Never trust an algebraic geometer, they are always scheming.

My research interests are primarily in algebraic geometry and commutative algebra. In particular, I am interested in questions and ideas regarding derived categories, nonzero characteristic, and singularity theory. Lately, this includes understanding the structure of the derived category of bounded complexes of coherent sheaves for a variety over a field of prime characteristic.

- M. Ballard, P. Lank, Generation of derived categories in prime characteristic — In Preparation.

- “Generation of derived categories in prime characteristic”, Algebraic Geometry seminar, University of Utah, September 2022
- “Generation of derived categories in prime characteristic”, Algebraic Geometry & Singularity Theory Workshop, University of Washington, June 2022
- “Line Bundle-valued Quadratic Forms”, University of South Carolina, Algebraic Geometry Number Theory Seminar, March 2021
- “Riemannian Curvature For Schemes”, University of South Carolina, October 2020
- “Algebraic Psuedo-Riemannian Geometry”, Algebra & Geometry Seminar, University of New Mexico, November 2019
- “Higher Weakly Enriched Categories” Algebra & Geometry Seminar, University of New Mexico, November and December 2018
- “On An algebraic & Geometric Connection Of The Beal Conjecture”, Women in Mathematics in New England (WIMIN 2016) at Smith College, MA, September 2016
- “On A Geometric Connection Of The Beal Conjecture & Arithmetic Topology”, MAA Northeast Spring Section Meeting at University of New England, ME, June 2016

- “Differentiation of Lie algebras”, University of South Carolina, Lie Algebra Seminar, June 2022
- “Dimension for derived categories”, University of South Carolina, Algebraic Geometry & Commutative Algebra Seminar, April 2022
- “Generation and dimension for derived categories”, Commutative Algebra Regional Expository Seminar, April 2022
- “Generation in derived categories”, University of South Carolina, Algebraic Geometry & Commutative Algebra Seminar, March 2022
- “$F$-thick varieties: A Survey”, University of South Carolina, Algebraic Geometry & Commutative Algebra Seminar, February 2022
- “Singularity categories in birational geometry”, University of South Carolina, Algebraic Geometry & Commutative Algebra Seminar, October 2021
- “Regularity in prime characteristic via Kunz”, Commutative Algebra Regional Expository Seminar, October 2021
- “Techniques in prime characteristic”, University of South Carolina, Algebraic Geometry & Commutative Algebra Seminar, October 2021
- “Classification of irreducible representation for rigid motions”, University of South Carolina, Representation Theory Seminar, July 2021
- “Characters of Induced Representation’s in Characteristic Zero”, University of South Carolina, Representation Theory Seminar, June 2021

- Derived Categories, Moduli Spaces, and Hyperkähler Varieties, University of Michigan, July to August 2022
- Algebraic Geometry and Singularities Learning Workshop & Conference, University of Washington at Seattle, June 2022
- Advances in Mixed Characteristic Commutative Algebra & Geometric Connections, Casa Matemática Oaxaca (CMO), May 2022 (Virtual)
- Graduate Course on Tight Closure of Ideals and its Applications, May to July 2022
- Joint Mathematical Meeting (Virtual), April 2022
- Homological Mirror Symmetry, University of Miami, April 2022 (Virtual)
- AMS Spring Central Sectional Meeting (formerly at Purdue University), March 2022 (Virtual)
- AMS Sectional Meeting, Special Session on Commutative Algebra, October 2021 (Virtual)
- Derived, Birational, and Categorical Algebraic Geometry, Banff International Research Station, November 2021 (virtual)
- University of Utah, Oct 24-25, 2020, Special Sessions on Building bridges between commutative algebra and nearby areas (Virtual)
- University of Tennessee at Chattanooga, Oct 10-11, 2020, Special Session on Homological Commutative Algebra (Virtual)
- Simmons Conference “K-Stability” September 28th to October 2nd 2020 (Virtual)
- Quebec-Maine Number Theory Conference 2020, September 26-27 (Virtual)
- Palmetto Joint Arithmetic, Modularity, and Analysis Series, September 19-20 (Virtual)
- Fall Central Sectional Meeting (formerly at the University of Texas at El Paso) September 12 - 13, 2020 (Virtual)
- Motivic Geometry, Center of Advanced Studies, University of Oslo, September 7-11 2020 (Virtual)
- Connecticut Summer School in Number Theory, June 2020 (Virtual)
- Early Commutative Algebra Researchers, June 2020
- Geometric Representation Theory, Premier Institute of Theoretical Physics, June 2020 (Virtual)
- Electronic Computational Homotopy Theory Seminar, May 2020, Gijs Heuts, Utrecht University, Unstable homotopy groups
- A Zoom Special Session on DG Methods in Commutative Algebra and Representation Theory, May 2020
- Southwest Local Algebra Meeting, SLAM 2019, El Paso, Texas, February 2019