Research Areas:  algebraic geometry, derived categories, homological algebra, symplectic geometry

Topics I am interested in: enumerative geometry, mirror symmetry, quantum cohomology and stable maps, localization arguments in equivariant cohomology

My research background focuses on derived categories of smooth toric varieties and toric Deligne-Mumford stacks which are global quotients of smooth toric varieties by finite abelian groups. In my dissertation, I developed a cellular resolution of the diagonal for toric D-M stacks, and my current research project focuses on implications of this resolution of the diagonal for full strong exceptional collections of line bundles on toric D-M stacks. 

Materials from the Specialty Exam (QEII) at Kansas State University:

• QEII Minor Syllabus

• QEII Major Syllabus

• Reference for QEII Major Exam

• Major Exam Transcription and Questions

Some Publications and Pre-Prints

1. "Strong Full Exceptional Collections for Unimodular Toric Surfaces." In Progress. arXiv preprint: https://arxiv.org/abs/2403.09663

2. A Resolution of the Diagonal for Smooth Toric Varieties. Submitted to Mathematical Proceedings of the Cambridge Philosophical Society. arXiv preprint: https://arxiv.org/abs/2403.09653

3. A Resolution of the Diagonal for Toric Deligne-Mumford Stacks. Submitted to Mathematical Proceedings of the Cambridge Philosophical Society.

4.  A Resolution of the Diagonal for Toric Deligne-Mumford Stacks. Selected portions of my PhD dissertation for Kansas State University. https://arxiv.org/abs/2303.17497 

5. ``The Hilbert Polynomial as an Embedded Subvariety": 10.13140/RG.2.2.16238.69443. https://www.researchgate.net/publication/363796564_The_Hilbert_Polynomial_as_an_Embedded_Subvariety. 23 September 2022.

6.  Anderson, Reginald C. ``What is an Infinitesimal?" AMS Graduate Student Blog, 28 August 2019. Web. https://blogs.ams.org/mathgradblog/2019/08/28/32749

7. Anderson, R. and D. Havlick. ``History and Values in Ecological Restoration Workshop." Ecological Restoration 31.1 (2013): 7-10. Web.

8. Anderson, Reginald C. ``Growing Up Between." The Good Men Project - Ethics and Values. Ed. Wisdom Amouzou. The Good Men Project, 3 June 2016. Web.

A current version of my dissertation .

Daniel Erman mentioned the results of my dissertation on a resolution of the diagonal near 37:50 and 45:15 from his Invited Address to JMM 2024 "From Hilbert to Mirror Symmetry."  video link

Sample Solution Sets

Mirror Symmetry textbook (Hori-Katz-Klemm-Pandharipande-Thomas-Vafa-Vakil-Zaslow). Notes and Solutions to Chapters 1-4.

Sample Solutions from Tu's An Introduction to Manifolds 

Sample solutions from Weibel's Homological Algebra 

(Handwritten) Notes on Hartshorne Chapter 1

Notes on Hartshorne's Algebraic Geometry

Notes from a Study Group on Milnor-Stasheff's Characteristic Classes 

A start to McDuff-Salamon's Symplectic Topology 

Huybrechts' Fourier-Mukai Transforms in Algebraic Geometry

Reviewer Service

I have been a reviewer for zbMath since 2023.