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Research Interests
Research Interests
Within commutative algebra, my research focuses on advancing the understanding of local cohomology modules with special interest in finding conditions on its vanishing. I explore the connections between local cohomology and singular homology, with a focus on how it encodes topological properties of the prime spectrum of a ring. I further seek to understand the Bass numbers of local cohomology, an analog to Betti numbers for injective resolutions.
For more information, you can read my detailed research statement.
Papers and publications
Papers and publications
"Local cohomology of subspace arrangements and relative simplicial homology" - Abraham Pascoe and Emily E. Witt (to appear in the Journal of Algebra)
"Local cohomology of subspace arrangements and simplicial homology" - Abraham Pascoe - Advisor: Emily E. Witt - Doctoral Dissertation at KU
"Affine and Projective Planes" - Abraham Pascoe - Advisor: Les Reid - Master's Thesis at MSU
Research Talks, Conference Participation
Research Talks, Conference Participation
"Local cohomology modules of subspace arrangements and relative simplicial homology" - AMS Central Sectional Meeting's Special Session on "Algebraic and Homological Perspectives with a view towards Geometry" (Spring 2025)
"Local cohomology modules and simplicial homology" - MAA Missouri Section Meeting (Spring 2024)
"Local cohomology modules and simplicial homology" - University of Nebraska - Lincoln (Spring 2024)
Fairfax Algebra Days 2024 - George Mason University (Spring 2024)
"Local cohomology modules and simplicial homology" - poster session
"The Secrets of a Spectral Sequence" - University of Kansas Student Algebra Seminar (Spring 2024)
Introductory Workshop: Commutative Algebra - SLMath workshop participant (Spring 2024)
Connections Workshop: Commutative Algebra - SLMath workshop participant (Spring 2024)
"Local cohomology modules and simplicial homology" - poster session
"Local cohomology modules and simplicial homology" - Kansas Mathematics Graduate Student Conference (Fall 2023)
"Introductory Macaulay2 Workshop" - University of Kansas Student Algebra Seminar (Fall 2023)
"Local Cohomology and Simplicial Homology" - Centro de Investigación en Matemáticas (Fall 2023)
Macaulay2 Workshop & Mini-school - Institute for Mathematics and its Applications (Summer 2023)
Currently collaborating on a package regarding F-invariants with a group formed at this workshop
"Lyubeznik Numbers and Simplicial Homology" - Lightning Talk during the Workshop
"The Lyubeznik Number Disencumber" - Uninversity of Kansas Student Algebra Seminar (Fall 2022)
"Inceptive Injective and Cool Koszul" - University of Kansas Student Algebra Seminar (Fall 2022)
"Generalizing Vector Multiplication: A Brief Introduction to Module Theory" - University of California Santa Cruz No-Jargon Talk (Spring 2022; virtual)
D-Modules, Group Actions, and Frobenius: Computing on Singularities - ICERM Conference participant (Fall 2021; virtual)
KUMUNU Algebra Research Conference - Conference participant (Fall 2018)
"Fun With Bases: All About That Base" - MAKO Undergraduate Math Research Conference (Fall 2014; Missouri State University)
Scholarships, Awards, and Honors
Scholarships, Awards, and Honors
University of Kansas Summer Research Scholarship (Summer 2023; KU)
University of Kansas College of Liberal Arts and Sciences Graduate Research Assistantship (Fall 2022 - Spring 2023; KU)
Elbert Walker Graduate Scholarship in Mathematics (Summer 2022; KU)
Rashleigh Family Graduate Scholarship in Mathematics (Summer 2021; KU)
U.G. Mitchell Scholarship in Mathematics (Summer 2020; KU)
Finalist for the Florence Black Award for Excellence in Teaching (Spring 2020; KU)
Graduate Level Courses concerning Algebra
Graduate Level Courses concerning Algebra
"A Survey in Algebraic Singularity Theory" (Spring 2024; KU)
"Cohen-Macaulay and Regular Rings" (Fall 2022; KU)
"Algebraic Topology" (Spring 2022; KU)
"Directed Readings in Local Cohomology" (Fall 2021; KU)
"Lie Algebras" (Spring 2021; KU)
"Commutative Algebra focused on D-modules" (Spring 2021; KU)
"Directed Readings in Gröbner Bases" (Spring 2020; KU)
"Commutative Algebra" (Spring 2020; KU)
"Abstract Algebra" (Fall 2019; KU)
"Coxeter Groups" (Spring 2019; KU)
"Numerical Linear Algebra" (Spring 2019; KU)
"Modern Algebra" (Spring 2019; KU)
"Algebraic Combinatorics" (Fall 2018; KU)
"Linear Algebra II" (Fall 2018; KU)
"Abstract Algebra II" (Spring 2018; MSU)
"Abstract Algebra I" (Fall 2017; MSU)
"Applied Abstract Algebra" (Spring 2017; MSU)
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