions, with M. B. Milinovich, Journal of Number Theory, 139 (2014), 175-204. [journal]

Collaborations with Undergraduates at the SMALL 2014 REU

Publications

Gaps between zeros of GL(2) L-functions, with O. Barrett, B. McDonald, S. J. Miller, P. Ryan, and K. Winsor, Journal of Mathematical Analysis and Applications, 429 (2015), 204-232. [preprint] [journal]
Gaussian distribution of the number of summands in generalized Zeckendorf decompositions in small intervals, with A. Best, P. Dynes, X. Edelsbrunner, B. McDonald, S. J. Miller, K. Tor, and M. Weinstein, INTEGERS, 16 (2016), #A6. [preprint] [journal]

Conference Proceedings

Benford behavior of generalized Zeckendorf decompositions, with A. Best*, P. Dynes, X. Edelsbrunner, B. McDonald, S. J. Miller, and M. Weinstein, Combinatorial and Additive Number Theory II: CANT, New York, NY, USA, 2015 and 2016, Springer, New York, 2017. [preprint] [article]
Gaussian behavior of the number of summands in Zeckendorf decompositions in small intervals, with A. Best, P. Dynes, X. Edelsbrunner, B. McDonald, S. J. Miller, K. Tor, and M. Weinstein, Fibonacci Quarterly, 52 (2014), no. 5, 35-46. [preprint] [article]
Benford behavior of Zeckendorf decompositions, with A. Best, P. Dynes, X. Edelsbrunner, B. McDonald, S. J. Miller, K. Tor, and M. Weinstein, Fibonacci Quarterly, 52 (2014), no. 5, 47-53. [preprint] [article]

Book Contributions

From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond, with O. Barrett, F. W. K. Firk, and S. J. Miller, Chapter in Open Problems in Mathematics (editors John Nash Jr. and Michael Th. Rassias), Springer-Verlag (2016). [preprint] [chapter]
Some Results in the Theory of Low-lying Zeros, with B. Mackall, S. J. Miller, C. Rapti, and K. Winsor, in Families of automorphic forms and the trace formula (editors Werner Müller, Sug Woo Shin, and Nicolas Templier), Simons Symposia Series, Springer-Verlag. [preprint] [chapter]
Benfordness of the Cauchy Distribution and Generalizations, with X. Edelsbrunner, K. Huan, B. Mackall, J. Powell, and M. Weinstein, Section 3.6, an appendix to Benford’s Law: Theory and Applications, (S. J. Miller, editor), Princeton University Press, 2015. [chapter]

I love traveling the world with my partner, Ian, spending time with our fur baby, Pickles, and tap dancing.

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Education & Professional History

Previous Appointments

Highlights & Recent Activity

Organizations & Scholarly Affiliations

Current Courses

Research Interests

Research Related Travel & Talks

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

Current Courses

Preprints

Publications

Collaborations with Undergraduates at the SMALL 2014 REU

Publications

Conference Proceedings

Book Contributions

Office

Phone

Email

Curriculum Vitae