2023-24 Department of Mathematics and Statistics Events |
|
|
June, 2024 |
|
Wednesday |
Society for Industrial and Applied Mathematics (SIAM) FAU Student Chapter The SIAM officers will use part of the time to reflect on what SIAM has done in the past year and discuss future plans for the upcoming Fall and Spring semesters. Even if you have not attended a previous SIAM meeting, please join us to enjoy light refreshments and food with other graduate students and learn more about SIAM and how you can get involved. No need to RSVP, all are welcome! If you have any questions, feel free to let us know by sending us an email or reaching out to the SIAM faculty advisor, Dr. Francis Motta fmotta@fau.edu. |
|
|
July, 2024 |
|
Wednesday |
Ph. D. Defense Speaker: David Blessing, Ph. D. Candidate Advisor: Dr. Jason Mireles-James Title: Parameterization of Invariant Circles in Maps Abstract: We explore a novel method of approximating topologically trivial invariant circles in area preserving maps. The process begins by leveraging improvements on Birkhoff’s Ergodic Theorem via Weighted Birkhoff Averages to compute high precision estimates on several Fourier modes. We then set up a Newton-like iteration to further improve the estimation and extend the approximation out to a sufficient number of modes to yield a significant decay in the magnitude of the coefficients of high order. With this approximation in hand, we explore the phase space near the approximate invariant circle with a form numerical continuation where the rotation number is perturbed and the process is repeated. Then, we turn our attention to a completely different problem which can be approached in a similar way to the numerical continuation, finding a Siegel disk boundary in a holomorphic map. Given a holomorphic map which leads to a formally solvable cohomological equation near the origin, we use a numerical continuation style process to approximate an invariant circle in the Siegel disk near the origin. Using an iterative scheme, we then enlarge the invariant circle so that it approximates the boundary of the Siegel disk. Join Zoom Meeting: https://fau-edu.zoom.us/j/86001628559?pwd=eKBGhnaXIOpeF9YbyibI9qqMUUon7T.1 Meeting ID: 860 0162 8559 All are cordially invited. |
|
Thursday |
Analysis and Algebra Seminar Speaker: Parker Edwards, Assistant Professor Title: On computing local monodromy Abstract: A fundamental fact about zero sets of systems of polynomial equations over the complex numbers is that they decompose into a finite number of irreducible algebraic subsets. Knowing a thorough description of the irreducible components of an algebraic variety tells you quite a bit about it, and computing one is an essential preprocessing step to many numerical algorithms. Standard algorithms for computing this numerical irreducible decomposition combine some relatively sophisticated machinery. A main component is computing the monodromy action of certain linear projection maps using numerical continuation. What if one is instead interested in studying the geometric properties of an algebraic variety localized at a point? This puts you into the realm of singularity theory in complex analytic geometry, which is a rich and ongoing area of theoretical development. Every zero set of a system of complex-valued analytic functions has a local irreducible decomposition at each point. Computing a corresponding numerical local irreducible decomposition is similarly essential to developing a local approach to numerical algebraic geometry. I will discuss some recent work with Jon Hauenstein which culminates in an algorithm for doing so. My aim for these seminars is to give a thorough enough overview of the background to understand what the algorithm is doing. If there's interest, we can discuss enough to get at the main ideas of the proof that it works. Here's the breakdown:
|
|
Thursday |
Analysis and Algebra Seminar Speaker: Parker Edwards, Assistant Professor Title: On computing local monodromy (part II) Abstract: A fundamental fact about zero sets of systems of polynomial equations over the complex numbers is that they decompose into a finite number of irreducible algebraic subsets. Knowing a thorough description of the irreducible components of an algebraic variety tells you quite a bit about it, and computing one is an essential preprocessing step to many numerical algorithms. Standard algorithms for computing this numerical irreducible decomposition combine some relatively sophisticated machinery. This week's talk will cover some background on monodromy actions and how they're used to detect irreducible components of algebraic varieties. A main component is computing the monodromy action of certain linear projection maps using numerical continuation.
What if one is instead interested in studying the geometric properties of an algebraic variety localized at a point? This puts you into the realm of singularity theory in complex analytic geometry, which is a rich and ongoing area of theoretical development. Every zero set of a system of complex-valued analytic functions has a local irreducible decomposition at each point. Computing a corresponding numerical local irreducible decomposition is similarly essential to developing a local approach to numerical algebraic geometry.
I will discuss some recent work with Jon Hauenstein which culminates in an algorithm for doing so. My aim for these seminars is to give a thorough enough overview of the background to understand what the algorithm is doing. If there's interest, we can discuss enough to get at the main ideas of the proof that it works. Here's the breakdown:
|
|
Wednesday |
PhD Dissertation Defense Speaker: Abhraneel Dutta, Ph.D. Candidate; Florida Atlantic University Advancements in Cryptographic Efficiency: Elliptic Curve Scalar Multiplication and Constant-Time Polynomial Inversion in Post-Quantum Cryptography Advisor: Dr. Edoardo Persichetti Co-Advisor: Dr. Koray Karabina Abstract: An efficient scalar multiplication algorithm is vital for elliptic curve cryptosystems. The first part of this dissertation focuses on a scalar multiplication algorithm based on scalar recodings resistant to timing attacks. The algorithm utilizes two recoding methods: Recode, which generalizes the non-zero signed all-bit set recoding, and Align, which generalizes the sign-aligned columns recoding. For an ℓ-bit scalar split into d subscalars, our algorithm has a computational cost of ⌈⌈ℓ log_k(2)⌉/d⌉ point additions and k-scalar multiplications and a storage cost of k^(d−1) (k − 1) − 1 points on E. The “split and comb” method further optimizes computational and storage complexity. We find the best setting to be with a fixed base point on a Twisted Edwards curve using a mix of projective and extended coordinates, with k = 2 generally offering the best performance. However, k = 3 may be better in certain applications. The second part of this dissertation is dedicated to constant-time polynomial inversion algorithms in Post-Quantum Cryptography (PQC). The computation of the inverse of a polynomial over a quotient ring or finite field is crucial for key generation in post-quantum cryptosys-tems like NTRU, BIKE, and LEDACrypt. Efficient algorithms must run in constant time to prevent side-channel attacks. We examine constant-time algorithms based on Fermat’s Little Theorem and the Extended GCD Algorithm, providing detailed time complexity analysis. We find that the constant-time Extended GCD inversion algorithm is more efficient, per-forming fewer field multiplications. Additionally, we explore other exponentiation algorithms similar to the Itoh-Tsuji inversion method, which optimizes polynomial multiplications in the BIKE/LEDACrypt setup. Recent results on hardware implementations are also discussed. Please contact Dr. Hongwei Long <hlong@fau.edu> for an electronic copy of the dissertation. Zoom Meeting Information: https://fau-edu.zoom.us/j/84701837030?pwd=Sh4fqdX7iPRXAXWUqazvFWLijZ3A9u.1 |
|
Thursday |
Analysis and Algebra Seminar Speaker: Parker Edwards, Assistant Professor Title: On computing local monodromy (part III) Abstract: A fundamental fact about zero sets of systems of polynomial equations over the complex numbers is that they decompose into a finite number of irreducible algebraic subsets. Knowing a thorough description of the irreducible components of an algebraic variety tells you quite a bit about it, and computing one is an essential preprocessing step to many numerical algorithms. Standard algorithms for computing this numerical irreducible decomposition combine some relatively sophisticated machinery. This week's talk will cover some background on monodromy actions and how they're used to detect irreducible components of algebraic varieties. A main component is computing the monodromy action of certain linear projection maps using numerical continuation.
What if one is instead interested in studying the geometric properties of an algebraic variety localized at a point? This puts you into the realm of singularity theory in complex analytic geometry, which is a rich and ongoing area of theoretical development. Every zero set of a system of complex-valued analytic functions has a local irreducible decomposition at each point. Computing a corresponding numerical local irreducible decomposition is similarly essential to developing a local approach to numerical algebraic geometry.
I will discuss some recent work with Jon Hauenstein which culminates in an algorithm for doing so. My aim for these seminars is to give a thorough enough overview of the background to understand what the algorithm is doing. If there's interest, we can discuss enough to get at the main ideas of the proof that it works. Here's the breakdown:
|
|
|
August, 2024 |
|
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 ) |
|
|
February, 2025 |
|
Feb. 24 |
Florida GeoGebra Conference Registration link: https://fau.az1.qualtrics.com/jfe/form/SV_0cguWFiDo2UO2pg Description: Florida GeoGebra Conference February 24, 2025 Join us for an interactive workshop designed for STEM educators seeking to enhance their teaching of mathematics through the innovative use of GeoGebra. GeoGebra is a dynamic mathematics software that integrates geometry, algebra, spreadsheets, graphing, statistics, and calculus. In this workshop, we will explore how to leverage GeoGebra to create engaging and effective learning experiences in your STEM classroom. Workshop Highlights:
Who Should Attend:
Coffee and lunch will be provided! For more information, please contact: Dr. Katarzyna Winkowska-Nowak, Director of MST |
|
|
March, 2025 |
|
March 3-7 |
56th Southeastern International Conference on Combinatorics, Graph Theory, and Computing Celebrating its 56th year, the Conference brings together mathematicians and others interested in combinatorics, graph theory, and computing, and their interactions. The Conference lectures and contributed papers, as well as the opportunities for informal conversations, have proven to be of great interest to other scientists and analysts employing these mathematical sciences in their professional work in business, industry, and government. The Conference continues to promote a better understanding of the roles of modern applied mathematics, combinatorics, and computer science to acquaint the investigator in each of these areas with the various techniques and algorithms, which are available to assist in his or her research. Each discipline has contributed greatly to the others, and the purpose of the Conference is to decrease even further the gaps between the fields. |
