PUBLIC LECTURES
The African Institute for Mathematical Sciences (AIMSCameroon) invites renowned professionals and academics to share their ideas on a wide variety of interesting subjects through its Public Lecture Series. The series aims to enlighten, motivate and stimulate academic debate on diverse Mathematical and research domains in the minds of students. Each event is tailored in a way that encourages students to think across academic disciplines. Usually hosted at the AIMSCameroon lecture hall, our professors, external lecturers, and sometimes tutors and alumni, offer varied lectures from diverse and fascinating subjects. These public lectures and seminars play an important role in the lives of students, helping to broaden horizons and perspectives, and uphold the crucial spirit of intellectual inquiry and problemsolving in which AIMS believes.


The AIMSCameroon Public Lecture Series has opened for the 2020/2021 academic year with the first talk delivered by AIMSCameroon valedictorian of the 2019/2020 cohort.
Introducing 48 participants made up of students, tutors, and some AIMSCameroon alumnus to his essay project titled “Riemannian Geometry”, Romaric Kana, AIMSCameroon alumnus and valedictorian of the 2019/2020 cohort explained that the main objective of his work is to study the main basic concepts in Riemannian Geometry focusing particularly on the two fundamental notions of geodesic and curvature, with many examples.
In doing so, Romaric provided basic concepts in Riemannian Geometry by defining first, a differential manifold. He then defined a Metric on a Differential Manifold usually called a Riemannian Metric thus defining a structure of a Riemannian Manifold.
He went further to introduce the notion of covariant derivative where he explained one of the fundamental theorems of Riemannian geometry that shows the existence of a LeviCivita connection.
At the end of his talk, some participants were curious as to why the concept of Riemannian Geometry was developed and the applicability of the concept.
To answer this question, Romaric explained that this concept was developed to generalize the traditional Geometry that was limited to the Euclidean space of dimension 3. He further explained that the concept can be applicable in Theoretical Physics specifically in the area of General Relativity, and in Machine Learning where the concept of Geodesic can be used when working in Complex Neural Networks to find the shortest path between two nodes.
After his lecture, one of the participants, Dr. Armand Noubissie, AIMSCameroon tutor added some classical examples of the Riemannian Manifold such as the Torus, the Klein bottle, and the Moebius band.
Danny Parsons, Director and Mathematical Scientist at IDEMS International/AIMSCameroon lecturer, introduces the use of technology to support student’s learning through the provision of regular highquality feedback
During his talk titled “Providing High Quality Student Feedback through Electronic Assessment (quizzes!)”, Danny educated the AIMSCameroon students and tutors on the use of electronic assessment methods such as Moodle, an opensource course management system where students can get access to notes and STACK, a system for automated assessment of Mathematics using a computer algebra Kernel, all of which allows for extensive feedback and better learning opportunities.
Generally establishing some quite challenging conditions faced by students and lecturers at the undergraduate level especially in largesized universities, and particularly drawing from the case at the School of Mathematics, Statistics and Actuarial Science at Maseno University in Kenya, Danny said that the first year Mathematics and Statistics courses are often taken by students from a range of departments and there can be over 500 in a class of one lecturer and no teaching assistants. The lack of space and this very large class size limits students through the lack of highquality feedback and limits lecturers through a limited time for marking which resultantly impedes the provision of quality feedback.
To solve these problems, Danny unlocked some of the assessment strategies, feedback opportunities and student benefits offered by the STACK system and the response from some students of Maseno University, Kenya where it was used earlier this year in teaching two firstyear undergraduate courses.
“Even in small classes, the STACK system provides quizzes that can help students test themselves and get much more feedback than they could get in class. The feedback and randomization mean that they have so much more feedback hence more opportunities to learn”, Danny explained while pointing out the importance of such a system to an institution like AIMS.
The Moodle and STACK systems, already tested at AIMSCameroon during the just ended statistical problemsolving course, yielded lots of positive feedback from students. The system was equally envisaged to be vital during the AIMS students’ recruitment phase.
“Questions can be designed using the STACK system to be answered by the selected AIMS students before their arrival at AIMS. This will better equip them for the journey” Danny proposed. The seminar, which happened on Monday, October 28^{th,} 2019 at the AIMS Lecture hall, ended with lots of reactions from participants who were interested in how to set up the system, how the system works and a way to extend such knowledge to other universities.
Dr. Petmegni MBIEDA from the University of Yaounde 1 familiarizes AIMSCameroon Students with Another Research Area of Interest.
Speaking on Monday, December 09, 2019, at the AIMSCameroon lecture hall, Dr. Mbieda delivered a talk on “Dynamics of nonlinear periodic structures including their trapping and reshaping, in photonic fiber materials under specific conditions”. The aim was to excite student’s curiosity and challenge them to bring in their opinions on such a promising and trending topic, for the advancement of research for Africa as a whole.
“Since the creation of optical fibers, which is a transmission medium through which information can travel from point A to B, technology has made it possible to enhance the quality and time limit for the transmission of information by creating a new class of optical fibers known as Photonic Crystal Fibers (PCF’s)” he explained
“With this set of Photonic Crystal Fibers, the study aimed to generate a crystal of robust, shapepreserving, undistorted timemultiplex pulses (Trains of Soliton) that will transmit or carry the information (Photons) efficiently to the receiver”, he went on.
With the objective being to improve the transmission quality of multimode PCF’s, instead of transmitting single information (Progfille) by a single proton, he introduced the system of trapping and reshaping lowintensity profiles by a crystal of soliton. Dr. Mbieda went on to introduce 02 models and some conclusions, revealing that the structure is very efficient in multimode transmission, making it efficient, accurate with very low loss of information, not leaving out its efficiency for cloning.
He was, in the end, happy with the flux of questions that came in from students which proved a complete understanding of the subject matter. He equally provided students with a soft copy of the work to encourage them to indulge in such a research program.
AIMSCameroon Alumnus, Guy Fabrice Gounoue, Deliver a Talk Titled “Overview to NonLocal Operators”
With the aim of drawing student’s attention to a new concept and motivating them to dare study such, Guy Fabrice, AIMSCameroon alumnus of the 2015/2016 cohort, currently a Ph.D. student at Bielefeld University Germany, elaborated on the topic “Overview to nonlocal operators”.
Speaking on Monday, December 09 at the AIMS lecture hall, Guy noted that “Nonlocal operators” (especially the fractional Laplace operator) is a classical topic that is becoming impressively fashionable because of their connection with many realworld phenomena.
The topic, he said, more often describes the evolution of statistics (or the probability density functions) of a stochastic jump process. In other words, it represents the generator of the latter process.
“Indeed, nonlocal operators arise in the thin obstacle problem, in optimization, in finance, in phase transitions, ratified materials, in anomalous diffusion, in crystal dislocation, in soft thin films, in some models of semipermeable membranes and flame propagation, in conservation laws, in the ultrarelativistic limit of quantum mechanics, in quasigeostrophic flows, in materials science, and in water waves. More often, a nonlocal operator describes the evolution of statistics (or the probability density functions) of a stochastic jump process. In other words, it represents the generator of the latter process.” he went further.
Students at the end of his talk were curious as to the practicality of the concept.
“The interesting thing about such operators is that they turn out to become elliptic operators in limit which is relevant in numeric purposes” he explained.
AIMSCAMEROON TUTOR, ROCKEFELLER, DELIVERS A TALK TITLED “SHORT TERM WIND POWER FORECASTING: A BAYESIAN NEURAL NETWORK APPROACH”.
With an aim to introduce students to burgeoning climate change issues and raise awareness on how Mathematics coupled with Artificial Intelligence, can help address them, Rockefeller, AIMS DTPCS (AIMS Doctoral Training Program in Climate Science) Ph.D. fellow at Stellenbosch University, South Africa, presented on March 14^{th,} 2020, an introduction to his research work which uses deep learning approaches to improve short term wind power forecasting.
Given the increasing global energy demand over the last decade, thanks to population increase, fierce urbanization in developed countries and rapid global industrialization, Rockefeller revealed that there is an increase in the average temperature of the earth’s atmosphere which will persist and lead to grave environmental consequences if left unchecked.
“To curb this situation and at the same time, fulfill global energy demand in a sustainable way, new sources of energy such as wind, solar, hydro and marine energies, which, despite not being easy to store, transport, and especially given how they fluctuate, pause as a plausible way out”. He said.
In his talk, he made use of deep learning approaches by presenting the Mathematical formulation of the neural networks under the Bayesian framework, and how they can be applied to improve the forecast of shortterm wind power.
In the end, the students were curious as to where Data Science and Artificial Intelligence sit in such a research field.
In order to feed their curiosity, he made them understand that Physical models are the most reliable methods for wind forecast. But due to perturbations which lead to errors or inaccurate predictions, Deep Learning models are now considered as an alternative for weather forecast, since they are good approximators or complex systems.