Dmitrii Pedchenko
E-mail: dpedchenko at math dot ucla dot edu CV: pdf (Updated 8/1/21)
I am an Assistant Adjunct Professor of mathematics at UCLA in the Algebra group. My current research is in algebraic geometry with a focus on the geometry of moduli spaces of sheaves.
I am also part of the Financial Mathematics group and teach courses for the corresponding major. Here my interests lie in Machine Learning and its applications to Finance.
I completed my PhD under the mentorship of Jack Huizenga at Penn State.
Research
Recent papers: 3. Ehresmann connections in geometryIn preparation, 2022. Graduate level textbook that grew out of a reading course that I lead for the 2nd year graduate students.
2. The Picard group of the moduli space of sheaves on a quadric surface. (54 pages)
International Mathematics Research Notices, 2021. [arXiv, Journal]
1. The Arens-Michael envelopes of the Jordan plane and the quantum enveloping algebra of sl(2). (15 pages)
To appear in the Journal of Noncommutative Geometry, 2020. [arXiv]
Expository writings: The Picard group of the moduli space of vector bundles on the quadric surface: [Video] [Slides]
Short talk at the FRG Workshop on Moduli Spaces and Stability, December 2020.