2026-27 Department of Mathematics and Statistics Events |
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September 2026 |
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Thurs. |
Analysis & Applications Seminar Speaker: J.D. Mireles James, Professor, Department of Mathematics & Statistics, Florida Atlantic Universtiy Title: Validated numerical computations with power series for analytic functions - Part 2 This week I'll continue the discussion we started last week, but will move into talking about power series computations for stable/unstable manifolds. (So, the talk should be mostly independent from last time... if you missed it there will still be a lot here for you 😄) I'll be especially interested in the role of the dircrete Fourer transform (DFT) when the map is given as a numerical "black box", i.e. where then is no explicit formula for it. Abstract: I will talk about a method for computing mathematically rigorous enclosures of power series. This task is important in many different kinds of computer assisted proofs in nonlinear analysis and dynamical systems theory. The idea is to use an interpolation scheme on the boundary of a disk in the complex plane, which turns out to be equivalent to the discrete Fourier transform (DFT) for Fourier series. This interpolation introduces errors, which can they be bound using ideas from complex analysis. Moreover, one can take advantage of fast algorithms such as the FFT for the numerical computations. I will focus on obtaining bounds on the so called "aliasing" errors (which are really just interpolation errors, i.e. the mistake you make when you interpolate when you wanted to project... all of this will be discussed!). In later talks I will explain how these ideas appear in computer assisted proofs. In particular, I want to show you some computer assisted proofs of the existence of chaotic motion in mathematical billiards. Of course, I will introduce these models when the time comes. NOTE: There is an open invitation to all faculty and graduate students to talk in the seminar. If you would like to speak this semester, please just contact me or Professor Lundberg and we will get you on the schedule! |
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Tuesday |
Crypto Reading Seminar
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Thurs. |
Analysis & Applications Seminar Speaker: J.D. Mireles James, Professor, Department of Mathematics & Statistics, Florida Atlantic Universtiy Title: Validated numerical computations with power series for analytic functions - Part 3 Abstract: I will talk about a method for computing mathematically rigorous enclosures of power series. This task is important in many different kinds of computer assisted proofs in nonlinear analysis and dynamical systems theory. The idea is to use an interpolation scheme on the boundary of a disk in the complex plane, which turns out to be equivalent to the discrete Fourier transform (DFT) for Fourier series. This interpolation introduces errors, which can they be bound using ideas from complex analysis. Moreover, one can take advantage of fast algorithms such as the FFT for the numerical computations. I will focus on obtaining bounds on the so called "aliasing" errors (which are really just interpolation errors, i.e. the mistake you make when you interpolate when you wanted to project... all of this will be discussed!). In later talks I will explain how these ideas appear in computer assisted proofs. In particular, I want to show you some computer assisted proofs of the existence of chaotic motion in mathematical billiards. Of course, I will introduce these models when the time comes. NOTE: There is an open invitation to all faculty and graduate students to talk in the seminar. If you would like to speak this semester, please just contact me or Professor Lundberg and we will get you on the schedule! |
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Tues. |
Speaker: Hoai Nam Li Title: Optimal Bucket Set Construction for Multi-scalar Multiplication with Endomorphisms +Zoom (click here) Abstract: Multi-scalar multiplication (MSM), which computes a linear combination of elliptic-curve points of the form \sum_i a_iP_i, is a major computational bottleneck in many modern cryptographic protocols, particularly in proof systems. In 2023, Luo, Fu, and Gong (LFG) introduced a framework for accelerating MSM using a bucket set together with a multiplier set, allowing a trade-off between storage and online computation. In 2025, Fan, Sica, Kuchta, and Xu (FKSX) applied the LFG framework to efficient endomorphisms, exploiting units that can be applied essentially on the fly. This raises a natural optimization problem: Can we minimize the bucket size while still admitting an efficient Hamiltonian path for bucket accumulation? In this talk, I will present our construction from a geometric viewpoint over the Eisenstein integers. I will show how this viewpoint leads to an optimal hexagonal bucket set and also allows us to construct an efficient Hamiltonian path for the bucket accumulation step. Moreover, we generalize the construction to larger multiplier sets, providing further time-memory trade-offs when additional storage is available. This work will be presented at ASIACRYPT 2026 and is joint work with Professor Sica. |
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Tues. |
Dissertation Defense Speaker: Samith Kuruppu, Ph.D. Candidate Title: Multivariate Zero Subtracted CM Poisson Model for Applications and A Study of Hurricane Track Forecasting in the North Atlantic Basin Abstract: Count data arise in a wide range of fields and often exhibit correlation along with either overdispersion or underdispersion. To address such data, in the first project, we introduce a extension of the multivariate zero subtracted Poisson distribution, refereed to as the multivariate zero subtracted Conway Maxwell Poisson (MZSCMP) distribution. We derive the main properties of the distribution and develop an associated regression framework for modeling correlated multivariate count data. The performance of the model is evaluated through two simulation studies and compared with alternative models using maximum likelihood estimations, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). A real data application is also presented to show the proposed model works in practice. Overall, the findings demonstrate that the MZSCMP model provides a effective approach for analyzing correlated overdispersed multivariate count data. The second research project presents a comparative evaluation of six data driven models for forecasting tropical cyclone (TC) tracks in the north Atlantic basin. Two forecasting approaches are developed and analyzed. The first approach is based on neural network architectures (NNAs), consisting of four configurations: NNA1-R+, NNA1-R-, NNA2-R+ and NNA2-R-. The second approach uses multiple linear regression (MLR). The models are trained using output data from the Advanced Dvorak Technique (ADT 9.0) archive, maintained by the Cooperative Institute for Meteorological Satellite Studies at the University of Wisconsin Madison (UW-CIMSS). Historical TC data from 2003 to 2024 are used for model development, while data from the 2025 hurricane season are reserved as an independent test set for model evaluation. Each model is trained using the most recent 3 h historical observations. To provide a baseline for model comparison, a climatology persistence method, referred to as the geodesic persistence model (GPM), is also developed. Forecast performance is evaluated using overall predication error (PE), mean absolute error (MAE), root mean square error (RMSE) and mean track error (in km) for forecast horizons of 6 h, 12 h, 24 h and 48 h. The results indicate that, among all proposed models, the NNA1-based models consistently produce lower errors and demonstrate relatively better performance in predicting TC tracks in North Atlantic basin. |
