2025-26 Department of Mathematics and Statistics Events |
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April, 2026 |
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Wed. |
Dissertation Defense Speaker: Noah Corbett, Ph.D. Candidate, Florida Atlantic University Title: A Computational Approach to Periodic Orbits of State-Dependent Delay Differential Equations Abstract: The field of delay differential equations (DDEs) concerns the study of systems whose evolution depends on certain past states of the system. Of particular interest are the state-dependent DDEs, whose delay terms are non-constant and depend on the current state itself. In this thesis, we provide rigorous solution-finding techniques for a certain class of one-dimensional state-dependent DDEs, as well as a state-dependent delayed Van der Pol equation. This technique is inspired by the classical Picard-Lindelöf theorem and is successful in proving the existence and uniqueness of orbits in such systems under certain reasonable restrictions. We then employ the Lagrange-Chebyshev interpolating operator to frame our results in the computational setting, allowing us to algorithmically obtain periodic orbits of the systems in question. These algorithms are based on the Newton-Kantorovich theorem and the resulting illustrations and numerics are discussed in detail. |
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Thurs. |
Analysis & Applications Seminar Speakers: Erik Lundberg, Ph.D., Parker Edwards, Ph.D., Florida Atlantic University Title: Magnanini’s conjecture on hot spots and far spots Note: Part I of a two part presentation Abstract: Imagine a bounded domain whose boundary is held at zero temperature and whose interior contains a uniform heat source. After the system reaches equilibrium, the resulting temperature profile is the solution to a Poisson equation. How many hot spots (local maxima of the solution) can there be? Is the number of hot spots controlled by geometric features of the domain? The same PDE shows up in a variety of classical problems. Its solution is often referred to as the “torsion function” of the domain since it plays a prominent role in elasticity theory modeling the shear stress in a twisted cylindrical bar. It has more recently been referred to as the “localization landscape” in connection with localization of eigenfunctions of the Laplacian. A 2016 conjecture of R. Magnanini proposes that the number of hot spots does not exceed the number of local maxima of the distance to the boundary. In this view, the domain’s “far spots’’ should control its “hot spots.’’ In this talk, I will give an overview of critical points of the torsion function and describe ongoing joint work with Parker Edwards and Koushik Ramachandran. |
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Thurs. |
Riemannian Geometry reading group
Book: Lee. John M., Introduction to Riemannian Manifolds. ISBN: 978-3-319-91754-2 physical copy. Electronic access is available through the S.E. Wimberly Library. Join us for a weekly reading group! We will go through Lee's Introduction to Riemannian Manifolds. Anyone who's interested in joining us is welcome. For more information, please contact Prof. Parker Edwards . |
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Tuesday |
Reading seminar on Quantum Algorithms Speaker: TBA This reading seminar is devoted to quantum algorithms, following Buchmann’s recently published book in the AMS series: https://bookstore.ams.org/amstext-64 This seminar meets every other Tuesday, 10-10:50 AM in SE 271. If interested in participating, please email sicaf@fau.edu to subscribe to the crypto_math mailing list. * The schedule and topics of upcoming seminars can be found here: https://researchseminars.org/seminar/FAUcryptotopical |
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Thurs. |
Riemannian Geometry reading group
Book: Lee. John M., Introduction to Riemannian Manifolds. ISBN: 978-3-319-91754-2 physical copy. Electronic access is available through the S.E. Wimberly Library. Join us for a weekly reading group! We will go through Lee's Introduction to Riemannian Manifolds. Anyone who's interested in joining us is welcome. For more information, please contact Prof. Parker Edwards |
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Sunday |
Florida Women in Math Day Florida Atlantic University's student chapter of the Association of Women and Mathematics will host Florida Women in Math Day! For mor information, please contact Rosemary Yool-Vidal at ryoolvidal2021@fau.edu.
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Thurs. |
Riemannian Geometry reading group
Book: Lee. John M., Introduction to Riemannian Manifolds. ISBN: 978-3-319-91754-2 physical copy. Electronic access is available through the S.E. Wimberly Library. Join us for a weekly reading group! We will go through Lee's Introduction to Riemannian Manifolds. Anyone who's interested in joining us is welcome. For more information, please contact Prof. Parker Edwards |
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Tuesday |
Reading seminar on Quantum Algorithms Speaker: TBA This reading seminar is devoted to quantum algorithms, following Buchmann’s recently published book in the AMS series: https://bookstore.ams.org/amstext-64 This seminar meets every other Tuesday, 10-10:50 AM in SE 271. If interested in participating, please email sicaf@fau.edu to subscribe to the crypto_math mailing list. * The schedule and topics of upcoming seminars can be found here: https://researchseminars.org/seminar/FAUcryptotopical |
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Thurs. |
Riemannian Geometry reading group
Book: Lee. John M., Introduction to Riemannian Manifolds. ISBN: 978-3-319-91754-2 physical copy. Electronic access is available through the S.E. Wimberly Library. Join us for a weekly reading group! We will go through Lee's Introduction to Riemannian Manifolds. Anyone who's interested in joining us is welcome. For more information, please contact Prof. Parker Edwards |
