Nathaniel Gallup's Math Website

Research

I'm interested in infinite-dimensional objects in various algebraic categories. Here are some examples:

Decomposing infinite-dimensional representations of infinite quivers into indecomposables and classifying these indecomposables.
Extending Schubert calculus to certain infinite-dimensional flag varieties. This involves computing the Grothendieck and Chow rings of multigraded infinite polynomial rings.

Gabriel's Theorem for Infinite Quivers. Gallup, Nathaniel and Sawin, Stephen. 2023.
The Grothendieck Ring of Certain Non-Noetherian Group-Graded Algebras via $K$-series. Gallup, Nathaniel. 2023. arXiv:2304.06932 (Submitted)
Decompositions of Infinite-Dimensional $A_{\infty, \infty}$ Quiver Representations. Gallup, Nathaniel and Sawin, Stephen. Algebras and Representation Theory (2024): 1-23. (arXiv:2211.12984)
Well-Ordered Flag Spaces as Functors of Points. Gallup, Nathaniel. 2021. arXiv:2112.00327
Dots and Dominos, Zigzags and Squares. Gallup, Nathaniel. PhD thesis, 2020. AAI27671363
Topologically distinct Lagrangian and symplectic fillings. Cao, Chang and Gallup, Nathaniel and Hayden, Kyle and Sabloff, Joshua M. Math. Res. Lett. 21 (2014), no. 1, 85-99.

Macaulay2, Computational Algebraic Geometry and String Theory, 2024, at University of Utah in Salt Lake City, UT
URiCA, 2024, at University of Nebraska in Lincoln, NE
Spring Western AMS Sectional, 2024, at SF State in San Francisco, CA (Talk: The Grothendieck Ring of Multigraded Non-Noetherian Polynomial Rings via Hilbert Series)
Advances in Lie Theory, Representation Theory, and Combinatorics, 2024, at SLMath in Berkeley, CA
Recent Developments in Commutative Algebra, 2024, at SLMath in Berkeley, CA
SLAM, 2024, at University of Oklahoma in Norman, OK (Poster)
Introductory Workshop: Commutative Algebra, 2024, at SLMath in Berkeley, CA
Connections Workshop: Commutative Algebra, 2024, at SLMath in Berkeley, CA (Poster)
JMM 2024, in San Francisco, CA
Workshop on Syzygies and Regularity, 2023, UIC
WARTHOG (Infinite-dimensional methods in commutative algebra), 2022, University of Oregon
CIME School on Complex non-Kähler Geometry, 2018, in Cetraro, Italy
Bay Area Differential Geometry Seminar, 2014 and 2015 at MSRI, 2016, at Stanford
FPSAC, 2013, Paris
Sage Days 49, 2013, Paris