Education
[2023-present] PhD in Applied Mathematics at Cornell University, Ithaca, NY
[2020-2023] Masters in Applied Mathematics at Cornell University, Ithaca, NY
- A exam presentation: “A study of the long time behavior of hybrid dynamical systems using the Frobenius Perron Operator”, slides
[2017-2020] BSc in Mathematics with a minor in Computer Science at Constructor University Bremen
- Bachelor thesis: “Mean field approximations of the Bose Einstein condensate with three particle Hamiltonians”
Publications
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A Study of the Long-Term Behavior of Hybrid Systems with Symmetries via Reduction and the Frobenius-Perron Operator, Maria Oprea, Aden Shaw, Robi Huq, Kaito Iwasaki, Dora Kassabova, and William Clark, SIADS, 2024
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Measure-Theoretic Time-Delay Embedding, Jonah Botvinick Greenhouse, Maria Oprea, Yunan Yang and Romit Maulik, preprint, 2024
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Stochastic Inverse Problem: stability, regularization and Wasserstein gradient flow, Qin Li, Maria Oprea, Li Wang and Yunan Yang, preprint, 2024
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Optimal Control of Reduced Left-Invariant Hybrid Control Systems, William Clark, Maria Oprea, CDC 2024
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Learning the Delay in Delay Differential Equations, Robert Stephany, Maria Oprea, Mark Walth, Gabriella Nothaft, Arnaldo Rodriguez-Gonzales, William Clark, ICLR 2024 Workshop on AI4Differential Equations in Science.
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Optimality of Zeno Executions in Hybrid Systems, William Clark and Maria Oprea, American Control Conference, 2023
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Optimal Contol of Nonholonomic Systems via Magnetic Fields, Maria Oprea, Max Ruth, Dora Kassabova and William Clark, IEEE Control Systems Letters 7, 793-798, 2022
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How do we walk? Using hybrid holonomy to approximate non-holonomic systems, Maria Oprea, William Clark, CDC 2022
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Optimal Control of Hybrid Systems via Hybrid Lagrangian Submanifolds, William Clark, Maria Oprea, 7th IFAC workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021
Teaching
Instructor :
- Fall 2022: Calculus
REU Mentor:
- Summer 2022
Teaching Assistant:
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At Cornell University:
— Spring 2024: Applied Functional Analysis
— Fall 2023: Manifolds and Differential Forms
— Spring 2023: Calculus II
— Fall 2021: Complex Analysis
— Spring 2021: Nonlinead Dynamics and Chaos
— Fall 2020: Multivariate Calculus for Engineers
- At Constructor University
- Fall 2019: Linear Algebra
- Spring 2018: Elements of Probability
- Fall 2018: Advanced Calculus
Outreach:
- Math Explorer’s club, Cornell University, 2024
- taught 2 sessions on Chaos and Fractals (links to slides and materials) at a highschool level.
Conferences and talks
- NANMAT, Cluj Napoca, November 5, 2024
- Talk title: A probabilistic version of Takens embedding theorem
- SIAM NNP, Rochester, NY, November 1-3 2024
- Talk title: Analysis of the stochastic inverse problem, slides
- MOPTA, Lehigh University, Bethlehem, PA
- Talk title: Embeddings in the 2-Wasserstein Tangent Space slides
- SIAM Annual Meeting
- Talk title: Probabilistic embedding in th Wasserstein Tangent Space, [slides](Probabilistic_Takens - copie.pdf)
- ICLR, Vienna, Austria, 2024
- Poster title: Learning the Delay in Delay Differential Equations
- Women in Optimal Transport, Vancouver, Canada
- Talk title: Embeddings in 2-Wasserstein Tangent Space, slides
- CDC, Cancun, Mexico, 2022
- Talk title: How do we walk? Using hybrid holonomy to approximate nonholonomic systems, slides
- ACC , San Diego, CA, 2023
- Talk title: Optinmality of Zeno Execturions in Hybrid Systems, slides
Summer Schools and Workshops
- Gene Golub Summer School, Quito, Ecuador, 2024
- Mathematical and Statistical Foundations of Digital Twins, IMSI Institute Chicago, IL, 2024
- Optimal Transport in the MIdwest Summer School, Madison, WI, 2024
- Summer School on Data Driven Methods for Computational Sciences, Dobiacco, Italy, 2023
- Complexity-GAINs International Summer School, Vienna, Austria, 2022