Nathaniel Gallup

Research

I'm interested in infinite-dimensional commutative algebra, algebraic geometry, and representation theory. Here are some examples:

Stillman-type bounds on projective dimension and CM regularity, especially in the multigraded setting.
Classification of infinite-dimensional representations of infinite quivers including various analogs of Gabriel's theorem in this setting.
Extending Schubert calculus to certain infinite-dimensional flag varieties, and in particular analogs of the Grothendieck and Chow rings of multigraded infinite polynomial rings.

Gabriel's Theorem for Locally Finite-Dimensional Representations of Infinite Quivers. Gallup, Nathaniel and Sawin, Stephen. 2024.
Multigraded Stillman's Conjecture. Cobb, John and Gallup, Nathaniel and Spoerl, John. 2024.
Gabriel's Theorem for Infinite Quivers. Gallup, Nathaniel and Sawin, Stephen. 2023. To Appear in Algebras and Representation Theory. (arXiv:2312.09904)
The Grothendieck Ring of Certain Non-Noetherian Group-Graded Algebras via $K$-series. Gallup, Nathaniel. 2023. (arXiv:2304.06932)
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. (arXiv:1307.7998)

Spec(Q¯(2πi)), 2024, at the Fields Institute in Toronto, CA (Talk: Multigraded Stillman's Conjecture)
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

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