Nathan Pflueger
Tamarkin Assistant Professor
Department of Mathematics
Brown University
Office: Kassar 219
CV
Contact: my last name (at) math (dot) brown (dot) edu
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.

Weierstrass semigroups on Castelnuovo curves. Submitted. arXiv.

On nonprimitive Weierstrass points. Submitted. arXiv.

BrillNoether varieties of kgonal curves. Accepted to Advances in Mathematics. arXiv. A video of me speaking about this result is here.

Special divisors on marked chains of cycles. Accepted to Journal of Combinatorial Theory, Series A 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
 "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.
Teaching this semester

Math 206: Algebraic Geometry II (Spring 2017)
Prior teaching

Math 205: Algebraic Geometry I (Fall 2016)

Math 158: Cryptography (Fall 2016)

Math 206: Algebraic Geometry II (Spring 2016)

Abelian Varieties reading group (Spring 2016)

Math 158: Cryptography (Fall 2015)

Math 42: Introduction to Number Theory (Spring 2015)

Math 9: Calculus I (Spring 2015)

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

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.