2023-24 Department of Mathematics and Statistics Events |
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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 II) 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. |
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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 |
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Wednesday |
Analysis and Applications/Colloquium Speaker: Dr. Matt Holzer, Mathematical Sciences, George Mason University Title: Pushed and pulled invasion fronts in parabolic PDEs Absract: Invasion fronts refer to fronts that propagate into unstable states. This talk will provide a review of some of the theoretical aspects of invasion fronts and discuss current research efforts. These fronts are often categorized as pushed or pulled and the talk will cover theoretical and numerical aspects of locating these fronts and identifying their speeds as well as their relevance to applications. All are welcome! |
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August, 2024 |
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August, 5-9 |
Young CryptograpHers Cybersecurity Summer Camp Young CryptograpHers is a Cybersecurity summer camp specially designed for high school girls. Participants will be introduced to the fundamental principles of cybersecurity and learn how to apply conceptual knowledge to real-world situations. The camp will focus on Post-Quantum Cryptography, the area of math that is in charge of protecting our information in the era of quantum technology. The program includes lectures and activities by FAU faculty, alumni and speakers from industry and government. Our goal is to motivate and inspire talented students who are interested in a cybersecurity career. ( flyer ) |
