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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. | ||
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# Papers | ||
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"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) | ||
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"Descent conditions for strong generation in derived categories" [arxiv version](https://arxiv.org/abs/2308.08080), submitted | ||
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"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 | ||
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"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 | ||
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# Misc. | ||
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"Intrinsic Curvature For Schemes." [M.Sc. thesis](https://digitalrepository.unm.edu/math_etds/176) (2020). | ||
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# Talks (last two years) | ||
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AMS Special Session on Commutative Algebra and its Applications, Howard University, Washington, DC, April 2024 | ||
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AMS Contributed Paper Session on Commutative Algebra and Related Topics at the 2024 Joint Mathematics Meetings, January 2024 | ||
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Algebraic Geometry seminar, University of Georgia, October 2023 | ||
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Syzygies and mirror symmetry worskhop, American Institute of Mathematics, September 2023 | ||
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New Directions in Group Theory and Triangulated Categories, May 2023 | ||
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Georgia Algebraic Geometry Symposium, University of Georgia, May 2023 | ||
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Categorical methods in moduli theory, University of Pennsylvania, April 2023 | ||
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AMS Special Session on Interactions between Noncommutative Ring Theory and Algebraic Geometry, Spring Central Sectional, April 2023 | ||
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AMS Special Session on Recent Developments in Commutative Algebra, Southeast Sectional, March 2023 | ||
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Algebraic Geometry seminar, University of Utah, September 2022 | ||
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Algebraic Geometry & Singularity theory workshop, University of Washington, June 2022 | ||
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