diff --git a/index.md b/index.md new file mode 100644 index 0000000..014bd31 --- /dev/null +++ b/index.md @@ -0,0 +1,44 @@ +My work falls into both landscapes of algebraic geometry and commutative algebra where I utilize the machinery +of derived categories to understand problems lying within these two subject matters. This direction +of research has interactions with singularity theory, and in essence the objective is to understand the behavior +through homological methods coming from derived categories. Broadly speaking, I am interested in +problems regarding the applications of derived categories in algebraic geometry and commutative algebra. + +# Papers + +"A note on generation and descent for derived categories of noncommutative schemes" joint with [Anirban Bhaduri](https://sc.edu/study/colleges_schools/artsandsciences/mathematics/our_people/directory/bhaduri_anirban.php) and [Souvik Dey](https://sites.google.com/view/souvikdey/research), [arxiv version](http://arxiv.org/abs/2312.02840) + +"Descent conditions for strong generation in derived categories" [arxiv version](https://arxiv.org/abs/2308.08080), submitted + +"Strong generation and (co)ghost index in module categories" joint with [Souvik Dey](https://sites.google.com/view/souvikdey/research) and [Ryo Takahashi](https://www.math.nagoya-u.ac.jp/~takahashi/)- [arxiv version](https://arxiv.org/abs/2307.13675), submitted + +"High Frobenius Pushforwards generate the bounded derived category" joint work w/ [Matthew Ballard](https://www.matthewrobertballard.com/), [Srikanth B. Iyengar](https://www.math.utah.edu/~iyengar/), [Alapan Mukhopadhyay](http://www-personal.umich.edu/~alapanm/), and [Josh Pollitz](https://www.joshpollitz.com/) - [arxiv version](https://arxiv.org/abs/2303.18085), submitted + +# Misc. + +"Intrinsic Curvature For Schemes." [M.Sc. thesis](https://digitalrepository.unm.edu/math_etds/176) (2020). + +# Talks (last two years) + +AMS Special Session on Commutative Algebra and its Applications, Howard University, Washington, DC, April 2024 + +AMS Contributed Paper Session on Commutative Algebra and Related Topics at the 2024 Joint Mathematics Meetings, January 2024 + +Algebraic Geometry seminar, University of Georgia, October 2023 + +Syzygies and mirror symmetry worskhop, American Institute of Mathematics, September 2023 + +New Directions in Group Theory and Triangulated Categories, May 2023 + +Georgia Algebraic Geometry Symposium, University of Georgia, May 2023 + +Categorical methods in moduli theory, University of Pennsylvania, April 2023 + +AMS Special Session on Interactions between Noncommutative Ring Theory and Algebraic Geometry, Spring Central Sectional, April 2023 + +AMS Special Session on Recent Developments in Commutative Algebra, Southeast Sectional, March 2023 + +Algebraic Geometry seminar, University of Utah, September 2022 + +Algebraic Geometry & Singularity theory workshop, University of Washington, June 2022 +