President International Science Council (ISC) . Department of Maths and Applied Maths , UCT, University of Cape Town, South Africa. (For the Inaugural Plenary Lecture)

*Title: “Modelling, analysis and computation in mechanics”.***Abstract:**Problems in the mechanics of continuous media typically take the form mathematically of systems of partial differential equations, inequalities, or as variational problems. Studies of the well-posedness of such problems provide valuable insights into the range of validity of parameters describing material behaviour, and of the models themselves. The development of approximate solutions and accompanying numerical simulations are an essential component of investigations, given the intractability of all but the simplest cases. This

presentation will provide an overview of some problems in linear and nonlinear solid mechanics of recent and current interest. Key results will be presented on well-posedness, the development of algorithms for numerical approximations, and the determination of conditions for convergence of such approximations.

presentation will provide an overview of some problems in linear and nonlinear solid mechanics of recent and current interest. Key results will be presented on well-posedness, the development of algorithms for numerical approximations, and the determination of conditions for convergence of such approximations.

President of the Norwegian Mathematical Society, Institute of Mathematics, Bergen, NORWAY

*Title: On structure preservation in computational dynamics***Abstract:** In the design of numerical algorithms for integrating dynamic differential equations, the role of structure preserving- and geometric exact integration algorithms has become increasingly recognized in recent years. Whereas the conventional goal was to design stable algorithms with minimal error, the modern wisdom is that some errors are better than others. “Geometric integration is the art of erring in the right way.” Exactness in the discretization of certain geometric structures plays a crucial role in many simulations. A focus on differential geometry, symmetries and Lie group techniques in computational mathematics has lead close collaborations between areas of pure and applied mathematics, which is leading to significant new developments in algebra, differential geometry and computational algorithms.

President, Chineese Mathematical Society, School of Mathematical Sciences, (IMU Executive Committee member). University, Beijing, P.R.China, 100871. CHINA.

*Title: "Geometric flows and applications"***Abstract:**Geometric flows provide a very important tool in the study of spaces with desired structures. One of the most famous examples is Perelman’s solution of the Poincaré conjecture by using the Ricci flow. In this expository lecture, I will start with a classical result on surfaces and explain more recent approach to prove it. Next I will outline ideas in solving the Poincaré conjecture and the Geometrization conjecture for 3-manifolds. We will then discuss some new applications of Ricci flow and new geometric flows.

President, Finnish Mathematical Society. Department of Mathematics and Statistics, University of Helsinki, FINLAND

*Title: 'Multiplicative chaos and its many connections'***Abstract:**I will explain the notion 'Gaussian multiplicative chaos' and describe its many connections inclöuding statistical physics models and Riemann zeta function'.

Next Executive Director of CIMPA from September 1, 2020.

*Title: "Rational points on curves over finite fields" ***Abstract:**"In 1985, Jean-Pierre Serre taught at Harvard University a series of lectures on rational points on curves over finite fields. He described this topic as a good benchmark to see if the developments of algebraic geometry during the last century can say something new in this simple arithmetic context.

We will give an overview of what has been achieved since then and some recent results obtained in joint work with Jonas Bergström, Everett Howe and Elisa Lorenzo García."

We will give an overview of what has been achieved since then and some recent results obtained in joint work with Jonas Bergström, Everett Howe and Elisa Lorenzo García."

Department of Mathematics, University of Oslo, NORWEY

*Title: On sandwiched stochastic differential equations driven by Volterra noises***Abstract:**We study a stochastic differential equation with an unbounded drift and general Hölder continuous noise of an arbitrary order. We give examples of such Volterra noises and criterion for Hölder continuity. The corresponding equation turns out to have a unique solution that, depending on a particular shape of the drift, either stays above some continuous function or has continuous upper and lower bounds, i.e. lies in a sandwich. Our study is motivated by rough volatility in financial modelling and we give some examples in this setting. Some numerical illustrations are also provided.

Institute of Matemetics. Federal University, Rio de Janeiro – BRAZIL

*Title : "Metastability for stochastic dynamics"***Abstract:**As an interesting and rather common phenomenon in nature, metastability has been studied from multiple viewpoints, with different goals and a big variety of tools. Its modeling has been object of many mathematical studies. In this lecture, I plan to start by revisiting some aspects of the metastable behavior in the frame of stochastic dynamics. Through a class of concrete (but somehow generic) examples, I hope to discuss some of the basic motivations and to review a small fraction of the related mathematical literature, concluding with more recent results applicable to the stochastic Ising model in the two-dimensional lattice. These were obtained in collaboration with Alexandre Gaudilli`ere and Paolo Milanesi, both from Universit ́e Aix-Marseille.

Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa

**Abstract:**Mathematical modelling of engineering and biological systems play a crucial role in nation building and technological advancement. Modelling of engineering and biological systems have evolved to become an indispensable cost effective partner of experimental work. It provides the analytical basis for innovation, design and control, new technologies, disease control, food security, biodiversity sustainability, new products development, improve medical care, improve services and equipment for the benefit and wellbeing of the society at large. In this presentation, the tremendous potential of mathematical modelling in elucidating mechanisms and tackling seemingly complex engineering and biological problems are delineated. As illustration, the role of techno-mathematics (with respect to

nanotechnology) in dealing with challenging problems of thermal management in engineering devices, as well as mathematical biology in dealing with epidemiological problems are discussed.

Title: Mathematical Modelling of Engineering and Biological Systems – A Key to Nation Building and Technological Advancement

nanotechnology) in dealing with challenging problems of thermal management in engineering devices, as well as mathematical biology in dealing with epidemiological problems are discussed.

Knight in the International Order of Academic Palms of CAMES,

Member of CRE (Regional Commission of AUF Experts),

Marien Ngouabi University, CONGO-BRAZZA (Brazzaville). ( Representing Central Africa)

*Title: **Lie-Rinehart algebras and applications in differential geometry***Abstract:**After having defined the notion of Lie-Rinehart algebra in the new sense, we define Lie-Rinehart Jacobi algebras (Lie-Rinehart Poisson algebras respectively) and symplectic Lie-Rinehart algebras. We show that a manifold admits a locally conformal symplectic struc-

ture if and only if the module of vector fields carries a symplectic Lie-Rinehart algebra structure. We also show that a manifold admits a contact structure if and only if the module of differential operators of order ≤ 1 carries a symplectic Lie-Rinehart algebra structure. The characterization of Jacobi algebras (of Poisson algebras respectively) by the vanishing of the Schouten-Nijenhuis bracket is also given.

Member of CRE (Regional Commission of AUF Experts),

Marien Ngouabi University, CONGO-BRAZZA (Brazzaville). ( Representing Central Africa)

ture if and only if the module of vector fields carries a symplectic Lie-Rinehart algebra structure. We also show that a manifold admits a contact structure if and only if the module of differential operators of order ≤ 1 carries a symplectic Lie-Rinehart algebra structure. The characterization of Jacobi algebras (of Poisson algebras respectively) by the vanishing of the Schouten-Nijenhuis bracket is also given.

Foundation Professor of Mathematics, School of Mathematical and Statistical Science, Arizona State University

*Title: "*Mathematics of the Dynamics and Control of the COVID-19 Pandemic *"***Abstract:**The novel coronavirus that emerged in December of 2019 (COVID-19), which started as an outbreak of pneumonia of unknown cause in the city of Wuhan, has become the most important public health and socio-economic challenge humans have faced since the 1918 Spanish flu pandemic. Within weeks of emergence, the highly transmissible and deadly COVID19 pandemic spread to every part of the world, so far accounting for over 100 million confirmed cases and 2.1 million deaths (as of the end of January 2021), in addition to incurring severe economic burden, social disruptions and other human stresses, globally. In this talk, I will discuss our work on the mathematical modeling and analysis of the spread and control of COVID-19, with emphasis on the assessment of the population-level impact of the three currently-available anti-COVID vaccines (namely, the Pfizer-Biontech, Moderna and Oxford-AstraZeneca vaccines). Specifically, we will explore conditions for the elimination of the pandemic using the vaccines (vis a vis achieving vaccine-derived herd immunity) and it combinations with other nonpharmaceutical interventions, such as face masks usage and social-distancing.

University Distinguished Professor and Associate Dean at Morgan State University in Baltimore, Maryland, USA.

*Title: *A promenade in the world of periodicity

**Abstract:**

In this talk, we will present from the point of vue of differential equations several concepts of periodicity and their generalizations motivated by some periodic phenomena. We will give an elementary proof of the celebrated Massera Theorem for periodic differential equations. We will prove also that under some appropriate conditions, a second-order semilinear elliptic almost periodic equation has no almost periodic solution (in the sense of Bohr), but many almost automorphic and almost periodic (in the sense of Besicovitch) solutions in the envelope of the equation. We apply the results to study an almost periodically forced pendulum.

Institute of Mathematics, Vietnam Academy of Science and Technology, President of Vietnam Mathematical Society and Chair of the Section Mathematics of the National Foundation for Science and Technology Development

*Title: "Depth function of symbolic powers"***Abstract:** Symbolic power is the abstract version of the set of polynomials whose partial derivatives up to an order vanish on a given set of points. This lecture addresses the behavior of the function depth R/I^(t) = dim R − pd I^(t) − 1, where I^(t) denotes the t-th symbolic power of a homogeneous ideal I in a polynomial ring R and pd denotes the projective dimension. It was an open question whether the function depth R/I^(t) is nonincreasing if I is a squarefree monomial ideal. We will see that depth R/I^(t) is almost non-increasing in the sense that depth R/I^(s) ≥ depth R/I^(t) for all s ≥ 1 and t in the ranges i(s − 1) + 1 ≤ t ≤ is, i ≥ 1. There are examples showing that these ranges are the best possible, which gives a negative answer to the above question. Another open question asked whether the function depth R/I^(t) is always constant for t ≫ 0. We are able to show that for any positive numerical function φ(t) which is periodic for t ≫ 0, there exist a polynomial ring R and a homogeneous ideal I such that depth R/I^(t) = φ(t) for all t ≥ 1. These results are taken from a joint paper with Nguyen Dang Hop in Invent. Math. 218 (2019).

of the Hassan II Academy of Sciences and Technology, Rabat, Morocco.

Title: Doubly Reflected Backward Stochastic Differential Equations in the Predictable Setting

In this paper, we introduce a specific kind of doubly reflected backward stochastic differential equations (in short DRBSDEs), defined on probability spaces equipped with general filtration that is essentially non quasi-left continuous, where the barriers are assumed to be predictable processes. We call these equations predictable DRBSDEs. Under a general type of Mokobodzki’s condition, we show the existence of the solution (in consideration of the driver’s nature) through a Picard iteration method and a Banach fixed point theorem. By using an appropriate generalization of Itô’s formula due to Gal’chouk and Lenglart we provide a suitable a priori estimates which immediately implies the uniqueness of the solution.We extend this in the case of divided stopping times, called also quasi stopping times, introduced by Bismut and Skalli . Based on a joint work with Siham Bouhadou and Ihsan Arharas

University Cheikh Anta Diop of Dakar, Sénégal

Title: Shapes and Geometries**Abstract:**

*Keywords*: shape, geometry, geometric measure, partial differential equations, optimal mass transport

Title: Shapes and Geometries

The aim in this talk is first, to give an overview of the subject. Secondly,

we focus on theoretical work done in recent years with real-life motivations. To illustrate this, we will discuss some issues related to coastal erosion, transport problems, quadrature surface or image morphology.

we focus on theoretical work done in recent years with real-life motivations. To illustrate this, we will discuss some issues related to coastal erosion, transport problems, quadrature surface or image morphology.

University of Sfax, Tunisia.

Title: ON POLYNOMIAL CONJECTURES OF NILPOTENT LIE GROUPS UNITARY REPRESENTATIONS**Abstract:**

Title: ON POLYNOMIAL CONJECTURES OF NILPOTENT LIE GROUPS UNITARY REPRESENTATIONS

Let G be a connected and simply connected nilpotent Lie group of Lie al- gebra g, K an analytic subgroup of G, χ a unitary character of G and π an irreducible unitary representation of G. In this setting, the orbit method allows to identify the uni- tary dual of G to the space of coadjoint orbits. Using the enveloping algebra of the complexified Lie algebra of g, we consider two algebras of differential operators Dπ(G)K and Dτ (G/K) associated respectively to the restriction π|K of π to K and to the mono- mial representation τ = IndGK χ. Under the assumption that these representations are of finite multiplicities, the polynomial conjectures stating that Dπ(G)K and Dτ(G/K) are K-invariant polynomial rings hold.

In this lecture, I will overview some history of the conjectures and some restrictive cases. Once restricted to codimension one normal subgroups of G, the study of the geometry and the saturation of coadjoint orbits plays a crucial role in the general proof.

In this lecture, I will overview some history of the conjectures and some restrictive cases. Once restricted to codimension one normal subgroups of G, the study of the geometry and the saturation of coadjoint orbits plays a crucial role in the general proof.