Nathan Pflueger
Assistant Professor
Department of Mathematics and Statistics
Amherst College
Office: Seeley Mudd 401
CV
Contact: My first initial and last name (at) amherst (dot) edu
Spring 2019 teaching

Math 252: Mathematics of PublicKey Cryptography

Math 272: Linear Algebra with Applications
 My office hours in SMUD 401 (tentative):
 Tuesday 1:453:15
 Wednesday 1:453:15
 Friday 1:302:30
Research
I study algebraic curves using combinatorial methods, particularly through young tableaux and generalizations of them. I am particularly interested in BrillNoether theory, which studies the variety of ways that a chosen curve is realized in projective space. My methods revolve around degeneration to singular curves, especially chains of elliptic curves. I also study analogous questions in the setting of tropical geometry, and the relation between these persepctives via nonArchimedean analytic geometry. Some of my papers are listed below.

The GiesekerPetri theorem and imposed ramification (with M. Chan and B. Osserman). Submitted. arXiv

Euler characteristics of BrillNoether varieties (with M. Chan). Preprint. arXiv

Weierstrass semigroups on Castelnuovo curves. To appear in Journal of Algebra. arXiv.

On nonprimitive Weierstrass points. Algebra and Number Theory 12 (2018), no. 8, 19231947 arXiv.

BrillNoether varieties of kgonal curves. Advances in Mathematics 312 (2017) 4663. arXiv. A video of me speaking about this result is here.

Special divisors on marked chains of cycles. Journal of Combinatorial Theory, Series A 150 (2017) 182207. arXiv.

Genera of BrillNoether curves and staircase paths in Young tableaux (with M. Chan, A. López Martín, and M. Teixidor i Bigas). To appear in Transactions of the AMS. arXiv

Bitangents of tropical plane quartic curves (with M. Baker, Y. Len, R. Morrison, and Q. Ren). Mathematische Zeitschrift 282:3 (2016) 10171031. arXiv

On linear series with negative BrillNoether number. Submitted. arXiv

Graph reductions, binary rank, and pivots in gene assembly. Discrete Applied Mathematics 159:17 (2011) 21172134. arXiv
Source code

Enumeration of semigroups of maximum effective weight: source (C++), output
Exposition
 Lecture notes on calculus.
 First semester
 Second semester
 I wrote these for the firstyear calculus sequence at Harvard. They are in need of proofreading and revising; I hope to make time for this project in the next couple years. But I will continue to make them freely available here, since many people have found them useful over the years.
 "Tropical Curves." My minor thesis. pdf

An introduction to tropical curves, with an emphasis on how they are analogous to algebraic curves, both formally and informally.
Previous Teaching

Math 105: Calculus with Algebra

Math 350: Groups, Rings, and Fields

Math 121: Intermediate Calculus

Math 272: Linear Algebra with Applications

Math 111: Introduction to the Calculus (Fall 2017).

Math 272: Linear Algebra with Applications (Fall 2017)

Math 206: Algebraic Geometry II (Spring 2017, at Brown)

Math 205: Algebraic Geometry I (Fall 2016, at Brown)

Math 158: Cryptography (Fall 2016, at Brown)

Math 206: Algebraic Geometry II (Spring 2016, at Brown)

Math 158: Cryptography (Fall 2015, at Brown)

Math 42: Introduction to Number Theory (Spring 2015, at Brown)

Math 9: Calculus I (Spring 2015, at Brown)

Math 19: Calculus 2 for Physics and Engineering (Fall 2014, at Brown)

Math 1A: Introduction to Calculus (Fall 2013, at Harvard)

Math 1B: Calculus, Series, and Differential Equations (Fall 2011, at Harvard)
Links

The Math Circle: a wonderful program for young students enthusiastic about pure mathematics. I have taught for them since 2011.

Budapest Semesters in Mathematics: A study abroad program for American undergraduates (from any college). I attended in fall 2007.