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

I am interested in derived algebraic geometry (category theory, homological algebra), and 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 (strong, full) exceptional collections of line bundles on toric D-M stacks. My long-term research interests include symplectic geometry, homological mirror symmetry, intersection theory, and deformation theory within the setting of derived algebraic geometry. 

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). Chapters 1-3. 

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.