2022 Department of Mathematics Events 
November 2022 

Thursday Nov., 3 SE 215 11:00 am 
Analysis and Applications Seminar 

Thursday Nov. 3 SE 215 5:00 pm 
FAU's Math Club All are invited to attend and join the Math Club. We look forward to seeing you there. 

Friday Nov. 4 SE 215 11:00 am 
MS Exam (Presentation) Speaker: JeanSebastien Roger Title: A Generalizable BrainComputer Interface (BCI) Using Machine Learning for Feature Discovery Abstract: This presentation discusses the process and techniques used in a work analyzing the efficacy of generalized neural signal classification for braincomputer interface (BCI). The experiment was aimed at producing and testing a classification framework for BCI which can be generalized to many motor movements and many features of input from electroencephalography (EEG) data. Some current approaches to classification are dependent on identifying key action potentials in EEG data, a generalized approach as the one offered in this article relies on a stochastic search on a sample of neural networks trained on all features in the data. This results in less requirement for extensive domain knowledge and apriori information specific to the desired outcome. Overall, the results of the proposed method are comparable to some of the top methods proposed on credentialed datasets. All are cordially invited. 

Sat. Nov. 5 PS 109 2:304:00 pm 
Math Circle for Middle School Math Circle for Middle School is your opportunity to have some fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, and playing mathematical games. Math Circle for Middle School will be meeting every other Saturday, beginning Saturday, September 24, 2022. Math Circle for Middle School Flyer For more information: http://www.math.fau.edu/mathcircle/ 

Thursday Nov., 10 SE 215 11:00 am 
Analysis and Applications Seminar ***CANCELLED DUE TO HURRICANE NICOLE 

Thursday Nov. 10 
American Mathematics Competitions (AMC 10/12A) ***CANCELLED DUE TO HURRICANE NICOLE FAU's Department of Mathematical Sciences will host the AMC 10/12A on the Boca Raton Campus. Please regsiter your student for the AMC 10/12A. 

Wednesday Nov. 16 
American Mathematics Competitions (AMC 10/12B) FAU's Department of Mathematical Sciences will host the AMC 10/12B on the Boca Raton Campus. Please regsiter your student for the AMC 10/12B. 

Wednesday Nov. 16 SE 215 3:00 pm 
MS Exam (Presentation) Master's Degree Canidate: Collin Bakken Title: Discovering Governing Equations from Data: Sparse Identification of Nonlinear Dynamical Systems Abstract: A quantitative comprehension of dynamic balances and constraints has led to rapid growth in many areas, including aircrafts, combustion engines, and many more. Through this work, we will tie together machine learning algorithms with sparsity techniques in order to discover equations based on previously measured data. An essential assumption must be made for this to work: we must assert that only a few important terms govern the dynamics, which means that these equations are sparse. The main goal is to use sparse regression, which minimizes the number of governing equations needed to represent the data accurately. The outcomes are models that are often balancing complexity of data with accurate descriptions of data, while not being overwhelming. Here, we take a deeper look into a range of problems, including the Lorenz system, to further our understanding of sparse identification. 

Wednesday Nov. 16 SE 215 4:00 pm 
Florida Atlantic University's Student Chapter of the Association for Women in Mathematics (AWM) will host Department of Mathematical Sciences Chess Tournament 

Thursday Nov. 17 SE 215 11:00 am 
PhD Dissertation Defense Ph. D. Candidate: Floyd Johnson Title: Selected Topics in Quantum and PostQuantum Cryptography CoAdvisors: Dr. Shi Bai and Dr. Rainer Steinwandt Abstract: In 1994 when Peter Shor released his namesake algorithm for factoring and solving the discrete logarithm problem he changed cryptography forever. Many of the stateoftheart cryptosystems for internet and other computerized communications will become obsolete with the advent of quantum computers. Two distinct approaches have grown to avoid the downfall of secure communication: quantum cryptography which is based in physics and information theory, and postquantum cryptography which uses mathematical foundations believed not to be weak against even quantum assisted adversaries. In this defense we will be covering a variety of recent advances in topics including cryptanalysis of quantum signature schemes, cryptanalysis of weak instances of the NTRU problem, and two constructions based on latticebased primitives.
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Thursday Nov. 17 SE 215 5:00 pm 
Math Club Speaker: Dr. Robert Lubarsky, FAU Title: Logic  What is It? Abstract: One can go merrily along doing mathematics without thinking about the meaning behind it, as mathematicians had for millenia. With a bit of selfreflection though, you can ask what it is that you're ultimately doing. Such questions grew out of actual mathematical practice in the late 19th century, and led to a whirlpool of unclarities and paradoxes. This talk will focus on the issues that came up in this context, and their culmination in arguably the first major theorem in mathematical logic, Godel's Incompleteness Theorems. 

Friday Nov. 18 SE 215 4:00 pm 
FAU Department of Mathematical Sciences Colloquium Speaker: Dr. Shi Bai Title: Recent developments of practical lattice reduction algorithms Abstract: Lattice reduction algorithms have received much attention in recent years due to their relevance in cryptography. We will discuss some of the recent developments on enumerationbased lattice reduction algorithms which are used in practice. We will start with the classic FinkePost and Kannan enumeration algorithm and then introduce some modern variants. In particular, we will discuss a lattice reduction algorithm that achieves root Hermite factor k^(1/(2k)) in time k^(k/8 + o(k)) and polynomial memory. This improves the previously bestknown enumerationbased algorithms which achieve the same quality, but in time k^(k/(2e) +o(k)). 

Saturday Nov. 19 PS 109 2:304:00 pm 
Math Circle for Middle School Math Circle for Middle School is your opportunity to have some fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, and playing mathematical games. Math Circle for Middle School will be meeting every other Saturday, beginning Saturday, September 24, 2022. Math Circle for Middle School Flyer For more information: http://www.math.fau.edu/mathcircle/ 

Monday Nov. 21 SE 215 4:00 pm 
MS Exam Presentation Speaker: Hansraj Jangir Title: Worstcase to Averagecase Reduction for SIS Abstract: We will give an introduction to computationally hard problems based on lattices and some basic theorems on LWE (learning with errors) and SIS (shortest integer solution). We will then use Gaussian measures on lattices and high dimensional Fourier transform for smoothing as a tool to come up with worstcase to averagecase reductions for SIS. In a nutshell, the worstcase to averagecase reductions show how to transform any algorithm that solves SIS on the average into an algorithm that solves “approximate short vector problems” on worstcase lattices. Hansraj Jangir's MS presentation will also be accessible remotely via Zoom.
Join Zoom Meeting
Meeting ID: 726 327 6757 Passcode: Fall2021 

October 2022 

Thursday Oct. 6 SE 215 5:00 pm 
FAU's Math Club All are invited to attend and join the Math Club. We look forward to seeing you there. 

Saturday Oct. 8 PS 109 2:304:00 pm 
Math Circle for Middle School Math Circle for Middle School is your opportunity to have some fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, and playing mathematical games. Math Circle for Middle School will be meeting every other Saturday, beginning Saturday, September 24, 2022. Math Circle for Middle School Flyer For more information: http://www.math.fau.edu/mathcircle/ 

Thursday Oct., 17 SE 215 11:00 am 
Analysis and Applications Seminar Speaker: Dr. Vincent Naudot, Florida Atlantic Univeristy Abstract/Title: Bogdanov Takens bifurcations Abstract: In this talk, we study the bifurcations that arise in the unfolding of a (nondegenerate) BogdanovTakens equilibrium. We present an overview of the techniques used to prove the results. We generalize the bifurcation 

Tuesday October 18 SE 215 4:00 pm 
Speaker: Dr. Shi Bai, Florida Atlantic University For title and abstract, please visit the Crypto Café website: http://www.math.fau.edu/crypto_cafe.php. 

Thursday Oct. 20 SE 215 5:00 pm 
FAU's Math Club All are invited to attend and join the Math Club. We look forward to seeing you there. 

Friday Oct. 21 SE 215 4:00 pm 
Department of Mathematical Sciences Colloquium Speaker: Ashkaan Fahimipour Title: When to quit of you're being exploited Abstract: This presentation discusses the process and techniques used in a work analyzing the efficacy of generalized neural signal classification for braincomputer interface (BCI). The experiment was aimed at producing and testing a classification framework for BCI which can be generalized to many motor movements and many features of input from electroencephalography (EEG) data. Some current approaches to classification are dependent on identifying key action potentials in EEG data, a generalized approach as the one offered in this article relies on a stochastic search on a sample of neural networks trained on all features in the data. This results in less requirement for extensive domain knowledge and apriori information specific to the desired outcome. Overall, the results of the proposed method are comparable to some of the top methods proposed on credentialed datasets. 

Saturday Oct. 22 PS 109 2:304:00 pm 
Math Circle for Middle School Math Circle for Middle School is your opportunity to have some fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, and playing mathematical games. Math Circle for Middle School will be meeting every other Saturday, beginning Saturday, September 24, 2022. Math Circle for Middle School Flyer For more information: http://www.math.fau.edu/mathcircle/ 

Thursday Oct., 27 SE 215 11:00 am 
Analysis and Applications Seminar Speaker: Dominic Gold, Florida Atlantic University Title: Applications of Homomorphic Encryption to Data Analysis Abstract: Data analysis is the umbrella term for mathematical techniques used to describe, classify, and illustrate data. However, certain types of data are privacyprotected by law (medical records, MRI scans, etc.). Homomorphic encryption allows us to circumvent this hurdle by encrypting the original data (also known as the plaintext) into ciphertext, and then performing operations on this ciphertext that are analogous to the usual operations performed on the plaintext. This tool allows for the extension of many popular data analysis techniques, such as regression, clustering, and even neural networks into the ciphertext domain. Furthermore, this technique permits the user to rely on a computationally superior semihonest thirdparty (e.g. a cloud server) to perform the data analysis without a breach of user privacy. We will first discuss homomorphic encryption as a blackbox technique, then transforming an existing (plaintext) algorithm into its homomorphic encryption counterpart on ciphertext, and finally some applications of homomorphic encryption in the data science field. These examples include, but are not limited to, secure matrix multiplication, secure Euclidean distance for kMeans classification and kCentroids clustering, and finally the topic of my dissertation which is the adaptation of persistence homology, the main driver behind topological data analysis (TDA), into the ciphertext domain. We conclude by explaining the significance of this research to privacyprotected medical data. 

Thursday Oct. 27 SE 215 5:00 pm 
FAU's Math Club All are invited to attend and join the Math Club. We look forward to seeing you there. 

Friday Oct., 28 SE 215 4:00 pm 
FAU Department of Mathematical Sciences Colloquium Speaker: Dr. Francesco Sica, Florida Atlantic University Title : Elliptic Curve Cryptography: past, present and future. Abstract : I will survey some of my work in the area of elliptic curve cryptography, both in its implementation and its security. I will then propose some problems that could be of interest to graduate students. 

Friday

FAU Department of Mathematical Sciences Colloquium Speaker: Dr. Francesco Sica, Florida Atlantic University Title : Elliptic Curve Cryptography: past, present and future. Abstract : I will survey some of my work in the area of elliptic curve cryptography, both in its implementation and its security. I will then propose some problems that could be of interest to graduate students. 

Date/Time/Location 
September 2022 

Thurs., Sept. 8 SE 215 11:00 am 
Analysis and Applications Seminar* * The Analysis and Applications Seminar will take place every Thursday in SE 215 at 11:00 a.m. (Fall, 2022) Speaker: Erick Lundberg Title: What is the expected number of limit cycles that bifurcate from a randomly perturbed center? Abstract: We consider the average number of limit cycles bifurcating from a perturbed linear center where the perturbation consists of random (bivariate) polynomials with independent coefficients. This problem reduces, by way of classical perturbation theory of the Poincaré first return map, to a problem on the real zeros of a random univariate polynomial. Even though real zeros of random univariate polynomials have been studied in great depth, the particular model arising in this problem falls right at the edge of the wellstudied cases. We present the solution to this problem and discuss other interesting questions related to limit cycles of planar systems with random coefficients. All are invited! 

Wed., Sept. 14
SE 215 4:00 pm 
Crypto Cafe
Speaker
: Sulani Thakshila, Florida Atlantic University Abstract: The NTRU cryptosystem is a computational problem introduced in 1996 based on lattices. ModuleNTRU lattices generalize NTRU lattices and possess more benefits on the flexibility of ring dimension. In this talk, I will present FiatShamir signatures based on the inhomogeneous variant of ModuleNTRU problem. I will present two signature schemes. The first scheme is a lossy identification scheme secure in the QROM. The second scheme is a BLISSlike signature secure in the classic ROM. Zoom: https://fauedu.zoom.us/j/81002845566?pwd=SUVyWktMTHRSd1FiMVM3dy9UUFM0QT09 

Thurs., Sept. 15 SE 215 11:00 am 
Analysis and Applications Seminar Speaker: Dr. Jason MirelesJames Title: A trefoil knot in the Lorenz equations Abstract: A two parameter family of threedimensional vector fields is said to have a Tpoint if there is a value of the parameters so that the one dimensional stable and unstable manifolds attached to the equilibrium solutions intersect so that they form a trefoil knot. This requires us to move two parameters, as the intersection of onedimensional curves in threedimensional space is very degenerate. The existence of Tpoints has important dynamical implications, which I will review very briefly. It has been conjectured (based on numerical evidence) that the Lorenz equations (with one parameter fixed and two free) admit T points. I'll develop a functional equation which, if it has a solution, establishes the existence of a Tpoint. Using power series representations we can project the functional equation into finite dimensions, and then solve it using Newton's method. Once a good enough numerical approximation has been found, one can try to establish the existence of a true solution nearby by verifying the hypotheses of a NewtonKantorovich theorem. This provides a recipe for a computer assisted proof of the existence for T points in explicit two parameter families like the Lorenz system. This is joint work with Sheldon Newhouse. 

Thurs., Sept. 15 SE 215 57 pm 
FAU's Math Club First meeting of FAU's Math Club for the 20222023 Academic Year! All are invited to attend and join the Math Club. We look forward to seeing you there. 

Thurs. Sept. 22 SE 215 11:00 am 
Speaker: Dr. Jason MirelesJames Title: A trefoil knot in the Lorenz equations Abstract: A two parameter family of threedimensional vector fields is said to have a Tpoint if there is a value of the parameters so that the one dimensional stable and unstable manifolds attached to the equilibrium solutions intersect so that they form a trefoil knot. This requires us to move two parameters, as the intersection of onedimensional curves in threedimensional space is very degenerate. The existence of Tpoints has important dynamical implications, which I will review very briefly. It has been conjectured (based on numerical evidence) that the Lorenz equations (with one parameter fixed and two free) admit T points. I'll develop a functional equation which, if it has a solution, establishes the existence of a Tpoint. Using power series representations we can project the functional equation into finite dimensions, and then solve it using Newton's method. Once a good enough numerical approximation has been found, one can try to establish the existence of a true solution nearby by verifying the hypotheses of a NewtonKantorovich theorem. This provides a recipe for a computer assisted proof of the existence for T points in explicit two parameter families like the Lorenz system. This is joint work with Sheldon Newhouse.


Thurs., Sept. 22 SE 215 5:00 pm 
FAU's Math Club First meeting of FAU's Math Club for the 20222023 Academic Year! All are invited to attend and join the Math Club. We look forward to seeing you there. 

Sat., Sept. 24 PS 109 2:304:00 
Math Circle for Middle School Math Circle for Middle School is your opportunity to have some fun with mathematics while learning something in the process. We will be discussing and solving problems, having friendly competitions, and playing mathematical games. Math Circle for Middle School will be meeting every other Saturday, beginning Saturday, September 24, 2022. Math Circle for Middle School Flyer For more information: http://www.math.fau.edu/mathcircle/ 

Tues., Sept. 27 SE 215 4:00 pm 
Crypto Café Speaker: Dr. Edoardo Persichetti Topic(s): Ongoing work on postquantum cryptographic group actions, in various contexts (type of groups, etc). All are invited to attend! For the list of past talks, please see http://www.math.fau.edu/crypto_cafe.php
A new mail list
crypto_math@lists.fau.edu is created for crypto related annoucements. 

Fri., Sept. 30 SE 215 4:00 pm 
TeaTime , hosted by FAU's Student Chapter of the Association for Women in Mathematics (AWM). Special Guest: Amish Mishra Topic(s): Summer internship experience, Summer, 2022 Join us for some pizza and enjoy listening to Amish's story. All are invited. Please register here: https://forms.gle/1QMmPqzHgeJtygbT8 and forward this invitation to anyone who may be interested. 

August 2022 

Fri., Aug 5 


Aug., 11 
PhD Dissertation Defense (Thursday, August 11, 1:00 pm) in SE 215 (inperson with remote access): Speaker: Bikram Bhusal, PhD Candidate Title: Stability Analysis and Parameter Estimation of a Stochastic Logistic Growth Model with Multiplicative AlphaStable Lévy Noise. Advisor: Dr. Hongwei Long Abstract: Since the population growth systems may suffer impulsive environmental disturbances such as earthquakes, epidemics, tsunamis, hurricanes, and so on, stochastic differential equations (SDEs) that are driven not only by Brownian motion but also by alphastable Lévy noises are more appropriate to model such statistical behavior of nonGaussian processes with heavytailed distribution, having infinite variance and in some cases infinite first moment. In this dissertation, we study stochastic processes defined as solutions to stochastic logistic differential equations driven by multiplicative alphastable Lévy noise. We mainly focus on onedimensional stochastic logistic jumpdiffusion processes driven by Brownian motion and alphastable Lévy motion. First, we present the stability analysis of the solution of a stochastic logistic growth model with multiplicative alphastable Lévy noise. We establish the existence of a unique global positive solution of this model under certain conditions. Then, we find the sufficient conditions for the almost sure exponential stability of the trivial solution of the model. Next, we provide parameter estimation for the proposed model. In parameter estimation, we use the least square method to get optimal and applicable estimators of the drift parameters. We also investigate the consistency and asymptotics of the proposed estimators. We assess the validity of the estimators with a simulation study. Meeting information: Topic: Ph.D. Dissertation Defense for Bikram Bhusal Time: Aug 11, 2022 01:00 PM Eastern Time (US and Canada) Join Zoom Meeting https://fauedu.zoom.us/j/81740421843?pwd=ekN5dTNpd2d2V01CQ2g5Y2lwRzFldz09 

Aug., 17 
PhD Dissertation Defense (inperson with remote access). Speaker: Duval Zephirin (Ph.D. candidate) Title: Optimal Portfolio for the Informed Investor in Mispriced Lévy Market with Stochastic Volatility and Power Utility Advisor: Dr. Hongwei Long Abstract: We consider a portfolio optimization problem in stochastic volatility jumpdiffusion model. The model is a mispriced Levy market that contains informed and uninformed investors. Contrarily to the uninformed investor, the informed investor knows that a mispricing exists in the market. The stock price follows a jumpdiffusion process, in which the mispricing and volatility are modelled by OrnsteinUhlenbeck (OU) process and CoxIngersollRoss (CIR) process, respectively. We only present results for the informed investor whose goal is to maximize utility from terminal wealth over a finite investment horizon under the power utility function. We employ methods of stochastic calculus namely HamiltonJacobiBellman equation, instantaneous centralized moments of returns and threelevel CrankNicolson method. We solve numerically the partial differential equation associated with the optimal portfolio. Under the power utility function, analogous results to those in the jumpdiffusion model under logarithmic utility function and deterministic volatility are obtained. Meeting information: Topic: Ph.D. Dissertation Defense for Duval Zephirin Time: Aug 17, 2022 02:00 PM Eastern Time (US and Canada) Join Zoom Meeting https://fauedu.zoom.us/j/89312497707?pwd=K3lQQWxNOTc1TlFmaUZ6OUxOTG5OUT09 

Aug 1421

2022 Combinatorics, Computing, Group Theory and Applications in South Florida Early Registration: June 1, 2022 

Aug., 31
SE 215 5:00 pm 
Crypto Cafe is back on Wednesdays, every other week this fall, 2022! Join us for Crypto Cafe on Wednesday, August 31th. The Crypto Cafe Schedule and recording will appear the the Crypto Cafe Website
Speaker
: Francesco Sica, Florida Atlantic University 

July 2022 

Jul., 2529
8:30 am5:00 pm 
Young CryptograpHers Summer Camp (In the Sandbox) 

Jul., 19 
MS Exam: Keegan Lee (on ZOOM) Title: A SubexponentialTime Quantum Algorithm for the Dihedral Hidden Subgroup Problem Abstract: We examine the Hidden Subgroup Problem of finding a subgroup H of group G using an oracle function which maps an element of G into set S based only on the coset of H containing G. We present a subexponential complexity algorithm for the special case where G is dihedral of order 2^n, and we discuss expansion of the algorithm for application to dihedral groups of unspecified order. Join Zoom Meeting: 

Jul., 18 
MS Exam: Dominic Blanco (on ZOOM) Title: The Sitnikov Problem, Low Energy Transfers, and The Economic Feasibility of Asteroid Mining Abstract: Asteroid mining can be profitable; however, it is currently not economically feasible. Space companies have reduced the cost of missions by using low energy transfer. Low energy transfer uses connecting orbits requiring much less energy to move a spacecraft. To demonstrate low energy transfer, I investigate the Sitnikov Problem with eccentricity of and . The Sitnikov Problem is a form of the gravitational threebody problem with two heavy bodies orbiting in a plane while a light third body moves perpendicular to the plane. I compute the Poincaré map and find connecting orbits. I then compare past missions that used low energy transfer to similar missions which did not. In all cases, using low energy transfer lowered the cost. This shows that we should investigate the use of low energy transfer in asteroid mining missions to reduce cost. Join Zoom Meeting Meeting ID: 843 0491 4882 

June, 2022 

Fri., June 10 
PhD Dissertation Defense Speaker: Binod Rimal (Ph.D. Candidate) Title: Financial Timeseries Analysis with Deep Neural Networks Advisor: Dr. William Hahn, Florida Atlantic University, 2016 Abstract: Financial timeseries data are noisy, volatile, and nonlinear. The classic statistical linear models may not capture those underlying structures of the data. The rapid advancement in artificial intelligence and machine learning techniques, availability of largescale data, and increased computational capabilities of a machine opens the door to developing sophisticated deep learning models to capture the nonlinearity and hidden information in the data. Creating a robust model by unlocking the power of a deep neural network and using realtime data is essential in this tech era. This study constructs a new computational framework to uncover the information in the financial timeseries data and better inform the related parties. It carries out the comparative analysis of the performance of the deep learning models on stock price prediction with a wellbalanced set of factors from fundamental data, macroeconomic data, and technical indicators responsible for stock price movement. We further build a novel computational framework through a merger of recurrent neural networks and random compression for the timeseries analysis. The performance of the model is tested on a benchmark anomaly timeseries dataset. This new computational framework in a compressed paradigm leads to improved computational efficiency and data privacy. Finally, this study develops a custom trading simulator and an agentbased hybrid model by combining gradient and gradientfree optimization methods. In particular, we explore the use of simulated annealing with stochastic gradient descent. The model trains a population of agents to predict appropriate trading behaviors such as buy, hold, or sell by optimizing the portfolio returns. Experimental results on S\&P 500 index show that the proposed model outperforms the baseline models. Please contact Dr. Hongwei Long <hlong@fau.edu> for an electronic copy of the dissertation. A hardcopy of the dissertation is not displayed in the departmental office in order to avoid multiple people touching the same hardcopy at this pandemic time. 

May, 2022 

Thurs., May 19 SE 215 2:00 pm 
Ph.D. Dissertation Defense: Archana Timsina Title: Identifiability Analysis and Optimal Control of Infectious Diseases Epidemics and Parameterization Method for (Un)Stable Manifolds of Implicitly Defined Dynamical Systems CoAdvisors: Dr. Necibe Tuncer and Dr. Jason MirelesJames
Abstract: This dissertation is a study about applied dynamical systems on two concentrations. Frist, based on the growing association between opioid addiction and HIV infection, a compartmental model is developed to study dynamics and optimal control of two epidemics: opioid addiction and HIV infection. We show that the diseasefreeequilibrium is locally asymptotically stable when the basic reproduction number R_0= max (R_0^{u}, R_0^{v})< 1, here R_0^{v} is the reproduction number of the HIV infection, and R_0^{u} is the reproduction number of the opioid addiction. The addictiononly boundary equilibrium exists when R_0^{u} > 1 and it is locally asymptotically stable when the invasion number of the opioid addiction is R_{inv}^{u}< 1. Similarly, HIVonly boundary equilibrium exists when R_0^{v}> 1 and it is locally asymptotically stable when the invasion number of the HIV infection is R_{inv}^{v}< 1. We study structural identifiability of the parameters, estimate parameters employing yearly reported data from Central for Disease Control and Prevention (CDC), and study practical identifiability of estimated parameters. We observe the basic reproduction number ¬¬¬¬ R_0 using the parameters. Next, we introduce four distinct controls in the model for the sake of control approach, including treatment for addictions, health care education about not sharing syringes, highly active antiretroviral therapy (HAART), and rehab treatment for opiate addicts who are HIV infected. US population using CDC data, first applying a single control in the model, and observing the results, we better understand the influence of individual control. After completing each of the four applications, we apply them together at the same time in the model and compare the outcomes using different control bounds and state variable weights. We conclude the results by presenting several graphs. Similarly, we fit a SARSCoV2 model to US data of COVID19 cases and deaths. We conclude that the model is not structurally identifiable. We make the model identifiable by prefixing some of the parameters from external information. Practical identifiability of the model through Monte Carlo simulations reveals that two of the parameters may not be practically identifiable. With thus identified parameters, we set up an optimal control problem with social distancing and isolation as control variables. We investigate two scenarios: the controls are applied for the entire duration and the controls are applied only for the period of time. Our results show that if the controls are applied early in the epidemic, the reduction in the infected classes is at least an order of magnitude higher compared to when controls are applied with twoweek delay. Further, removing the controls before the pandemic ends leads to rebound of the infected classes. 

Fri., May 6 SE 215 ZOOM option 11:00 am 
Speaker: Theresa Buscemi (in person presentation): Title: Enumeration of Spanning Trees in a Graph by the Matrix Tree Theorem Abstract: In Graph Theory, a graph is called a tree if it is connected, undirected, and acyclic, i.e. any two vertices in the graph are connected by exactly one path. A subgraph H of a connected graph G is called a spanning tree if H is a tree which includes all the vertices of G. Now, let G be a connected graph with vertex set V = {v_1, v_2, ..., v_n} and edge set E = {e_1, e_2, ..., e_m}. After arbitrarily assigning orientations to the edges of G, we can define the incidence matrix M of G, whose (i, j)th entry is equal to 1 if e_j leaves v_i, 1 if e_j enters v_i, and 0 if e_j is not incident with v_i. The Matrix Tree Theorem states that the number of spanning trees of G is given by (the absolute value of) the determinant of any (n1) x (n1) submatrix of the augmented adjacency matrix D := MM^T. We provide a proof of the Matrix Tree Theorem and demonstrate how the theorem can be applied to count the number of spanning trees in example graphs. Virtual Option (ZOOM) Zoom link: https://fauedu.zoom.us/my/tbuscemi2020?pwd=cHJOZE9QTDZmcXFacTVoNGJGbVludz09 All are cordially invited. 

Fri., May 13 10:00 am ZOOM 
Prelim Exam: Sulani Thakshila Summary: One of the most promising fields in the security based problems in Cryptography are utilized lattices due to its hardness and efficiency. The digital signature schemes(DSSs) in latticebased cryptographic primitives are now very practical in compared with traditional cryptosystems like RSA or DSA which are based on factoring problem or discrete logarithm problem. Unlike the NTRUSign and HashandSign, FiatShamir(FS) transformation in DSSs first build an identification scheme in a certain form and then convert it into a DSS. In particular, identification scheme that has challenge as a polynomial is transformed into a DDS by improving length of the signature and making collisions resistant hash function family. While security in the identification scheme is based on approximate short vector in the standard model and Random Oracle Model(ROM), security of the DDS is depend on the finding collisions in the family of hash functions. The hardness assumptions here are used in ringSIS(Short Integer Solution) problem and now it has been adapted to ringLWE(Learning With Erros) which decreases the size of the signature and keys thereby improving the efficiency. I will explain FStransformation schemes and how it is related to signature schemes. In particular, Abdalla et al. in [1] introduced the idea of lossy identification scheme and give tight reductions in Quantum Random Oracle Model(QROM). The lossy identification scheme comes with an additional lossy key which is the output of the key generation algorithm and computationally indistinguishable from honestly generated ones. The security of the lossy identification scheme is a notion of impersonation of the lossy keys with respect to an adversary has access to lossy public keys and simulated transcript of the model. The NIST submissions TESLA and Dilithium are practical examples of lattice instantiation of [1]. For nonlossy latticebased identification schemes has underlying signatures in Ducas et al. in [2]. The security of such schemes is nontight and use the Forking Lemma. For example BLISS signature scheme Ducas et al. in [2] improved the rejection sampling by bimodal Gaussian instead of shifted Gaussian distributions. I will explain the lossy signature scheme and BLISS signature scheme in more detail in the notions of FS transform in lattices. The module lattices is the most appealing aspects of the latticebased protocols because of strong security proof based on hardness assumptions in worst case problems. I will explain the importance and advantages of modules lattices. The cyclotomic ring Zq[x]/(xn + 1) where n is a power of two plays a big role in constructing latticebased protocols and the small polynomials invertibile under special congruence conditions, q ≡ 5 (mod 8). Nguyen in [3] showed how to omit this congruence condition instead analysing zeroes in CRR(Chinese Remainder Representation) of small polynomials. Concretely, without the prime condition, Nguyen in [3] provide a upper bound in terms of probability for the nonexistence of a short vector in a random module lattice. I will explain nonexistence of prime condition improve the tight security in QROM, however with a less speed.
Join Zoom Meeting 

April, 2022 

April 7

Speaker: Thomas Benitez (in person) Title: A New ZeroKnowledge Protocol for the Syndrome Decoding Problem and CodeBased Signature Abstract: Zeroknowledge proofs are an important tool for many cryptographic protocols and applications. The threat of a coming quantum computer motivates the research for new zeroknowledge proof techniques for (or based on) postquantum cryptographic problems. One of the few directions is codebased cryptography for which the strongest problem is the syndrome decoding of random linear codes. In this presentation, we introduce a new zeroknowledge proof for the syndrome decoding problem on random linear codes. This protocol achieves a soundness error of 1/n for an arbitrary n. We provide an optimized version of this zeroknowledge protocol which achieves arbitrary soundness through parallel repetitions and merged cutandchoose phase. While turning this protocol into a signature scheme, we achieve a signature size of 17 KB for a 128bit security. This represents a significant improvement over previous constructions based on the syndrome decoding problem for random linear codes. All are cordially invited. 

April 8 SE 216 
MS Exam Presentation Speaker: Lariza Ramsammy (in person presentation) Title: Variations on Valuation Domains Abstract: It is common knowledge, in Commutative Algebra, that valuation domains are GCD domains with linearly ordered prime ideals. In his 1995 paper in Communications in Algebra, Ayman Badawi gave other characterizations of integral domains with linearly ordered prime ideals, thus providing an alternative proof of this equivalence. In this presentation, we will explore one of these characterizations as well as its implication for local integral domains with related properties, including pseudovaluation domains and divided domains. Finally, we will discover how these equivalent characterizations lead to a chain of implications among the properties considered. All are cordially invited.


April 11
1:00 p.m. SE 271 
Master of Science Exam (Presentation) Speaker: Raya Shimshi (in person) Title: Super Convergence of Ergodic Averages for Quasiperiodic Orbits (Quantitative Quasiperiodicity) 

April 14 10:00 am SE 215 
Crypto Café Zoom: https://fauedu.zoom.us/j/88045709062?pwd=NjN2NGRnVDhkdExwcUxlOHBPUjErUT09 Speaker : Emrah Karagoz, Florida Atlantic University Title : Correlation Power Analysis on AES Abstract : The main goal of side channel attacks is to gain physical information (such as timing information, power consumption, electromagnetic leaks etc.) from a cryptographic algorithm implemented on a computer device, and to obtain the cryptographic keys by using this information. Power analysis is a type of side channel attack in which the attacker aims to extract the cryptographic keys by studying the power consumption of the device. On the other hand, AES (Advanced Encryption Standard) is a symmetric algorithm standardized by NIST in 2001, and it has been deployed mostly everywhere to encrypt the sensitive data because of its strong cryptographic security. In this presentation, we will explain how correlation power analysis works on AES so that an attacker can extract the AES key very easily, and therefore we will point out that the implementation of a cryptographic algorithm is as important as its cryptographic security.


April 19
4:00 pm ZOOM 
Society for Industiral and Applied Mathematics (SIAM) student chapter presents: Speaker: Dr. Dan Wilburne, MITRE Corporation. A flyer for the event can be downloaded from the link below: https://drive.google.com/file/d/1hb184hSqxRpsr2GmjoVrY11RNX0uQZ/view?usp=sharing Title: My journey as an Applied Mathematician Zoom: https://fauedu.zoom.us/j/89219435411?pwd=UWFUaFliS25lcUJ1NGFBaWxweXBXUT09 Meeting ID: 892 1943 5411 Passcode: Siam2022 Also, please feel free to visit (or subscribe to) our Youtube channel: https://www.youtube.com/channel/UCLLIwl8E06aAfks2dNKve0g for previous talks and follow our Twitter page (@FAU_SIAMstudent): https://twitter.com/FAU_SIAMstudent for upcoming announcements. 

Thurs., April, 21 Sandbox (Library) 36 pm 
DATA and AI RESEARCH EXHIBITIONS This event is presented by the FAU DataDriven Science and AI Conference which will be held in the Student Union on Saturday, May 21, 2022, 8:00 am5:00 pm. Both the conference and the exhibition are open to to all students. If you attend the event on April 21st, 2022 for DATA and AI RESEARCH EXHIBITIONS at the Sandbox, you will receive the free registration to the May 21^{st} DataDriven Science and AI Conference! There is also an opportunity to present your research in the poster session at the DataDriven Science and AI Conference. Any poster presenters will also have registration reimbursement for the Conference. If you are willing to participate in the poster session in the conference, please contact Dr. Wazir Muhammad. The email: wmuhammad@fau.edu, and visit the following link to submit your poster information. https://forms.gle/WK7RNHTxd1ZoWDGG8 Please submit if you haven’t already. Thank you for your interest in DataDriven Science and AI Conference. If you have any questions or need additional information about DATA and AI RESEARCH EXHIBITIONS, please feel free to contact Dr. Maria Provost (mprovost@fau.edu) or visit the website: DataDriven Science and AI Conference See you all there on April 21^{st} at Sandbox! 

Thurs., April 21 ZOOM 6:30 p.m. 
Math Club  History of AI (Final Math Club event of the semester)
FAU's Math Club and the Society of Women Engineers will host, for its final event of the semester, a talk entitled, Hisotry of AI.
All are invited. We hope tp see you there! Zoom link: https://fauedu.zoom.us/j/84967758783?pwd=alhOOUg1dGtUcDVLUGNRYW43ODhPdz09 

Tues., April 26 
Prelim Exam: This event is open to all graduate faculty. Speaker: David Urizar, Ph.D. Candidate Summary: The proposed preliminary exam would present the fundamentals of rigidity theory. The student will define key terms: Graph realizations, Laman condition, Laman number, infinitesimal motion, and pure condition. Furthermore, he will develop some further theory in the case of 2dimensional rigidity, considering angle constraints in addition to length constraints for barandjoint frameworks. He will explain how algebraic relations of higher degree translate into linear relations on the columns of the rigidity matrix. He will provide combinatorial characterizations for the number of unique realizations of a rigid body modulo its rigid motions. The student will reformulate the problem of determining rigidity in terms of the algebraic geometry of the configuration space, and present numerous examples to illustrate these ideas. The student will be prepared to answer questions relating to structural rigidity and its applications. 

March 2022 

Thurs, March 3
10 am SE 215 
The Crypto Café is back! Join us for the first talk of the 2022 edition of our biweekly cryptography seminar, starting this Thursday, March 3, at 10:00 a.m. Topics will include mathematics and computer science that relate to codes, cryptography, and information security. Join us either inperson or virtaully this Thursday, March the 3rd, 2022. Speaker : Edoardo Persichetti, Florida Atlantic University Title : Codebased Signatures: New Approaches and Research Directions Abstract : Codebased cryptography is one of the main areas of research within the context of quantumsecure communication. Yet, designing an efficient and secure codebased signature scheme has been a challenging problem for the last few decades. In this talk, I will summarize some of the long history of codebased signatures, and then illustrate current work and future research directions for this important topic. Everyone welcome and there will be coffee, and donuts! Attend virtually on Zoom: Zoom: https://fauedu.zoom.us/j/88045709062?pwd=NjN2NGRnVDhkdExwcUxlOHBPUjErUT09 For future/past sessions, also see http://www.math.fau.edu/crypto_cafe.php 

Mon.Fri., Mar 711
8:00 am6:00 pm. 
53rd Southeastern International Conference on Combinatorics, Graph Theory and Computing, March 711, 2022


Thurs., Mar 17 10:00 am SE 215 
Crypto Café presents: Speaker : Abhraneel Dutta, Florida Atlantic University Title : Two Constant Time Polynomial Inversion Algorithms for PostQuantum Cryptosystems Abstract : A very common primitive in codebased cryptography is computing the inverse of a binary polynomial over a binary polynomial ring and making such algorithms constant time helps achieve the prevention against timing side channel attacks. This presentation will focus on a brief introduction to two recent time polynomial inversion algorithms which are capable to run in constant time: BernsteinYang's "SafeGCD" polynomial inversion, based on the Extended GCD algorithm and constant time ItohTsuji Inversion (ITI) derived from Fermat's Little Theorem. To join virtually on Zoom: Zoom: https://fauedu.zoom.us/j/88045709062?pwd=NjN2NGRnVDhkdExwcUxlOHBPUjErUT09 For future/past sessions (growing list), also see http://www.math.fau.edu/crypto_cafe.php 

Fri., March 18 2:00 p.m. SE 215 
An informal meeting to discuss... Reflection and Celebration of Diversity, Equity and Inclusion. Everyone is welcome to be a part of this important conversation! Join us! 

Fri., Mar 25 1:00 pm SE 215 
PhD Dissertation Defense: Sean Perry (Doctoral candidate) Advisor: Dr. Erik Lundberg This Doctoral Defense is also being presented on ZOOM. 

Thurs., March 31 10:00 am SE 215 
Crypto Café 

February 2022 

Thurs., Feb 3 6 pm The Sandbox 

Mon, Feb 7 12:00 pm SE 271 
Cryptography Presentation 

Tues, Feb 8 
Cryptography Presentation 

Thurs, Feb 10 
Cryptography Presentation (virtual) Title: Some Problems in IsogenyBased Cryptography Join Zoom Meeting: https://fauedu.zoom.us/j/3373397013?pwd=dzhlc2RaS0FJdUl0VzB0M2g2ZzlHQT09 Meeting ID: 337 339 7013 

Fre, Feb 11 
The student chapter of SIAM presents: CLICK HERE FOR THE OFFICIAL FLYER Title: What got you here won’t get you there: Landing a position in Data Science, Data Engineering and Machine Learning Join via Zoom: https://fauedu.zoom.us/j/87951200366?pwd=alN6NXFZRXRUbm91b3AwSTRhaTJldz09 Meeting ID: 879 5120 0366 

Sat., Feb 19 8:00 am6:00 pm. 

Sat., Feb 19 
The FAU Student Chapter of the Association for Women in Mathematics (AWM) presents: Guest Speakers: Dr. William Hahn (FAU) and Dr. Katherine Stange (University of Colorado). All information about the event, along with the registration information and event schedule, can be found on the event website. 

January 2022 

MonWed., Jan 35 85 pm 
International Symposium on Artificial Intelligence and Mathematics (ISAIM 2022). this meeting is being held virtually. Regsitration is free. The link will be distributed to those who regsiter for the ISAIM 2022 Conference at the ISAIM 2022 website. 

Mon.Wed., Jan 1013
96:00 p.m. 
Logical Foundations of Computer Science (LFCS, 2022) Wyndham Deerfield Beach Resort. 

Sat., Jan. 22
92 pm 
AMC8 Middle School Math Day 2022 Register Here 

Fri., Jan 28 4:00 pm SE 215 
An Afternoon Tea Time


Sat., Jan 29

MuAlphaTheta Math Competition  An event with 13 contests for individuals, teams and school. Florida Atlantic University, Davie campus 