2023-24 Department of Mathematics and Statistics Events |
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April, 2024 |
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Monday |
Join the faculty and students of Cryptography for a biweekly reading seminar on multi-party computations. |
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Wednesday |
Join your friends and other math enthusiasts at FAU's Math Club events! The purpose of our Club is to improve academic ability, spread awareness of mathematics’ importance, and share a passion for all fields of mathematics! The club is open to all majors and all math backgrounds. Activities at the club will include:
Snacks are always available! See you there! |
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Thursday |
Analysis and Applications Seminar Speaker : J.P. Lessard, McGill University Title : Computer-assisted proofs for differential equations with non-polynomial nonlinearities via the FFT. Abstract : This presentation introduces a methodology for generating computer-assisted proofs (CAPs) establishing the existence of solutions for nonlinear differential equations with non-polynomial analytic nonlinearities. Our approach integrates the Fast Fourier Transform (FFT) algorithm with interval arithmetic and a Newton-Kantorovich argument to construct CAPs effectively. Notably, to rigorously manage the Fourier coefficients of the nonlinear term Fourier series, we leverage insights from complex analysis and the Discrete Poisson Summation Formula. We showcase the applicability of our method through two examples: firstly, verifying the existence of periodic orbits in the Mackey-Glass (delay) equation, and secondly, proving the existence of periodic localized traveling waves in the two-dimensional suspension bridge equation. |
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Saturday |
Welcome to Math Circle! The main purpose of the circle is to have fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, playing mathematical games. The purpose of this circle is to amplify the mathematical knowledge of students who like math, and do it in a fun way, we will also look at some AMC problems, and see how what was seen in the circle applies. We will be meeting every other Saturday, beginning Saturday, September 23, 2023. It is important to emphasize what these circle meetings are NOT. They are not classes or lectures. Students are free to walk about and talk. Source of the Problems: The majority of problems will come from very diverse sources, old AMC competitions, the Moscow Math Circle Problem book, historical sources (for example Fibonacci's Liber Abaci), etc. A few will be made up by us. Sources will not usually be credited but credits will be revealed upon request, if we know the source. Registration is FREE! Register Here for Fall, 2024 Math Circles |
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Monday |
Speaker : Dr. Francesco Sica, Assistant Professor, Florida Atlantic University +Zoom (click here) Title : Acceleration of multiscalar multiplication for zkSNARKs FLYER Abstract : The main computational bottleneck in the implementation of zero-knowledge succinct arguments of knowledge (zkSNARKs) based on elliptic curves, such as Pinocchio, is the evaluation (called multiscalar multiplication) ∑i=1naiPi\sum_{i=1}^n a_i P_i , where the aia_i ’s are scalar and the PiP_i ’s are fixed elliptic curve points. We will review currently used techniques and introduce new improvements. This is joint work with Xinxin Fan, Veronika Kuchta and Lei Xu. |
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Monday |
MS Presentation Speaker: Francis Boateng, MS Candidate Title: Influencing Under-Five Mortality in Rural-Urban Ghana: An Applied Survival Analysis Abstract: In this presentation, we explore the application of the Breslow Method for Ties in analyzing survival probability, utilizing data from the 2014 Ghana Demographic and Health Survey (GDHS). Focusing on Ghana's rural and urban contexts, we investigate the socio-economic and demographic factors influencing under-five mortality. This approach assumes a constant hazard function within each interval between event times. Our findings highlight maternal age, mother's education, household wealth index quintile, place of delivery, and birth order as significant determinants of child survival in Ghana. Moreover, the influence of these determinants varies between urban and rural settings. The study sheds light on the nuanced dynamics shaping child survival outcomes, contributing to understanding health disparities across different socio-economic contexts. All are cordially invited. |
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Monday |
SIAM Meeting (FAU Student Chapter) SIAM (Society for Industrial and Applied Mathematics) fosters the development of applied mathematical and computational methodologies needed in various application areas. Applied mathematics, in partnership with computational science, is essential in solving many real-world problems. Through publications, research, and community, the mission of SIAM is to build cooperation between mathematics and the worlds of science and technology. We hope to see you there! |
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Thursday |
Analysis and Applications Seminar Speaker: Joan Gimeno, Universitat de Barcelona Title: New Solutions from Functional Perturbed Uniformly Hyperbolic Trajectories
Abstract: We develop a method to construct solutions of some (retarded or advanced) equations. We assume that the equations considered are formally close to an ODE and that the ODE admits hyperbolic solutions (that is, perturbations This is a joint work with R. de la Llave and J. Yang. |
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Thursday |
Join your friends and other math enthusiasts at FAU's Math Club events! The purpose of our Club is to improve academic ability, spread awareness of mathematics’ importance, and share a passion for all fields of mathematics! The club is open to all majors and all math backgrounds. Activities at the club will include:
Snacks are always available! See you there! |
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Friday |
Complex Analysis and Nonlinear Dynamic colloquium Speaker: Alex Stokolos, Georgia Southern University Title: Geometric complex analysis and cycles detection in nonlinear dynamics Abstract: In the talk, I will discuss a remarkable connection between the problem of long cycles detection in nonlinear autonomous dynamical systems and geometric complex analysis. The presentation will be accessible to everyone who took a standard Complex Analysis course. |
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Saturday |
Welcome to Math Circle! The main purpose of the circle is to have fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, playing mathematical games. The purpose of this circle is to amplify the mathematical knowledge of students who like math, and do it in a fun way, we will also look at some AMC problems, and see how what was seen in the circle applies. We will be meeting every other Saturday, beginning Saturday, September 23, 2023. It is important to emphasize what these circle meetings are NOT. They are not classes or lectures. Students are free to walk about and talk. Source of the Problems: The majority of problems will come from very diverse sources, old AMC competitions, the Moscow Math Circle Problem book, historical sources (for example Fibonacci's Liber Abaci), etc. A few will be made up by us. Sources will not usually be credited but credits will be revealed upon request, if we know the source. Registration is FREE! Register Here for Fall, 2024 Math Circles |
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Monday |
Join the faculty and students of Cryptography for a biweekly reading seminar on multi-party computations. |
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Wednesday |
Join your friends and other math enthusiasts at FAU's Math Club events! The purpose of our Club is to improve academic ability, spread awareness of mathematics’ importance, and share a passion for all fields of mathematics! The club is open to all majors and all math backgrounds. Activities at the club will include:
Snacks are always available! See you there! |
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Thursday |
MS Presentation MS Candidate: Fatemeh Fogh Title: Parametrization Method for Stable and Unstable Manifolds for Studying Fixed Points Abstract: Utilizing a parametric representation of the stable and unstable manifolds, we demonstrate that for certain parameter values (specifically in the scenario initially explored by Hénon), the Hénon mapping exhibits a transversal homoclinic orbit. All are cordially invited. |
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Sunday |
Association for Women in Mathematics (FAU Student Chapter) presents Florida Women in Math Day 2024 All genders, backgrounds, and ages are welcome to attend and present at Florida Women in Math Day! Come and enjoy a career panel student posters a scavenger hunt and FREE Breakfast, lunch, and refreshments! FLYER for more information |
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Tuesday |
Ph.D. Dissertation Defense Speaker: Dominic Gold, Ph.D. candidate Advisor: Dr. Francis Motta Title: Privacy-Preserving Topological Data Analysis Using Homomorphic Encryption Abstract: Computational tools grounded in algebraic topology, known collectively as topological data analysis (TDA), have been used for dimensionality-reduction to preserve salient and discriminating features in data. This faithful but compressed representation of data through TDA's flagship method, persistent homology (PH), motivates its use to address the complexity, depth, and inefficiency issues present in privacy-preserving, homomorphic encryption (HE)-based machine learning (ML) models, which permit a data provider (often referred to as the Client) to outsource computational tasks on their encrypted data to a computationally-superior but semi-honest party (the Server). This work introduces efforts to adapt the well-established TDA-ML pipeline on encrypted data to realize the benefits TDA can provide to HE's computational limitations as well as provide HE's provable security on the sensitive data domains in which TDA has found success in (e.g., sequence, gene expression, imaging). The privacy-protecting technologies which could emerge from this foundational work will lead to direct improvements to the accessibility and equitability of health care systems. ML promises to reduce biases and improve accuracies of diagnoses, and enabling such models to act on sensitive biomedical data without exposing it will improve trustworthiness of these systems. To adapt the beginning steps of the TDA-ML pipeline, we create an HE-compatible arithmetic circuit of the fundamental map to compute PH on an encrypted boundary matrix for further use in downstream model development (with a complete construction, parameter selection guarantees, and error analysis). We achieve this by modifying the logical structure of the map and by developing new arithmetic circuits to replace its computational and conditional statements. We also show work in adapting the terminal steps of the TDA-ML pipeline to realize the boons TDA affords HE-ML models on the MNIST digits dataset using a logistic regression (LR) classifier. We demonstrated that the TDA methods chosen improve encrypted model inference with a 10-25 fold reduction in amortized time while improving model accuracy up to 1.4% compared to naive reductions that used downscaling/resizing, and we show the first steps in realizing these same improvements on encrypted model training. Please contact Dr. Hongwei Long for an electronic copy of the dissertation. Zoom Meeting link: https://fau-edu.zoom.us/my/dgold2012?omn=81121210837 All are cordially invited. |
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Wednesday |
Join your friends and other math enthusiasts at FAU's Math Club events! The purpose of our Club is to improve academic ability, spread awareness of mathematics’ importance, and share a passion for all fields of mathematics! The club is open to all majors and all math backgrounds. Activities at the club will include:
Snacks are always available! See you there! |
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Thursday |
Analysis and Applications Seminar This week in the Analysis and Applications Seminar, Dr. Jason Mireles-James will give the first of two or three talks which will continue for the next few weeks. Speaker: Dr. Jason Mireles-James Title: A stable manifold theorem for delay maps (part I) Abstract: I will go over the proof of a stable manifold theorem which can be applied to a class of delay maps (and to compositions of these maps). At the fixed points I would like to consider, there are finitely many unstable and center eigenvalues, and countably many stable eigenvalues accumulating to zero. The presence of center directions effects the setup of the proof. Also, the goal is to apply this stable manifold theorem in constructive computer assisted proofs. Because if this, you don't want to assume that the map is completely diagonalized. This also requires adjusting standard arguments. I will be careful to obtain not only explicit bounds on the location of the stable manifold (which is infinite dimensional), but also explicit bounds on Lipschitz constants of the derivatives. I will start with some basic discussion of delay maps, including the reason for the appearance of center directions. Indeed, at some moment it will be important to count exactly the number of eigenvalues on the unit circle, and to work out formulas for their eigenfunctions. Another facet of the discussion is that, to obtain the regularity results, I'll use a very nice theorem due to Lanford which partially extends the Arzela-Ascoli theorem to families of functions defined on Banach spaces (i.e. to functions with non-compact domain and range). I think it would be nice to work through the proof of Lanford's theorem, and this will be the content of the third (fourth?) talk in this little series. These will be ``working'' talks, so constructive criticism/comments/questions are really helpful. |
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Saturday |
Welcome to Math Circle! The main purpose of the circle is to have fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, playing mathematical games. The purpose of this circle is to amplify the mathematical knowledge of students who like math, and do it in a fun way, we will also look at some AMC problems, and see how what was seen in the circle applies. We will be meeting every other Saturday, beginning Saturday, September 23, 2023. It is important to emphasize what these circle meetings are NOT. They are not classes or lectures. Students are free to walk about and talk. Source of the Problems: The majority of problems will come from very diverse sources, old AMC competitions, the Moscow Math Circle Problem book, historical sources (for example Fibonacci's Liber Abaci), etc. A few will be made up by us. Sources will not usually be credited but credits will be revealed upon request, if we know the source. Registration is FREE! Register Here for Fall, 2024 Math Circles |
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Monday |
Join the faculty and students of Cryptography for a biweekly reading seminar on multi-party computations. |
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May, 2024 |
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Wednesday |
MS Exam (Presentation) Speaker: Nathan Blood, MS Candidate Title: Analysis of the Stability of HIV SIR Models Abstract: Using a Susceptible, Infected, and Recovered (SIR) model for spread of HIV, we determine conditions for a reproduction number which determine the circumstances for stability of the infected class. All are cordially invited. |
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Thursday |
Analysis and Applications Seminar This week in the Analysis and Applications Seminar, Dr. Jason Mireles-James will give the second of two or three talks which will continue for the next few weeks. Speaker: Dr. Jason Mireles-James Title: A stable manifold theorem for delay maps (part I) Abstract: I will go over the proof of a stable manifold theorem which can be applied to a class of delay maps (and to compositions of these maps). At the fixed points I would like to consider, there are finitely many unstable and center eigenvalues, and countably many stable eigenvalues accumulating to zero. The presence of center directions effects the setup of the proof. Also, the goal is to apply this stable manifold theorem in constructive computer assisted proofs. Because if this, you don't want to assume that the map is completely diagonalized. This also requires adjusting standard arguments. I will be careful to obtain not only explicit bounds on the location of the stable manifold (which is infinite dimensional), but also explicit bounds on Lipschitz constants of the derivatives. I will start with some basic discussion of delay maps, including the reason for the appearance of center directions. Indeed, at some moment it will be important to count exactly the number of eigenvalues on the unit circle, and to work out formulas for their eigenfunctions. Another facet of the discussion is that, to obtain the regularity results, I'll use a very nice theorem due to Lanford which partially extends the Arzela-Ascoli theorem to families of functions defined on Banach spaces (i.e. to functions with non-compact domain and range). I think it would be nice to work through the proof of Lanford's theorem, and this will be the content of the third (fourth?) talk in this little series. These will be ``working'' talks, so constructive criticism/comments/questions are really helpful.
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Saturday May, 11 |
Welcome to Math Circle! The main purpose of the circle is to have fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, playing mathematical games. The purpose of this circle is to amplify the mathematical knowledge of students who like math, and do it in a fun way, we will also look at some AMC problems, and see how what was seen in the circle applies. We will be meeting every other Saturday, beginning Saturday, September 23, 2023. It is important to emphasize what these circle meetings are NOT. They are not classes or lectures. Students are free to walk about and talk. Source of the Problems: The majority of problems will come from very diverse sources, old AMC competitions, the Moscow Math Circle Problem book, historical sources (for example Fibonacci's Liber Abaci), etc. A few will be made up by us. Sources will not usually be credited but credits will be revealed upon request, if we know the source. Registration is FREE! Register Here for Fall, 2024 Math Circles |
