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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Tuesday |
Master Thesis Defese Speaker: Diana Dancea, Masters degree candidate, Florida Atlantic University Title: A Computer Vision Approach to Analyzing Taxane Effects on Prostate Cancer Cells Abstract: Actin is a family of proteins that help create the structure of the cytoskeleton, which gives shape to the cell. In many chemotherapy treatments, researchers target actin because it controls the cell division process. Therefore, if they are able to understand the actin fibers, that may help in formulating methods to stop or slow down cancer cells from reproducing. Another important protein is PAK6, which regulates actin. In our research, a collaborative effort with the FAU Medical School, we use machine learning techniques to analyze knock-out cells, which had their PAK6 protein knocked out, and compare them to normal cells after taxane treatment, a popular family of chemotherapy drugs, has been introduced. Our aim is to observe if the knock-out process leads to any organizational and morphological changes in the cell, which ultimately may help with drug discovery in the future. |
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Thurs. |
Analysis & Applications Seminar Speaker: Parker Edwards, Ph.D., Florida Atlantic University Title: Computing far spots for algebraic torsion functions Abstract: Many geometric properties of a Euclidean subspace X are encoded by the distance-to-X function, $d_X$. From a computational geometry perspective, one never knows $d_X$ directly, and instead must make due by approximating $d_X$ by $d_P$, where $P$ is a "good" finite point sample near X. Subspaces of real solutions defined by polynomial equations abound, however, as examples arising from both mathematical and scientific sources. If one has a full specification of one such real algebraic subset, i.e. a list of polynomials defining it, you might hope to instead use the equations to compute properties of $d_X$ directly. My approach to this genre of problems is via numerical algebraic geometry solving methods. In this talk, I will discuss some of these methods in the context of an ongoing application in partial differential equations relating to a 2016 conjecture of R. Magnanini. Given a simply-connected planar domain D and a PDE on the domain with boundary conditions, a natural question which arises is whether and how the geometry of D impacts the solutions. Magnanini proposed that solutions to the torsional creep problem on such a domain, an archetypical example of this type of PDE with simple boundary conditions, should have at most as many local maxima ("hot spots") as the number of local maxima of the minimum-distance-to-boundary-D function $d_{\partial D}$ ("far spots"). When the boundary of the domain is a generic and smooth algebraic curve, there are finitely many far spots and they can be computed numerically. I will discuss a family of such algebraic examples and some aspects of how to count and certify the number of far spots. This work is joint with Erik Lundberg 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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Friday |
MAA - SIGMAA HOM Virtual Speaker Series Speaker: Colette Chilton, Florida Atlantic University Title: An Overview of the Usage of Ancient and Contemporary Vigesimal Numeral Systems Abstract: The modern base-10 decimal system originated during the 1st to 4th century A.D. and remains in place for most cultures. From the 3rd century B.C.E through the 17th Century A.D., the Maya had multiple ways of representing their numerals, one of which is the vigesimal system. In the mid 1990s, the vigesimal system was revamped by a contemporary group of marginalized mathematicians, and is still in use and being researched by universities to this day, but not without facing backlash. This presentation will include the historical context of the vigesimal numeral system within the Pre-Classic, Classic, and Post-Classic Maya periods, the contemporary vigesimal numeral system, and examples of how to perform arithmetic through both of these methods. Zoom Link: msu.zoom.us/j/94740679958 Passcode: Cardano |
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Sunday |
Florida Women in Math Day: A Celebration of Emmy Noether Florida Atlantic University's student chapter of the Association of Women and Mathematics will host Florida Women in Math Day: A Celebration of Emmy Noether FLYER Keynote Speaker: Dr. Amina A. Khennaoui, Assistant Professor, University of Constantine 2, Constantine, Algeria BIO: Dr. Amina A. Khennaoui is Fulbright Scholar and International Leader in Applied Mathematics and Fractional Dynamics. Read more Join us for a day of research talks, a keynote speaker presentation, break out sessions and so much more! |
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Tues. |
Speaker: Christophe Petit, Ph. D., (Université libre de Bruxelles (ULB) and University of Birmingham) Title: Quantum Security of the Vectorization Problem with Shifted Inputs +Zoom (click here) Abstract: Cryptographic group actions provide a basis for simple post-quantum generalizations of many cryptographic protocols based on the discrete logarithm problem (DLP). However, many advanced group action-based protocols do not solely rely on the core group action problem (the so-called vectorization problem), but also on variants of this problem, to either improve efficiency or enable new functionalities. In particular, the security of the CSI-SharK threshold signature protocol relies on the hardness of the Vectorization Problem with Shifted Inputs where (in DLP formalism) the adversary not only receives g and g^x, but also g^{xc} for multiple known values of c. A natural open question is whether the extra data provided to the adversary in this variant allows them to solve the underlying problem more efficiently. In this paper, we revisit the concrete quantum security of this problem. We start from a quantum multiple hidden shift algorithm of Childs and van Dam, which to the best of our knowledge was never applied in cryptography before. We specify algorithms for its subroutines and we provide concrete complexity estimates for both these subroutines and the overall algorithm. We apply our analysis to the CSI-SharK protocol. In prior analyses based on Kuperberg’s algorithms, group action evaluations contributed to a significant part of the overall T-gate cost. For CSI-SharK suggested parameters, our new approach requires significantly fewer calls to the group action evaluation subroutine, leading to significant complexity improvements overall. We describe two instances of our approach, one which lowers the T-gate complexity, and the other the QRAM requirements. We obtain significant speedups – even in both metrics simultaneously – and we quantify the degradation of the quantum security of the protocol when the number of curves in the public key increases. This is based on joint work with Paul Frixons, Valerie Gilchrist, Péter Kutas and Simon Merz and Lam Pham Bio: Christophe Petit is an Associate Professor at the University of Birmingam and the Free University of Brussels. His research interests are in cryptography, particularly cryptanalysis and mathematical aspects. |
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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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Friday |
Colloqium
Speaker: Zachary Himes, Department of Mathematics, University of Michigan ON ZOOM in SE43, room # 215 |
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Tuesday |
Colloquium
Speaker: Zachary Himes, Department of Mathematics, University of Michigan ZOOM Link: https://fau-edu.zoom.us/j/87416674775?pwd=ZbyYgbcn7EvhkMRygVCydhlsNoZwxq.1 |
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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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Tuesday |
Colloquium Speaker: Brian Toner, Ph.D., University of Arizona Title: Mathematical Frameworks to Advance Quantitative MRI: Accelerated T2 Mapping and Robust Uncertainty Quantification Abstract: Magnetic resonance imaging (MRI) provides excellent soft tissue contrast without ionizing radiation, but its clinical utility is often limited by its sensitivity to motion, relatively slow acquisition times, and qualitative images (unitless signal intensity). Quantitative MRI (qMRI) addresses this final limitation by using MRI to measure physical biomarkers that hold significant diagnostic value. However, qMRI requires fitting multiple co-registered images to a physical model, which exacerbates scan time and motion artifacts. This talk presents mathematical and computational frameworks designed to overcome these limitations through two primary avenues: image reconstruction and parameter estimation. First, to address the need for accelerated imaging, we introduce a deep learning reconstruction method for highly undersampled, free-breathing abdominal T2 mapping. We demonstrate the ability to reconstruct high-quality T2 maps of the entire abdomen in clinically feasible scan times. Second, to ensure these rapid measurements are statistically robust, we present a novel framework for uncertainty quantification (UQ) in qMRI. By deriving both frequentist and Bayesian methods, we enable the generation of accurate confidence and credible intervals for each voxel. These UQ maps can be evaluated side-by-side with parameter maps to provide clinicians with a clear visualization of estimate reliability. ZOOM Link: Here is the zoom link: https://fau-edu.zoom.us/j/81190699808?pwd=5Smx3907wCA1um8oT2dQZMUIbmiApu.1 |
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Thurs. |
Analysis & Application Seminar Speaker: Amina Aicha Khennaoui. Ph.D., ssistant Professor at University of Constantine 2, Constantine, Algeria Title: Six counting problems for Single input and almost completely controllable dynamical systems Abstract: Control theory seeks to understand when and how a dynamical system can be driven to a desired state. We study single-input linear systems of dimension 𝑛, where each system corresponds uniquely to a partition 𝜆 whose diagram encodes the complete algebraic structure of the single input system. Six natural counting problems arise. Applying vector space duality to a single-input controllable system in 𝑉 produces an almost completely controllable system characterized by the decomposition V∗=U∗⨁<e,Te,T2e,…..>. The six counting problems on the single-input side carry over, via duality, to six counting problems on the almost completely controllable side. Furthermore, duality determines the precise placement of the unique additional controller needed to recover full controllability: position the top cell of the longest column of the Young diagram. |
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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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Friday |
Colloquium Speaker: Dr. J.P. Lessard, McGill University Title: A constructive approach for proving existence of periodic orbits in differential equations with large state-dependent delays Abstract: State-dependent delay equations (SDDEs) pose significant theoretical and computational challenges, as the delay depends on the evolving state through nonlinear composition terms. In contrast with ODEs, parabolic PDEs, or delay equations with constant delays, SDDEs may fail to generate a semiflow. Even when a semiflow exists, the dynamics evolve on an infinite-dimensional phase space, with the composition operator introducing additional analytical difficulties. As a result, periodic solutions, which are central to understanding recurrent dynamics, are particularly challenging to study in this setting. In this talk, we present a computer-assisted, constructive method to prove the existence of periodic solutions in genuinely state-dependent delay equations, without relying on perturbative reductions to ODEs or PDEs. Our approach combines Fourier expansions with a Newton–Kantorovich argument in a low-regularity Banach space. The nonlinear composition terms are handled rigorously using discrete Fourier transforms, contour integrals, and the discrete Poisson formula. We illustrate the method on a representative toy model. This is joint work with Jan Bouwe van den Berg (VU University Amsterdam), Maxime Breden (École Polytechnique), Matthieu Cadiot (École Polytechnique), and Kevin Church (CRM, Montréal). |
