2025-26 Department of Mathematics and Statistics Events |
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August, 2025 |
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August |
CryptoTeens in South Florida summer camp is a five - day camp for high-school students who want to discover the technology and the science behind cryptography. Participants will be introduced to the fundamental principles of c ryptography 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 stimulating lectures, inspiring talks by alumni and speakers from industry and government , and engaging exercise sessions. |
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Tuesday |
Reading seminar on Quantum Algorithms 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 215. 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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Wednesday |
Riemannian manifolds 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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September, 2025 |
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Tuesday |
Speaker: Hansraj Jangir, Ph.D. student, Florida Atlantic University Title: A Quasi-polynomial time Quantum Algorithm for the Extrapolated Dihedral Coset Problem. FLYER Abstract: The Learning With Errors (LWE) problem, introduced by Regev (STOC’05), is one of the fundamental problems in lattice-based cryptography, believed to be hard even for quantum adversaries. Regev (FOCS’02) showed that LWE reduces to the quantum Dihedral Coset Problem (DCP) and later, Brakerski et al. (PKC 2018) extended this to the more general Extrapolated Dihedral Coset Problem (EDCP). In this talk, we present a quasi-polynomial time quantum algorithm for solving EDCP over power-of-two moduli, using a quasi-polynomial number of samples. We stress that our algorithm does not affect the security of LWE with standard parameters, as the reduction from standard LWE to EDCP limits the number of samples to be polynomial. Bio: Hansraj is a PhD student in the Department of Mathematics and Statistics at Florida Atlantic University, Boca Raton. Prior to starting his doctoral studies, he worked as a Junior Research Fellow at the Defense Research and Development Organization (DRDO), Delhi. His research interests include lattice based cryptography and quantum algorithms. |
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Wednesday |
Riemannian manifolds 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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Thursday |
Analysis and Applications Speaker: Lousi Merlin, Ph.D., Associate Professor, Florida Atlantic University, Department of Urban Planning Title: Finding the Right Formula for Land-Use Mix |
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Friday |
Graduate Student Seminar Speaker: Addie Randolph, Florida Atlantic University Title: Invariant Circles of the Standard Map Abstract: Our goal with the following study is to lead to finding quasiperiodic orbits of the Circular Restricted Three Body Problem. A flow has quasiperiodic behavior if the associated Poincare map has quasiperiodic behavior. This encourages us to first look first at maps, and in this case, we look at a very well-known map, the standard map. An orbit exhibits Quasiperiodic behavior in a map if it is topologically conjugate to a rigid rotation of an irrational number. As given in the systematic recipe by Dr. Mireles James and David Blessing, we first compute the rotation number of the quasiperiodic orbit using the weighted Birkhoff averaging method. Then we use a Newton scheme to solve a conjugacy equation describing the circle resulting in the Fourier expansion of the quasiperiodic invariant circle. Finally, we observe the error of this method on multiple initial conditions. |
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Tuesday |
Speaker: Nurdaulet Shynarbek, Mathematics Educational Program Coordinator (In-person) Title: Novel Representations of log 2 Through Polynomial Continued Fractions FLYER Abstract: This presentation explores new representations of the mathematical constant log 2 using polynomial continued fractions. Building on previous work in continued fraction theory, we investigate a conjecture by Zhu He which proposes a specific polynomial continued fraction for log 2. We will demonstrate the validity of this conjecture and introduce an infinite family of new polynomial continued fractions for log 2. |
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Tuesday |
Speaker: Alibek Orynbassar, Senior Lecturer, Department of Pedagogy of Natural Sciences, SDU University Title: Complete Classification of Quadratic Irrationals with Period Two FLYER Abstract: This talk presents a full classification of quadratic irrationals whose continued fraction expansions have period length two. While it is known that the continued fraction of N is periodic, the distribution of period lengths is less understood. We establish precise conditions for the period-two case and illustrate the results with numerical examples. Bio: Alibek Orynbassar is a Senior Lecturer in the Department of Pedagogy of Natural Sciences at SDU University in Kaskelen, Kazakhstan, a position he has held since July 2023. He is currently pursuing a PhD in Mathematics and Natural Sciences at SDU. He earned both his Master’s (2017) and Bachelor’s (2014) degrees in Mathematics and Natural Sciences from SDU. From July 2022 to June 2023, he was a Visiting Scholar at Teachers College, Columbia University, where he expanded his expertise in mathematics education and research. Prior to his current role, he served as Mathematics Program Coordinator in the Department of Education at SDU (2020–2022) and as Senior Lecturer (2017–2022). Earlier in his career, he taught mathematics in secondary schools (2013–2017), where he prepared students for mathematics Olympiads. He has also contributed as a jury member for regional school mathematics Olympiads and scientific project competitions (2018–2020). |
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Wednesday |
Riemannian manifolds 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 |
Speaker: Dung Bui, LIP6, Sorbonne Université, France Title: FOLEAGE: F4OLE-Based Multi-Party Computation for Boolean Circuits FLYER Abstract: Secure Multi-party Computation (MPC) allows two or more parties to compute any public function over their privately-held inputs, without revealing any information beyond the result of the computation. Modern protocols for MPC generate a large amount of input-independent preprocessing material called multiplication triples, in an offline phase. This preprocessing can later be used by the parties to efficiently instantiate an input-dependent online phase computing the function. To date, the state-of-the-art secure multi-party computation protocols in the preprocessing model are tailored to secure computation of arithmetic circuits over large fields and require little communication in the preprocessing phase, typically O(N · m) to generate m triples among N parties. In contrast, when it comes to computing preprocessing for computations that are naturally represented as Boolean circuits, the state-of-the-art techniques have not evolved since the 1980s, and in particular, require every pair of parties to execute a large number of oblivious transfers before interacting to convert them to N-party triples, which induces an Ω(N^2 · m) communication overhead. In this paper, we introduce FOLEAGE, which addresses this gap by introducing an efficient preprocessing protocol tailored to Boolean circuits. FOLEAGE exhibits excellent performance: It generates m multiplication triples over F2 using only N · m + O(N^2 · log m) bits of communication for N-parties, and can concretely produce over 12 million triples per second in the 2-party setting on one core of a commodity machine. Our result builds upon an efficient Pseudorandom Correlation Generator (PCG) for multiplication triples over the field F4. Roughly speaking, a PCG enables parties to stretch a short seed into a large number of pseudorandom correlations non-interactively, which greatly improves the efficiency of the offline phase in MPC protocols. Our construction significantly outperforms the state-of-the-art, which we demonstrate via a prototype implementation. This is achieved by introducing a number of protocol-level, algorithmic-level, and implementation-level optimizations on the recent PCG construction of Bombar et al. (Crypto 2023) from the Quasi-Abelian Syndrome Decoding assumption. Bio: Dung Bui is a postdoctoral researcher at LIP6, Sorbonne Université, France. She completed her PhD at IRIF, Université Paris Cité. Her research interests are in various aspects of both practical and theoretical cryptography, including secure multiparty computation, zero-knowledge proofs, and post-quantum cryptography. Contact email: dung.bui@lip6.fr |
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Wednesday |
Riemannian manifolds reading group Prof. Parker Edwards 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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Thursday |
Analysis & Applications Seminar Speaker: Dr. Ivan Sudakow Title: Modeling Critical Transitions in Complex Systems: From Local Interactions to Global Regime Shifts Abstract: When do local interactions trigger a global regime change, and how can we identify the mechanism? I present a Universal Dynamical Approximation (UDA) framework—parameterized universality for finite-dimensional, structurally stable dynamics—that places multiple model classes in a common normal form; in these coordinates, the bifurcation diagram yields reduced-order models. UDA is realized across reaction–diffusion systems, interfacial fluid flows, center–satellite network ODEs, and stochastic lattice spin models. Case studies include climate tipping points, ecosystem dynamics, evolutionary dynamics, and data-driven modeling supported by modern data analysis and interpretable machine learning. |
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Friday |
Graduate Student Seminar (GSS) Speaker : Mr. Ali Ittayem Title : Computational Methods for Identifying Chaotic Dynamics in the Sakarya System Abstract : In this work, we investigate the onset of chaotic dynamics in the Sakarya system through the construction and analysis of Poincaré maps. By computing periodic orbits on a chosen cross-section and evaluating the associated monodromy matrices, we extract the stability properties of these orbits and characterize the eigenvalue structure of the corresponding Poincaré return maps. The stable and unstable manifolds of hyperbolic periodic points are approximated using parameterization methods and iterative schemes, allowing for the detection of transversal intersections that signal the presence of Smale horseshoe dynamics. These results provide strong evidence for the existence of chaotic behavior in the Sakarya system, linking local manifold geometry to global dynamical complexity. Beyond offering a framework for analyzing this particular system, our methodology demonstrates how Poincaré maps serve as a powerful tool for identifying and verifying chaotic structures in nonlinear dynamical systems. |
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Tuesday |
Analysis and its Applications Seminar Speaker: Youngsuk Ko who is currently at the Department of Epidemiology of Microbial Diseases, Yale School of Public Health, New Haven, USA Title: From Real-World Data to Decision-Ready Models for Public Health: Mathematical and Statistical Approaches Abstract: How can mathematical and statistical modeling, grounded in real-world data, inform public health policy—and what should we do when the data are messy? This talk presents a pipeline that connects individual-level records to population-level decisions across diseases. First, using COVID-19 as a case study, I build an event-level likelihood directly from individual confirmed-case records (e.g., onset and report dates, demographics) and use maximum likelihood to estimate parameters of a mechanistic model. This enables head-to-head evaluation of vaccine-prioritization policies under limited supply—for example, prioritizing older adults versus the general adult population. Second, for dengue in Brazil, I use catalytic models to recover age- and state-specific forces of infection and immunity profiles, then embed these estimates in an age-structured transmission model to assess allocation strategies when supply is constrained. The result is state-level susceptibility maps and decision curves that clarify where—and to whom—doses should go first. Throughout, I emphasize identifiability, transparent assumptions, and uncertainty quantification so that conclusions remain interpretable and reproducible. I close with brief directions for extending the same pipeline to other vector-borne and respiratory pathogens and to additional data streams. youngsuk.ko@yale.edu |
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Wednesday |
Riemannian manifolds 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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Thursday |
Analysis and Applications Seminar Speaker: Yu Xiang https://sites.google.com/site/yuxianghomepage/home Title: Robust Learning from Heterogeneous Data Abstract: The theme of my talk will be principled robust learning from heterogeneous data, where the heterogeneity arises naturally from either distribution shifts or decentralized settings. In the first part, I will focus on learning under distribution shifts from a causal perspective. Distribution shift is arguably the main challenge in today’s machine learning where one has to apply predictors learned from one dataset to a new dataset with a different distribution. One principled approach is to adopt the structural causal models (SCMs) by Pearl to describe training and test models, following the invariance principle which says that the conditional distribution of the response given its predictors remains the same across environments. However, this principle is often violated in practice when the response is perturbed in the unseen environment. We introduce invariant matching property, an explicit relation to capture interventions through an auxiliary feature, enabling a unified treatment of general perturbations on the response as well as the predictors. I will discuss its connection to self-supervised learning (SSL) and non-stationary time series settings. The second part of my talk will be centered around multiple testing via false discover rate (FDR), a rich line of work initiated by statisticians such as Turkey and later popularized by Benjamini and his coworkers. Naturally suitable for large-scale data and distribution-free guarantees, the notion of false discovery rate control has played a critical role in many recent developments such as variable selection and uncertainty quantification. I will discuss decentralized settings where each agent collects a large number of local measurements for efficient and accurate global decision-making, motivated by internet of things and mobile sensor applications. We have developed the state-of-the-art methodologies with provable FDR guarantees and strong empirical performance. I will also briefly cover robust variable selection with FDR control and my recent work on adversarial robustness of conformal novelty detection. Bio: Yu Xiang is an Assistant Professor in Electrical and Computer Engineering at the University of Utah. Prior to this, he was a postdoctoral fellow in the School of Engineering and Applied Sciences at Harvard University. He obtained his Ph.D. in Electrical and Computer Engineering from the University of California, San Diego. He received his B.E. with the highest distinction from the School of Telecommunications Engineering at Xidian University in China. His current research interests include learning under distribution shifts from a causal perspective and efficient multiple testing for novelty detection in networks. |
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Friday |
Association for Women in Mathematics (AWM) Student Chapter Join Us for Tea Time! Sip tea, matcha, spill some tea! FLYER We look forward to seeing you there!
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Tuesday |
Reading seminar on Quantum Algorithms 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 215. 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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October 2025 |
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Wednesday |
Riemannian manifolds 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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Thursday |
Analysis & Applications Seminar Speaker: Prof. Erik Lundberg, Florida Atlantic University Title: A problem of Erdos on the area of lemniscates Abstract: Consider the sublevel set {|p(z)|<1} of the modulus of a monic complex polynomial p of degree n. This set is referred to as a lemniscate. G. Szego determined the maximal area of lemniscates in 1928. In 1940, P. Erdos posed the extremal problem of studying the minimal area when the zeros of p are in the closed unit disk. He restated and elaborated on this problem several times throughout his career. Pommerenke proved in 1961 a lower bound of order n^(-4) on the minimal area, and Wagner proved in 1988 an upper bound of order (log log n)^(-1/2). In this talk I will report on current joint work with M. Krishnapur, F. Nazarov, and K. Ramachandran showing that the minimal area has order (log n)^(-1). This resolves the specific questions and conjectures that were stated by Erdos on this problem. |
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Friday |
Graduate Student Seminar Speaker: Sophie Faris Title: Introduction to Rigidity Theory Abstract: Rigidity Theory is the study of conditions that a geometry framework maintains its shape in a given space. This is done primarily using techniques from linear algebra. In this talk, I will be discussing the difference between equivalent and congruent shapes, and what makes a shape rigid. I’ll introduce a matrix called the rigidity matrix, and how to use said matrix to determine if a shape is rigid. Finally, a brief discussion on alternative approach, angular rigidity theory, where angles will be fixed versus the length as done in traditional rigidity theory. |
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Tuesday |
Reading Seminar on Quantum Algorithms 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 215. 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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Wednesday |
Riemannian manifolds 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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Thursday |
Analysis and its Applications Seminar Speaker: Dr. Eric Lundberg Title: A problem of Erdos on the area of lemniscates (Part II)
Abstract: In this continuation of the previous talk, I will present some ideas in the proofs estimating the minimal area of lemniscates {|p(z)|<t} of a monic complex polynomial p of degree n, with particular attention on the case |
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Saturday |
Applied Algebra and Cryptography Workshop Program Schedule University of South Florida and Florida Atlantic University welcome you to the Applied Algebra and Cryptography Workshop. As part of the NSF-funded Research Training Group in Applied Algebra, the Center for Cryptographic Research organizes the Florida Applied Algebra Days. These are a series of workshops featuring presentations on cryptography, coding theory, and quantum computing. From October 11 to 12, we will be hosting the second edition of the Applied Algebra Days at Florida Atlantic University. Registration is free for FAU faculty and students! Read more! |
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Tuesday |
Speaker: Anil Kumar Pradhan, Founding Cryptographer and Cryptography Research Lead, Vaultree Title: Beyond Theory: Industry Challenges in Adopting Homomorphic Encryption Abstract: Fully Homomorphic Encryption (FHE) promises quantum-resilient, privacy-preserving computation for sensitive data across industries. However, despite academic breakthroughs, the leap from laboratory models to enterprise-scale adoption remains daunting. Industry faces formidable obstacles, including computational resource demands, implementation complexity, slow processing speeds, and high costs, aggravated by a shortage of FHE talent and lack of standardized practices. Integrating FHE into legacy and cloud systems requires extensive technical overhaul, often with questionable ROI. The disconnect between academic solutions and practical business needs, especially regarding scalability, cost, and integration continues to deter widespread implementation. Emerging technologies and optimization strategies, such as hardware acceleration and real-world application benchmarking, may help bridge the gap, but genuine adoption will require collaborative efforts and a shift in focus from theoretical promise to operational feasibility. Bio Anil Kumar Pradhan is a cryptographer specializing in practical privacy-enhancing technologies and their deployment in real-world systems. At Vaultree, he works at the intersection of advanced cryptography and industry adoption, focusing on fully homomorphic encryption (FHE), encrypted machine learning, and secure computation at scale. With a background spanning both academic research and enterprise engineering, he bridges the gap between theoretical innovation and operational feasibility. Anil has contributed to projects that bring cutting-edge cryptographic methods into production environments, with particular attention to performance optimization, compliance, and developer experience. He is passionate about making strong cryptography usable, scalable, and impactful across industries that handle sensitive data. Anil Kumar Pradhan is the Founding Cryptographer and Cryptography Research Lead at Vaultree Ireland, and has over a decade of experience in applied cryptography. He holds an M.Sc. in Mathematics from the Indian Institute of Technology, Delhi, and a B.Sc. (Hons) in Mathematics and Computing from the Institute of Mathematics and Applications, Bhubaneswar. |
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Wednesday |
Riemannian manifolds 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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Thursday |
Analysis and its Applications Seminar Speaker: Dr. Joan Gimeno, Universitat de Barcelona Title: Periodic Collinearity Orbits: A First Look
Abstract:
Periodic syzygy orbits -trajectories that force celestial bodies to become collinear on a repeating schedule- may offer a sharp lens on exoplanet dynamics. Syzygies and collinear states trace back to Euler (1765) and Lagrange (1772). Building on Poincaré's periodic solutions (1890s), subsequent regularization and continuation advances (Levi-Civita, Sundman, McGehee), and systematic numerical and stability studies by Hénon and Broucke (1970s). |
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Thursday |
Graduate Student Seminar Speaker: James Klinkenburg, Ph.D. Student, Florida Atlantic University Title: Introduction to Frame Theory Abstract: When studying a topological space, one is typically concerned not only with the open sets of the topology, but also the points of the space. For example, the Hausdorff condition states that any two points in the space can be separated by disjoint open sets. Sometimes, however, it is wise to look at things from a different angle by discarding the points and simply look at the open sets. It turns out that the open sets of a topology form what is known as a frame. In this talk, we will explore the basics of frame theory, starting by defining a frame as a complete lattice that satisfies a strong distributive law. We will define concepts such as compact and prime elements, algebraic frame, and the finite intersection property. We will explore examples of frames coming from topological spaces, lattice-ordered groups, and commutative rings with identity. Finally, time permitting, we will explore what current research in this area looks like by looking at the Lemma on Ultrafilters. |
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Friday |
Colloquium Speaker: Luke Peterson, Department of Aerospace Engineering, University of Texas, Austin Title: Celestial Mechanics Problems in Cislunar Space
Abstract: Cislunar space-the region between Earth and the Moon-has reemerged as a critical area for space exploration. From a mathematical perspective, this region is governed by multi-body dynamics that give rise to rich structures, including invariant manifolds, resonant orbits, and homoclinic chaos. This talk will introduce classical and modern tools from celestial mechanics to analyze motion in the Earth-Moon system, with an emphasis on restricted 3- and 4-body problems. We will discuss how perturbative methods (normal forms) and invariant manifold theory (parameterization method) reveal the underlying organization of the phase space. Particular attention will be placed on connecting the perturbative regime, where classical methods apply, with the realistic system, which often lies far outside that regime, using computer-assisted techniques. Our ultimate goal is to establish rigorous results for the real solar system while enhancing the engineering capabilities needed to design and fly missions, highlighting how mathematics contributes both to theory and to the practical challenges of contemporary space exploration. |
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Tuesday |
Reading Seminar on Quantum Algorithms 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 215. 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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Wednesday |
Riemannian manifolds 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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Thursday |
Analysis & Its Applications Seminar Speaker: Lue Peterson, University of Texas, Austin Title: Melnikov Methods in Realistic Solar System Models: Resonant Orbits & Homoclinic Phenomena Abstract: Cislunar space—the region between Earth and the Moon—has reemerged as a critical area for space exploration. From a mathematical perspective, this region is governed by multi-body dynamics that give rise to rich structures, including invariant manifolds, e.g., resonant orbits and homoclinic connecting orbits. In the cislunar region of the solar system, understanding the dynamics of a satellite or asteroid necessarily involves incorporating perturbations from periodic forces (e.g., gravity of the Sun, ellipticity, inclination) to the restricted 3-body problem. As resonant and connecting orbits help to govern global dynamics of a system, studying their persistence under periodic perturbations is key to understanding this region of the real solar system. In this talk, we employ Melnikov methods, both subharmonic and homoclinic, to study the persistence of resonant and homoclinic orbits under periodic forcing. We will see how the subharmonic Melnikov method reduces the persistence problem to a simple integral computation à la single-variable calculus. Further, by means of continuation into the Sun-Earth-Moon system, we will show that the resonant orbits and homoclinic phenomena are directly related. Finally, we will discuss the relationship between the Melnikov and parameterization methods for invariant manifolds, and how they can be used to set up readily replicable computer-assisted proofs. |
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Monday |
Ph.D. Defense Speaker: David Snyder, Ph.D. Candidate Title: Representation Theory of Algebras: Classification of systems of two invariant subspaces Abstract: Click Here A copy of the dissertation is on display in SE 234. |
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Tuesday |
Speaker: Dr. Sohyun Jeon, Ewha Womans University Title: LastRings: Lattice-based Scalable Threshold Ring Signatures FLYER
Abstract:
This talk presents the first lattice-based threshold ring signature scheme with signature size scaling logarithmically in the size of the ring while supporting arbitrary thresholds. Our construction is also concretely efficient, achieving signature sizes of less than 150kB for ring sizes up to N=4096 (with threshold size T=N/2, say). This is substantially more compact than previous work. |
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Wednesday |
Riemannian manifolds 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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Thursday |
Analysis & Its Applications Seminar Speaker: Robert Lubarsky, Ph.D., Florida Atlantic University Title: The Ultraproduct Construction Abstract: Ultraproducts are a way of averaging a family of structures of the same type (e.g. a collection of groups, or a collection of metric spaces). Surprisingly, even though the construction has an algebraic feel, and is useful throughout mathematics, it seems not to be well known beyond logicians. This talk will give the basic definitions and results behind the ultraproduct, and applications to logic, algebra, analysis, and set theory. |
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Friday |
Graduate Student Seminar Speaker: Christian Corbett, Ph.D. Student, Florida Atlantic University Title: Introduction to theorem proving in Lean 4 Abstract: Large language models have recently started showing flashes of mathematical insight (which still feels a little uncanny), and much of that talent seems to come from how well they handle formal languages like Lean 4, where math and programming finally stop pretending they’re different things. Lean 4 is a modern theorem prover (think of it as a calculator for proofs, except it yells at you until you’re right) that lets us build mathematics from the ground up with total precision. In this talk, I’ll walk through what Lean actually is, how it works, and why it’s both more intuitive and more philosophical than it first appears. We’ll see how a few lines of code can define a structure, prove a theorem, or perhaps completely crash the program, and I’ll wrap up by showing a bit of my own work in lattice theory. Come and enjoy the talk, time with colleagues, and donuts! Happy Halloween! |
