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I am a PhD student at Pennsylvania State University.
My research interests include symplectic geometry, dynamical systems and convex geometry. I am especially interested in symplectic capacities and symplectic embedding problems, Viterbo's conjecture, billiard connection between Viterbo's and Mahler's conjectures, outer and symplectic billiards, Ivrii's conjecture and other questions about periodic orbits.
My advisor is Sergei Tabachnikov.
My CV
Email: sharipova {dot} math {at} gmail {dot} com
Publications and preprints:
Ivrii’s conjecture for some cases in outer and symplectic billiards, Discrete and Continuous Dynamical Systems (journal, arXiv), 2024
Convex bodies with all characteristics planar (with Roman Karasev), International Mathematics Research Notices, (journal, arXiv), 2023
Viterbo’s Conjecture for Certain Hamiltonians in Classical Mechanics (with Roman Karasev), Arnold Math Journal , (journal, arXiv), 2019
Elementary approach to closed billiard trajectories in asymmetric normed spaces (with Arseniy Akopyan, Alexey Balitskiy, Roman Karasev), Proc. Amer. Math. Soc. (journal, arXiv), 2016
Talks:
Billiard Online Meetings, "Ivrii's Conjecture for some cases in outer and symplectic billiards, slides, April 2025
Dynamics Student Days 2024 at UMD, "Ivrii's Conjecture for some cases in outer and symplectic billiards", slides, April 2024
JMM, "Convex bodies with all planar characteristics", slides, January 2024
Simons Center Workshop: Mathematical Billiards, "Convex bodies with all planar characteristics", video, November 2023
Heidelberg Symplectic Geometry Seminar, "Convex Bodies with all Planar Characteristics", July 2023
IAS/Princeton University Symplectic Geometry Seminar, "Convex bodies with all planar characteristics", January 2023
Penn State Geometry Lunch Seminar, "Convex bodies with all planar characteristics", December 2022
Penn State Dynamical System Seminar, "Outer billiard characterization of a ball", October 2022
Kylerec 2022 Workshop, "Introduction to capacities", June 2022
Northern California Symplectic Geometry Seminar, "Viterbo’s Conjecture for Certain Hamiltonians in Classical Mechanics", slides, May 2022
Heidelberg Symplectic Geometry Seminar, "Viterbo’s conjecture for the Ekeland- Hofer-Zehnder capacity", July 2021
Education:
Math PhD candidate 2025, Pennsylvania State University. Advisor: Sergei Tabachnikov
Master of Science, Mathematical and Theoretical Physics Program, Skoltech + Department of General and Applied Physics, MIPT, Russia
Bachelor of Science, Department of General and Applied Physics, MIPT, Russia
Teaching:
Read about my teaching experience here.
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