Erik Hoy (Rowan University)
Using Maple+QuantumChemistry Toolbox for Nanoelectronics
Nanoscale electronic devices such as switches, resistors, and transistors built from single molecules have attracted significant experimental and theoretical interest as potential replacements for/supplements to silicon-based electronics. Compared to traditional electronic components, these devices offer both additional miniaturization potential and unique charge transport properties. Designing effective nanoscale devices, however, requires an accurate theoretical description of charge transport at the quantum level. Using the quantum mechanical tools provided by Maple's QuantumChemistry Toolbox, we have designed a series of worksheets for both designing nanoscale electronics and calculating their transport properties. We will demonstrate how to use Maple worksheets to construct a series of molecular resistors to investigate non-classical conductance patterns.

Samir Hamdi (University of Toronto)
New Gauss Hypergeometric Solutions of the Quartic Equation and Summation Identities of Reciprocal of First Derivatives of Polynomials
We present new fundamental solutions for the quartic polynomial equation in terms of hypergeometric function. The solution method is based on reducing the cubic resolvent to a trinomial that can be solved using the classical Gauss hypergeometric function using Maple. The new closed form formula is compact compared to existing solutions for the quartic. We also extend the Newton's and Vieta's formulas by introducing new identities for the sums that involve the reciprocals of the first derivatives evaluated at the roots of the polynomial. These identities are general and valid for any polynomials P(x) of any degree with nonzero distinct roots and with nonzero first derivatives at roots. In this work, we present only the summation identities for the quartic equation, which can be derived using a computer algebra system such as Maple. Several applications of the new hypergeometric solutions of the quartic and the polynomial summation identities are presented. We derive travelling solitary pulse solutions for a high order boundary value equation governing the FitzHugh-Nagumo model for an excitable reaction- diffusion neuron system. The quartic solution is applied for the analytical inversion of the specific energy–depth relationship of water flow in open channels with parabolic cross sections. We present applications for computing solutions for water flow with smooth change in channel width, and flow under sluice gate.

Jean-François Hermant (ESIEE-IT)
Using Maple to Compute a Tight Upper Bound on Worst-case Searches for a t-leaf Balanced m-ary Tree
In this paper, we compute a tight upper bound on worst-case searches for a t-leaf balanced m-ary tree. More specifically, we compute Xi^t_k, the worst-case search time for isolating k leaves in a t-leaf balanced m-ary tree, which satisfies the following recursive equation: Xi^t_k = 1 + max{Xi^t/m_{k_1} + ... + Xi^t/m_{k_m}}, with: k_1 + ... + k_m = k and (k_1, ..., k_m) in {0, ..., t/m}^m, if k in { 2, ..., t }, Xi^t_k = 0 if k = 1, and Xi^t_k = 1 if k = 0, where: t=mⁿ, m in N^*\{1}, n in N^*. We use Maple to help us solve the previous recursive equation, which is far from being trivial.

Luis Felipe Tabera (Universidad de Cantabria), Rafael Losada-Liste (Sociedad Asturiana de Educación Matemática Agustín de Pedrayes), Tomás Recio (Universidad Antonio de Nebrija), and Carlos Ueno (CEAD-Las Palmas)
Handling a cube through Maple and GeoGebra
In our contribution we will reflect on the issues involved in the modeling of linkages through GeoGebra, a widespread program that combines dynamic geometry (DGS) and Computer Algebra systems (CAS) features. As it is standard in the DGS context, the performance of the graphic model (i.e. the positions of the other vertices when dragging a given one) must correspond to a mathematically rigorous, symbolic computation driven output. We will exhibit the different, quite challenging programming, geometric and algebraic problems arising in this context, by focusing on a specific, apparently simple, structure: the cubic linkage, i.e. the spatial linkage formed by the vertices and rigid edges that constitute the frame of a regular cube. The mathematical model for our treatment of linkages embedded in a Euclidean space has a strong algebraic flavour, since we associate to a linkage an algebraic (non-necessarily irreducible) variety (sometimes over R^n, sometimes over C^n). Among the obtained results, we will describe the seemingly evident, but hard to prove, complete determination of the dimension of the cubic linkage from an algebraic geometry perspective, achieved through the indispensable concourse of Maple. Moreover, we will exhibit different GeoGebra books allowing advanced (and mathematically sound) 3D visualizations of this structure.

Bennett Palmer (Idaho State University)
Construction of Equilibria with Symmetry for Anisotropic Surface Functionals
The surfaces we see in the real world occur as interfaces between immiscible materials or between distinct phases of a single material. Thermodynamics tells us that the interface forms so as to attempt to minimize a particular potential energy. When one of the constituent materials is in an ordered phase (e.g. crystalline, or liquid crystalline), the potential energy is anisotropic, i.e. it may depend on the direction of the surface. This accounts for the obvious difference between the shape of an equilibrium drop of liquid and an equilibrium crystal. In this talk, we discuss algorithms for the generation of equilibrium shapes for certain types of anisotropic surface energies. We present Maple graphics of the resulting surfaces.

Yagub Aliyev (ADA University)
Cayley’s Centro-Surface: Old and New Attempts to Draw this Elusive Surface and Some New Ideas Around It
In the talk we will discuss a little less known chapter in the history of mathematics: Cayley’s attempt to find the shape of the surface containing all the centers of the principal curvatures of an ellipsoid. Cayley called it the centro-surface of an ellipsoid. Nowadays, this surface is known as focal surface of an ellipsoid, Cayley’s Astroid or by more popular name (because of applications in Optics and related fields) caustic of an ellipsoid. Arthur Cayley’s paper from 1873 contains sophisticated algebraic calculations followed by an attempt to draw this surface. He says: "I constructed on a large scale a drawing of the centro-surface for the values a²= 50,b²=25,c² = 15. (These were chosen so that a,b,c should have approximately the integer values 7, 5, 4, and that a² + c² should be well greater than 2b² ; they give a good form of surface,…"

After A. Cayley there were many attempts to recreate this surface both as drawings and as 3-D models. With the dawn of computer graphics era the quality and accuracy of these recreations increased and we can now find many interesting and colorful renderings of this surface in books, articles and websites. The author of the current abstract, after spending more than a year of online Calculus teaching, tried to find some new motivating examples for his students of the use of modern computer technology in tandem with the methods of vector calculus to create colorful images of surfaces which are not easy to describe using equations. I used Maple for this purpose. The talk contains colorful images from history of mathematics and more modern computer graphics as comparison for how mathematics evolved over the centuries.

Philip Yasskin (Texas A & M University)
You Too Can Put Manipulatable 3D Graphics in Your Webpage
Maple can export 3D plots in the x3doc format. I will show you how to incorporate these into your webpage. Here is an example from my second semester calculus class:
https://www.math.tamu.edu/~yasskin/prevclas/172H.22a/Projects/

Here are two samples from my online calculus textbook, MY Math Apps Calculus:
https://mymathapps.com/mymacalc-sample/MYMACalc3/Part I - Geometry & Vectors/CurveProps/TNB.html
https://mymathapps.com/mymacalc-sample/MYMACalc3/Part%20I%20-%20Geometry%20&%20Vectors/CurveProps/Cubic.html

You can rotate these by dragging your mouse, zoom using the mouse wheel or pan these using Ctrl-mouse drag. I will also discuss some hurdles I overcame in getting these to work properly and where we go from here.

Beata Hebda and Piotr Hebda (University of North Georgia)
Making Typical Problems on the Trapezoidal Rule More Interesting and More Relevant to Students by Using Technology
The presentation will show an approach to Trapezoidal Rule problems that combines the use of a calculator with the use of Maple. As a result, students are more interested in solving typical problems, because they understand connections between the steps. The approach can be used in other situations that require approximating function values and calculating errors of such approximations.

We both use this approach to teaching the topic very successfully in our calculus classes. Students seem to be much more interested in solving typical approximation problems when they see a connection between by-hand, calculator, and Maple methods. The same idea can be used when teaching other approximation topics, for example, given by the Taylor or Mclaurin polynomials.

Serkan Dag (Middle East Technical University)
Maple-Aided Teaching in Mechanical Engineering Undergraduate Courses
This presentation outlines and details Maple-aided teaching activities in mechanical engineering undergraduate level courses Numerical Methods and Composite Structures. Maple worksheets are used in both courses in the teaching of the main approaches to solution methodologies. These worksheets illustrate how parametric algorithms are constructed, implemented, and executed to generate the complete set of numerical results pertaining to a given mathematical or engineering problem. The undergraduate level course Numerical Methods covers fundamental solution techniques regarding error analysis, root finding, linear system of equations, optimization, curve fitting, numerical integration and differentiation, and ordinary differential equations. Sample Maple worksheets for numerical methods will be presented with a discussion on the impact of Maple based instruction on student performance. The second course that is supported by Maple-aided instruction is the fourth year technical elective Composite Structures. The ultimate objective in this course is to impart the know-how and skills necessary for stress and failure analysis of general fiber-reinforced composite laminates. For this purpose, throughout the semester the students are acquainted with Maple scripts written for angle lamina analysis, stiffness matrix computation, thermal stress and failure analysis, and laminate design. Sample worksheets will be shown and their role in improving the programming skills of the enrolled students will be discussed. Lastly, Maple-aided instruction in online courses will be considered and web links for complete sets of related Maple worksheets will be provided.

Michael Monagan (Simon Fraser University)
What integration methods should we teach for a first integral calculus course?
I am presently teaching integral calculus using Stewart's text. For calculating antiderivatives, Stewart covers simple substitutions, integration by parts, trigonometric substitutions, and partial fractions in sections 5.5, 7.1, 7.3 and 7.4 respectively. To enable trigonometric substitutions, in section 7.2 Stewart also covers trigonometric integrals where the integrand is either of the form sin^m x cos^n x or tan^m sec^n x. There is also a review section 7.5 Strategies for Integration, so, 6 one hour lectures in total focused on calculating antiderivatives.

Given that we have computer algebra systems like Maple, many of us believe that the students would be better served if we replace one or two of those topics, perhaps 7.2 and 7.3, by a lecture on how to use Maple, or perhaps another application of integration. Indeed, for our integral calculus course for social science students we do not cover 7.2 and 7.3.

Dropping trigonometric integrals is problematic, however. The application Section 8.1 Arc Length generates integrals which need trigonometric substitution. There is also the desire to cover a second type of substitution so students are more skilled at manipulating integrals. We have dropped integrals with integrands of the form tan^m x sec^n x and have included instead the tan half angle substitution. The tan half angle substitution covers a wider class of functions (rational functions in sin x and cos x). For example it includes csc x which is useful. But it generates rational functions of rather high degree for which computing partial fractions is error prone. Another difficulty is inverting the tan half angle substitution. In the talk I will share the difficulties I ran into, how to program this in Maple and what to do so that students can more easily apply the tan half angle substitution.

Camille Pinto, Alban Quadrat (Sorbonne Université & Inria Paris), and Thomas Cluzeau (University of Limoges, XLIM)
Towards an Effective Integro-Differential Elimination Theory
In spite of the importance of calculus in mathematics and mathematical physics, the study of integro-differential equations does not seem to have attracted much attention from the computer algebra community. In particular, an effective elimination theory for integro-differential equations has not yet been developed. For linear systems of integro-differential equations, such an elimination theory is equivalent to the "coherence property" of rings of integro-differential operators. In 2013, Bavula gave a non-constructive proof of this property for the ring I₁ of integro-differential operators with polynomial coefficients.

To develop an effective integro-differential elimination for I₁, we shall first recall that a ring is coherent if the (left/right) annihilator of every element of I₁ is a finitely generated (left/right) ideal and the intersection of two (left/right) finitely generated ideals of I₁ is also finitely generated. In this talk, using the normal forms of elements of I₁, effective computations over the ring A₁ of differential operators with polynomial coefficients and linear algebra, we shall focus on the explicit characterization of the annihilators of the elements of I₁. The different results will be illustrated with explicit examples computed with the Maple packages IntDiffOp developed by Korporal-Regensburger and OreModules (built upon Ore_algebra) by Chyzak-Quadrat-Robertz.

Juan Pablo Gonzales Trochez (Western University)
Laurent Series and Puiseux Series in Maple
Let K be an algebraically closed field of characteristic zero. The field of fractions of the ring of formal multivariate power series over K, is called the field of formal multivariate Laurent series. In this document, we follow the ideas introduced by Monforte and Kauers in their paper Formal Laurent Series in Several Variables. Our objective is to report on a first implementation of formal multivariate Laurent series inside of Maple, and explain the challenges we had to overcome. In order to accomplish this goal, we make use of the already existing MultitivariatePowerSeries package, and its lazy evaluation scheme. In particular, we expose our ideas for adding and multiplying Laurent series with support inside different cones, where the support of a Laurent series is the set of all exponents of all non-zero monomials of our series. We also describe our biggest challenge, how to invert a Laurent series. Unfortunately, this problem cannot be completely solved in a lazy evaluation context. We describe some situations where we can solve the problem completely; our approach for the cases that fall outside of these situations; and how we let the user customize this approach, trading off between speed and the likelihood of an incorrect result.

The algebraic closure of the field of formal multivariate Laurent series is called the field of formal multivariate Puiseux series. As an extension of our current work, we also present our ideas for an implementation of a multivariate Puiseux series object inside of Maple.

Bertrand Teguia Tabuguia (Max Planck Institute for Mathematics in the Sciences)
Symbolic Powers of Functions Defined by Second-Order Linear ODEs
By symbolic power of a given function f, we shall mean fⁿ with a non-valued n so that fⁿ follows all the basic rules for exponentiation. An ordinary differential equation (ODE) satisfied by the symbolic power of f gathers ODEs fulfilled by any valued power of f. Therefore such an ODE encodes an uncountable set of ODEs.

We focus on ODEs with polynomial coefficients over a number field. Although D-finite functions form an algebra, it is generally impossible to automatically compute ODEs for their symbolic powers because of a linear dependency linking the order and the symbolic power. We prove that degree-two ODEs overcome this situation for second-order D-finite functions and some second-order D-algebraic functions. Our result emphasizes an advantage for guessing with quadratic ODEs, which we also demonstrate with many examples. Indeed, degree-two lower-order ODEs exist for big integer powers of the underlying generating functions.

Alexandre Lê (Sorbonne Université, Paris Université / Safran / Inria / CNRS)
On the Certification of the Kinematics of 3-DOF Spherical Parallel Manipulators
This presentation deals with the study of a Spherical Parallel Manipulator (SPM) with coaxial input shafts. Such a parallel robot provides three degrees of freedom (DOF) in orientation and is capable of unlimited rolling, in the context of stabilizing a set of cameras on a moving carrier. A special focus is made on the kinematics of this mechanism, especially taking into account uncertainties (e.g. on conception parameters, measures) and their propagation. Such considerations are crucial if we want to make sure to control our robot correctly without any undesirable behaviour in its workspace. One of the biggest issues of robots is singularities. These are configurations where the robot does not behave properly: either it loses at least one DOF or it gains at least one uncontrollable DOF. Such configurations should therefore be avoided. By studying the kinematics and singularities of this robot using Algebraic Geometry and Numerical Analysis techniques, we can compute a certified singularity-free zone in the work- and joint spaces, considering given uncertainties in the parameters. Problems related to the workspace will be solved using exact symbolic computation whereas the ones related to the joint space will be treated using a certified semi-numerical approach. This work of certification will allow us to use any control law to stabilize the upper platform of the robot, providing that the robot remains in the singularity-free zone.

Tomás Recio (Universidad Antonio de Nebrija) and M. Pilar Vélez (Universidad Antonio de Nebrija)
Dissecting Clough's Conjecture with Maple
Michael De Villiers is a well-known emeritus professor from South Africa, with world-leading research contributions on mathematics education and Dynamic Geometry. In different papers (De Villiers 2004, 2012) he worked on what he called “Clough’s conjecture”, namely that the sum of distances APc + BPa + CPb (see figure below, left) is constant. Trying to prove this result with the help of GeoGebra Discovery (see Kóvacs et. al. 2021) leads to a series of unexpected issues (figure above, right, showing how GeoGebra declares the result is “true on parts”), due to the complicated interlacing of real and complex algebraic geometry algorithms. In our contribution we will show how the use of different performing Maple packages and tools (PolynomialIdeals, algcurves, RegularChains, ConstructibleSetTools, SemialgebraicSetTools), allows to cleanly dissect the anatomy of Clough’s conjecture, yielding to a very coherent panorama of the geometry behind this nice result.

Cecilia Fissore, Francesco Floris and Marina Marchisio (Università di Torino)
Maple for the Development of Problem Solving Skills in Upper Secondary School
Among the eight key skills for lifelong learning to achieve success are mathematical competence, defined as the ability to develop and apply mathematical thinking to solve a variety of problems in everyday situations, and digital competence, which presupposes an interest in technologies and their use with critical thinking. Solving contextualized mathematical problems using Maple allows students to develop mathematical skills and digital skills at the same time. In particular, problem solving skills include several dimensions: understanding (analyzing the problematic situation, representing and interpreting data); identify (model the situation and identify the most suitable solution strategy); develop the solution process (resolve the situation problematic in a coherent, complete and correct way); and argue (comment and appropriately justify the applied process). The development of these skills, combined with digital skills, is particularly important for upper secondary school students who can be facilitated in university study or in the world of work. Our research question is: during a problem solving activity how much does the knowledge and effective use of Maple by students contribute to the development of problem solving skills? To answer this research question, the resolution of contextualized mathematical problems with Maple of about 100 secondary school students will be analyzed during a three-month online training. During this training the students learned how to use Maple and solved a mathematical problem every ten days, collaborating with the other students. Student resolutions were assessed by university tutors using an assessment grid that takes into account all dimensions of problem solving (understanding, identifying, developing, arguing, using maple). The research methodology consists of a quantitative analysis (of the evaluations of the students' resolutions during the training) and qualitative (the satisfaction questionnaires filled in by the students). The results of the analysis show how the use of Maple for problem solving activities positively influences the development of all problem solving skills. Explanatory examples are also given to show how Maple supports the development of problem solving skills and in particular argumentation skills. These results are useful for understanding the impact of this learning methodology and the use of technologies in the teaching and learning of Mathematics.

Fabio Roman, Alice Barana, Marina Marchisio and Valeria Fradiante (Università di Torino)
Developing Civic Education and Digital Citizenship Skills by Solving Mathematical Problems with Maple
In recent years, European reference frameworks have stressed the importance of developing Civic Education and Digital Citizenship skills in education, providing young people with means to live as active citizens in today's digital era. Civic Education, or Civics, means the provision of information and learning experiences to empower citizens to participate in society processes. Digital Citizenship is related to the positive engagement with digital technologies and data, so that people can participate actively and responsibly in today's digital society. Since 2020, Civic Education has become compulsory in all Italian upper secondary schools: teachers of all disciplines must dedicate some of their lessons to Civics, therefore adopting an interdisciplinary approach.

The objectives of this study are to understand how to design mathematical problems with Maple to develop Civics and Digital Citizenship skills, and how the use of Maple can enable upper secondary school students to develop this kind of skills. This study concerns a set of 40 contextualized mathematical problems to be solved with Maple on Civics and Digital Citizenship topics. They were conceived to help students develop these kinds of competences, besides Mathematics and problem-solving skills. A selected group of 542 upper secondary school students worked collaboratively in solving these problems with Maple through the Digital Learning Environment of the Digital Math Training project of the University of Turin funded by the Fondazione CRT. At the same time, the 108 Mathematics teachers of the students involved in the project were trained in a six-hour course aimed at showing how to use these problems in their teaching to engage students in Digital and Civic Citizenship Education. For this study, we have analyzed the task design of the 40 problems and how Maple was used in task design. We also studied how students and teachers reacted to the use of this type of problems through questionnaires submitted at the end of the project. From the analysis, we draw a model for the design of interdisciplinary mathematical problems to be solved with Maple. Moreover, the results show that students were quite aware of having developed digital and problem-solving skills, and teachers really appreciated how the problems helped students build Civics and Digital Citizenship competences. These results could help Mathematics teachers develop Civic Education activities within their teachings and encourage them to use an interdisciplinary problem-solving approach to make students develop different kinds of competences.

Alexandre Cavalcante, Sarah Lu and Sisi (Xiao) Feng (University of Toronto / OISE)
Exploring Open-Ended Tasks in Secondary Mathematics with Maple Learn - the Case of Functions
Teaching mathematics with a focus on mathematical processes (such as problem solving) often leads teachers to approach situations with single solutions. In doing so, students are presented with narrow ideas of what these processes can be. Problem solving, for example, can lead to open-ended explorations when students investigate a mathematical situation and need to make assumptions about aspects of the situation. In this presentation, we will introduce examples of Maple Learn activities that promote an open-ended perspective in mathematics explorations. The platform offers multiple features that allow students to identify their own assumptions about mathematical situations and work with them to create unique and individual solutions to problems, all the while still providing automated support to student learning. The presentation will focus particularly on the concept of functions from grade 9 to 12, starting with linear and quadratic functions. The presentation is part of an ongoing collaboration between Maplesoft and OISE (University of Toronto) to create Maple Learn resources that reflect contemporary mathematics education research.

John Pais (Ladue Horton Watkins High School)
Qubit Tensor Product Circuits Modeling Boolean Functions
This Maple interactive text develops the standard reversible extension (SRE) of an n-ary Boolean function by encoding each such function using an (n+1)-ary tensor product of qubit state spaces, with each n-tuple function argument encoded in the first n tensor product components and the corresponding value of the function encoded using the (n+1)st tensor product component. Each SRE of an n-ary Boolean function is represented by a unitary permutation matrix acting on the (n+1)-ary tensor product space, which when viewed as a quantum gate is reversible in the sense that it has a matrix inverse. This is in contrast to classical computing n-ary gates which are not reversible or invertible as functions.

In addition, for some small values of n, the matrix group of all such SREs that represent an n-ary Boolean function is generated and interactively explored, including its subgroups. Furthermore, the matrix tensor product of these and various other quantum gates, including the Hadamard gate, are developed and used to present a matrix group approach to several quantum computing algorithms, including the Deutsch Problem, the Deutsch-Jozsa Problem, Bernstein-Vazirani Problem and the Simon Problem.
This is the fifth in a sequence of Maple interactive texts that are being developed in order to introduce quantum computing to high school students. The target audience for this course is comprised of students that have already taken Calculus III (vector calculus) and/or AP Computer Science A. It is not assumed that the students have studied quantum mechanics or that they are familiar with Dirac notation, which is not used.

The Mathieu functions, which are also called elliptic cylinder functions, were introduced in 1868 by Émile Mathieu in order to help understand the vibrations of an elastic membrane set within a fixed elliptical hoop. These functions still occur frequently in applications today. Our interest, for instance, was stimulated by a problem of pulsatile blood flow in a blood vessel compressed into an elliptical cross-section. This talk surveys the historical development of both the theory of Mathieu functions and the methods used to compute them, with a particular focus on some of the interesting people who did the major work: Émile Mathieu, Sir Edmund Whittaker, Edward Ince, and Gertrude Blanch. Time permitting, we will discuss some gaps in current software capability involving double eigenvalues of the Mathieu equation, and some possible ways to fill those gaps using methods developed by Blanch.

Dr. Robert M. Corless is Emeritus Distinguished University Professor at Western University, a member of the Rotman Institute of Philosophy and of The Ontario Research Center for Computer Algebra, and Adjunct Professor at the Cheriton School of Computer Science, the University of Waterloo. His is also Editor-in-Chief of Maple Transactions. His primary research interests are computational linear and polynomial algebra, computational dynamical systems, and computational special functions. His underlying principles are Computational Discovery and Computational Epistemology, and the Ethics of AI, especially in teaching. His current focus is the new field of Bohemian Matrices. He has collaborated and published widely, and is the winner of a Halmos-Ford prize for mathematical exposition.

Each of the products in the Maple Math Suite include tools that encourage highly visual point-and-click style explorations. While appropriately similar in some ways, each product offers its own unique advantages. In this session, you’ll discover some of the ways Maple Calculator, Maple Learn, and Maple offer students and educators a highly interactive approach to conceptual learning and problem solving, the particular strengths of each approach, different methods for sharing interactive content, and how these tools can be used together to further enhance the student experience.

Everyone is familiar with using packages in Maple, from the widely useful plots package to specialized packages like AudioTools, DifferentialGeometry, and PolyhedralSets. But have you ever considered creating your own? Packages provide structure and organization to your code, and they make your work easier to reuse and share. This session will reveal some of the secrets used by algorithm developers at Maplesoft to write packages. Along the way we will touch on some essential programming topics such as modules, code-edit regions, debugging, revision control, and sharing.

Come learn more about the artwork in the Maple Art and Creative Works Exhibit and the Maple Learn Showcase, and meet some of the artists. Make sure you visit the Art Gallery ahead of time and vote for your favorites for the People’s Choice Awards.

** CANCELLED **
This meeting is for the associate editors of the Maple Transactions open-access journal (mapletransactions.org). Attendance is by invitation only. Check your email for instructions on how to join the meeting.