CV

A PDF version is also available here.

Contact

• Office: Seeley Mudd Building, Room 401
• Address: 31 Quadrangle Drive
• City: Amherst, MA 01002
• Email: npflueger@amherst.edu
• Website: http://npflueger.github.io/

Professional Positions

Amherst College

• Associate Professor of Mathematics (7/2024-present)
• Assistant Professor of Mathematics (7/2017-6/2024)

Brown University

• Tamarkin Assistant Professor of Mathematics (9/2014-6/2017)

Research Interests

• Algebraic geometry, particularly algebraic curves.
• Young tableaux and applications in Brill-Noether theory.
• Tropical curves and linear series.

Education

Harvard University (9/2009-5/2014)

• Ph.D. in Mathematics, May 2014.
• Adviser: Joe Harris.
• Thesis: Regeneration of elliptic chains with exceptional linear series.

Stanford University (9/2005-6/2009)

• B.S. Mathematics with Honors and Minor in Computer Science, June 2009.
• J. E. Wallace Sterling Award (for top 25 graduating students in Humanities and Sciences).
• Spent Autumn 2007 in Hungary at Budapest Semesters in Mathematics.

Publications

Preprints and papers under review

1. An extended Demazure product on integer permutations via min-plus matrix multiplication. 26 pages. Preprint (2022).
   arXiv v1: June 2022 (Revising more before submitting)
2. (Hurwitz--)Brill--Noether general marked graphs via the Demazure product. 14 pages. Preprint (2022).
   arXiv v1: Jan. 2022 (Declined by one journal; in revision)

Publications

3. Twice-Marked Banana Graphs & Brill-Noether Generality (with N. Solomon). Algebraic Combinatorics, Volume 8 (2025) no. 5, pp. 1415-1457.
   arXiv v1: Nov. 2022 Published: 2025
4. Versality of Brill-Noether flags and degeneracy loci of twice-marked curves. Algebraic Geometry 12:4 (2025) pp. 497-518.
5. Weierstrass semigroups from cyclic covers of hyperelliptic curves (with E. Cotterill, N. Zhang). Bulletin of the Brazilian Mathematical Society, New Series 54, 37 (2023).
   arXiv v1: Dec. 2021 (Declined by one journal; in revision)
6. Linear series with ρ<0 via thrifty lego-building. Journal für die reine und angewandte Mathematik (Crelle), no. 797 (2023), pp. 193-228.
   arXiv v1: Jan. 2022 Accepted: Dec. 2022
7. Relative Richardson Varieties (with M. Chan). Mathematical Proceedings of the Cambridge Philosophical Society, 175:1 (2023), 161-186.
   arXiv v1: Sept. 2019 Accepted: June 2022
8. Combinatorial relations on skew Schur and skew stable Grothendieck polynomials (with M. Chan). Algebraic Combinatorics 4:1 (2021), 175-188.
   arXiv v1: Sep. 2019 Published: 2021
9. Euler characteristics of Brill-Noether varieties (with M. Chan). Transactions of the AMS 374:3 (2021) 1513-1533.
   arXiv v1: Aug. 2017 Published: 2021
10. Weierstrass semigroups on Castelnuovo curves. Journal of Algebra 582 (2021) 117-135.
    arXiv v1: Aug. 2016 Published: 2021
11. The Gieseker-Petri theorem and imposed ramification (with M. Chan, B. Osserman). Bulletin of the London Mathematical Society 51:6 (2019) 945-960.
    arXiv v1: March 2018 Published: 2019
12. On non-primitive Weierstrass points. Algebra and Number Theory 12:8 (2018) 1923-1947.
    arXiv v1: Aug. 2016 Published: 2018
13. Genera of Brill-Noether curves and staircase paths in Young tableaux (with M. Chan, A. López Martín, M. Teixidor i Bigas). Transactions of the American Mathematical Society 370 (2018), 3405-3439.
    arXiv v1: June 2015 Published: 2018
14. Brill-Noether varieties of k-gonal curves. Advances in Mathematics 312 (2017) 46-63.
    arXiv v1: Jan. 2017 Published: 2017
15. Special divisors on marked chains of cycles. Journal of Combinatorial Theory, Series A 150 (2017) 182-207.
    arXiv v1: Jan. 2017 Published: 2017
16. Bitangents of tropical plane quartic curves (with M. Baker, Y. Len, R. Morrison, Q. Ren). Mathematische Zeitschrift 282:3 (2016) 1017-1031.
    arXiv v1: April 2014 Published: 2016
17. Graph reductions, binary rank, and pivots in gene assembly. Discrete Applied Mathematics 159:17 (2011) 2117-2134.
    arXiv v1: March 2011 Published: 2011

Teaching

Amherst College

• Spring 2025:
  • Math 250, Number theory
  • Math 272, Linear algebra with applications
• Fall 2024:
  • Math 252, Cryptography
  • Math 410, Galois theory
• Spring 2024:
  • Math 281, Combinatorics
  • Math 385, Mathematical Logic
• Fall 2023:
  • Math 111, Introduction to the calculus
• Spring 2023:
  • Math 121, Intermediate calculus
  • Math 252, Cryptography
• Spring 2022:
  • Math 252, Cryptography
  • Math 271, Linear algebra
  • Math 498, Senior honors
• Summer and Fall 2021 (while on leave):
  • Math 498, Senior honors
• Spring 2020:
  • Math 220, Mathematical Reasoning and Proof
  • Math 252, Cryptography
  • Math 498, Senior honors
  • Math 390, Independent study on group theory and puzzles
  • Unofficial supervisor of a U. Mass graduate reading course on tropical geometry
• Fall 2019:
  • Math 350, Groups, rings, and fields
  • Math 272, Linear algebra with applications
  • Math 498, Senior honors
• Spring 2019:
  • Math 272, Linear algebra with applications
  • Math 252, Cryptography (new course)
  • Math 490, Independent study on Commutative Algebra
• Fall 2018:
  • Math 350, Groups, rings, and fields
  • Math 105, Calculus with algebra
• Spring 2018:
  • Math 272, Linear algebra with applications
  • Math 121, Intermediate calculus
• Fall 2017:
  • Math 272, Linear algebra with applications
  • Math 111, Introduction to the calculus

Brown University

• Spring 2017:
  • Algebraic Geometry II
• Fall 2016:
  • Cryptography
  • Algebraic Geometry I
• Spring 2016:
  • Algebraic Geometry II
• Fall 2015:
  • Cryptography
• Spring 2015:
  • Introduction to number theory
  • Calculus I
• Fall 2014:
  • Calculus II for physics and engineering

Harvard University

• Fall 2013: Introduction to Calculus
  • Wrote comprehensive lecture notes, still in use by students and professors as a course accompaniment.
• Spring 2013: Course Assistant for Tropical Geometry
• Spring 2012: Teaching Fellow for “Fat Chance” (basic probability course for non-majors)
• Fall 2011: Integration, Series, and Differential Equations
  • Wrote comprehensive lecture notes, still in use by students and professors as a course accompaniment.

The Math Circle (extra-curricular math program for Boston-area children)

• Spring 2016: taught students ages 13 to 15.
• Academic year 2013-2014: taught students ages 13 to 18.
• July 2014 and July 2016: co-organized a math circle teacher training institute in South Bend, IN.
• Academic year 2012-2013: taught students ages 13 to 18.
• Academic year 2011-2012: taught students ages 7 to 9.

Budapest Semesters in Mathematics

• 2010-2013: Coordinated and coached teams of American students to compete in the International Mathematics Competition for University Students in Blagoevgrad, Bulgaria. Wrote detailed preparation material on the competition problems.

Stanford University computer science department

• Spring 2009: section leader for Programming Abstractions and Methodology (C++).
• Winter 2009: section leader for Programming Abstractions (C++).
• Fall 2008: section leader for Programming Abstractions and Methodology (C++).
• Spring 2008: course helper for Programming Methodology (Java).
• Winter 2008: section leader for Programming Abstractions (C++).
• Spring 2007: section leader for Programming Methodology (Java).

Stanford University mathematics department

• 2006-2009: Tutor for linear algebra and multivariable calculus.
• 2005-2006: Course developer (wrote assignments and exams) for distance learning Calculus C course (through the Education Program for Gifted Youth).

Service

• Amherst College Fellowship Committee (2023-present; chair since 2024)
• Co-organizer for the Valley Geometry Seminar (2018-present).
• Co-organizer for the Bi-annual Tropical and Algebraic Meetings of Brown and Yale (2014-present), including serving at primary organizer of the Spring 2019 meeting at Amherst College.
• Served as referee for papers in the following mathematics journals: Advances in Mathematics; Algebra and Number Theory; Algebraic Combinatorics; Communications in Algebra; Documenta Mathematica; European Journal of Mathematics; Forum of Math Pi; International Mathematics Research Notices; Inventiones Mathematicae; Journal of the American Mathematical Society; Journal for Pure and Applied Algebra; Mathematische Zeitschrift; Notices of the American Mathematical Society.
• Organizer of the Walker Prize Examination at Amherst, 2022-2023.
• Math Comprehensive exam / honors qualifying exam co-coordinator (2019-2020)
• Co-organizer of the conference “Ideals, Varieties, and Applications,” including serving as Co-PI on an NSF grant funding the conference (June 2019).
• Faculty computing committee member (2019-2020).
• Title IX review committee member (2018-2019).
• Math-major advising (2018-present).
• College advising (2018-present).
• VAP Search committee member (2019).
• Department list keeper (2018-2019)
• Co-organizer of Putnam Exam preparation / problem-solving sessions (Fall 2018 and 2019).
• Chair of Connecticut Valley Colloquium at Amherst College (Fall 2018).
• Assist in grading of Mathematics Comprehensive Exam (2018-present).
• Minutes-taker for Mathematics and Statistics department meetings (2017-2018).
• Co-organizer for the Brown algebraic geometry seminar (2014-2017).
• Served as assistant coach for the San Francisco Bay Area team to the ARML mathematics competition (2008, 2009).

Invited Talks

• November 2024, Georgia Tech Algebra seminar.
• September 2024, AMS Central Sectional, special sessions: A Showcase of Algebraic Geometry at Undergraduate Institutions; and Non-Archimedean, Algebraic, Tropical Geometry and applications.
• April 2024, Williams College Faculty Colloquium.
• March 2024, U. Kentucky Algebra Seminar.
• July 2023, BIRS workshop on Curves: Algebraic, Tropical, and Logarithmic, in Banff, Alberta.
• May 2023, U. Mass. Combinatorics Seminar.
• April 2023, Harvard-MIT Combinatorics Seminar.
• June 2022, Workshop on Combinatorial Algebraic Geometry, ICTS Bengaluru (virtual).
• March 2022, Special Session on Moduli Spaces in Algebraic and Tropical Geometry, AMS Eastern Sectional Meeting.
• February 2022, Goethe University Frankfurt Algebra and Geometry Seminar (virtual).
• June 2021, Three-part minicourse on Tropical Curves (hosted by Fudan U., Shanghai).
• April 2021, Algebra, Geometry, and Combinatorics Day (hosted by Notre Dame).
• November 2019, Valley geometry seminar (hosted by U. Massachusetts).
• October 2019, Stanford algebraic geometry seminar.
• April 2019, Brown algebraic geometry seminar.
• April 2019, Williams College faculty seminar.
• June 2017, U.C. Irvine number theory seminar.
• March 2017, Brown discrete math seminar.
• February 2017, Valley geometry seminar (at U. Massachusetts).
• May 2016, “Brill-Noether Special Chains of Loops.” Algebraic, Tropical, and Nonarchimedean Analytic Geometry of Moduli Spaces, Oaxaca, Mexico.
• March 2016, Georgia Tech algebraic geometry seminar.
• March 2016, Special session in Interactions Between Algebraic and Tropical Geometry, AMS Spring Sectional Meeting, Athens, GA.
• June 2015, Special Session in Enumerative and Combinatorial Methods in Moduli Theory, AMS-EMS-SPM International Meeting, Porto, Portugal.
• October 2014, Special session on combinatorics and algebraic geometry, AMS Fall Sectional Meeting, San Francisco, CA.
• February 2014, Rice algebraic geometry seminar.
• January 2014, “Towards a tropical Castelnuovo-Severi inequality.” Special session on tropical and non-archimedean geometry, Joint Mathematics Meeting.
• November 2013, Harvard-MIT algebraic geometry seminar.
• November 2013, Brown algebraic geometry seminar.
• October 2013, U. Wisconsin algebraic geometry seminar.
• April 2013, Yale algebraic and tropical geometry seminar.

Honors and Awards

• NSF Graduate Research Fellowship, 2009-2013.
• Certificate of Distinction in Teaching, Harvard University, Spring 2012.
• Barry M. Goldwater Scholarship, awarded 2007.
• Putnam Mathematics Competition: 24th place (2008)
• International Mathematics Competition for University Students (Blagoevgrad, Bulgaria): 40th place (2008).
• Google Codejam competition: advanced to semifinal round (top 500 contestants) (2009, 2010, 2012).
• Boothe Prize for Undergraduate Writing: Finalist (Autumn 2005, Winter 2006), 2nd place (Autumn 2005). Prize selects the best essay written for the freshman Introduction to the Humanities requirement at Stanford.
• Hester-Franklin Prize for best original paper written in first-year French (2009).

Other Employment

University of Minnesota, Duluth (funding from NSF) (Summer 2008, 2009, 2010)

• R.E.U. in Combinatorics (Duluth, MN)
  • 2009: Student participant.
  • 2010 and 2011: Graduate student research adviser.

D.E. Shaw and Co. (Summer 2007)

• Quantitative Analyst Intern, Futures Group (New York, NY)
  • Researched, implemented, and tested computational methods for correlating high-frequency financial instruments.
  • Developed one chosen method into a versatile set of Java and Perl programs for use in research within the hedge fund.
  • Wrote several internal reports detailing the mathematical techniques I investigated.

University of Washington (funding from National Science Foundation) (Summer 2006)

• R.E.U. in Inverse Problems for Electrical Networks (Seattle, WA)

Updated: 2026-04-29