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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 & President of the Scientific Committee of CIMPA, Insititute 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 recognised 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 discretisation 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 of European Mathematical Society (EMS), Institute for Mathematics, Technical University of Berlin, Germany

*Title: "Hierarchical energy based modeling, simulation and control of multi-physics systems."
Author: Volker Mehrmann
***Abstract:**The next level of digitization will create digital twins of every product or process. To do this in a mathematical rigorous and risk and error controlled way, a new modeling, simulation and optimization paradigm is needed. While automated modularized modeling is common in some domains like circuit design or multi-body dynamics, it becomes increasingly challenging when systems from different physical domains are coupled, due to largely different scales or modeling accuracy, and very different software technologies.A recent system theoretic approach to address these challenges is the use of network based energy based modeling via constrained port-Hamiltonian (pH) systems, where the coupling is done in a physically meaningful way via energy variables. Furthermore, for each subsystem a whole model hierarchy is employed ranging from very fine grane models to highly reduced surrogate models arising from model reduction or data based modeling. The model hierarchy allows adaptivity not only in the discretization but also in the model selection.We will present an overview over the hierarchical pH modeling approach and illustrate the advantages: Very robust models which are close to the real physics, invariance of the structure under Galerkin projection discretization or model reduction as well as state and time dependent coordinate changes. The results are illustrated with numerical results at the hand of energy transport networks (gas and district heating).

President Brazilian Mathematical Society, (IMU Executive Committee member), University of Sao Paulo, BRAZIL

**Abstract:***To be announced soon*

President of IMU CDC, School of Mathematics, Tata Institute of Fundamental Research, Colaba, Mumbai, INDIA

*Title: "Multiplicities for tensor product on special linear groups versus classical groups."***Abstract:**We discuss the known natural bijective correspondence between irreducible (algebraic) selfd-ual representations of the special linear group with those of classical groups, and then discuss how this correspondence relates to tensor product of representations.

President of the London Mathematical Society, University of Oxford , UK.

**Abstract:**I will review what is known and not known about the joint moments of the characteristic polynomials of random unitary matrices and their derivatives. I will then explain some recent results which relate the joint moments to an interesting class of measures, known as Hua-Pickrell measures. This leads to the proof of a conjecture, due to Chris Hughes in 2000, concerning the asymptotics of the joint moments, as well as establishing a connection between the measures in question and one of the Painlevé equations.

Title: "Joint Moments of Characteristic Polynomials of Random Unitary Matrices"

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'.

President, Italian Mathematical Union.University of Rome “Tor Vergata”. ITALY

*Title: "First order mean field games with state constraints."***Abstract:**The theory of Mean Field Games (MFG) has been developed in the last two decades by economists, engineers, and mathematicians in order to study decision making in very large populations of “small" interacting agents. The approach by Lasry and Lions leads to a system of nonlinear partial differential equations, the solution of which can be used to approximate the limit of an N-player Nash equilibrium as N tends to infinity. This talk will mainly be focused on deterministic models, which are associated with a first order pde system. When agents are subject to state constraints, as is often the case in reality, the analysis becomes particularly challenging because classical pde techniques are of little help. Indeed, the existence of solutions will be obtained by the so-called Lagrangian approach, which interprets equilibria as certain measures on the space of paths that each agent can choose. Then, we will address regularity issues for such generalized solutions, deriving point-wise properties that allow to recover the typical MFG system. Finally, we will study the asymptotic behaviour of solutions to the constrained MFG system as time goes to infinity, borrowing ideas from weak KAM theory.

Next Executive Director of CIMPA from September 1, 2020.

*Title: "Rational points on curves over finite fields" ***Abstract:**In 1985, Jean-Pierre Serre gave a series of lectures at Harvard university on rational points on curves over finite fields. As Serre himself phrased it, his purpose was to see, after more than a century of general theorems in algebraic geometry, how much could be said in a very concrete case, here the maximal number of rational points on a curve of genus $g$ over a finite field. More than 30 years later, the question is still widely open. I will present an overview of the topic, with a special focus on $g=3$. We will see, how solving such an apparently innocent question involves a variety of tools from arithmetic to analysis and heavy experiments with computational algebra systems.

CEREMADE (CENTRE DE RECHERCHE EN MATHÉMATIQUES DE LA DÉCISION. Past ICIAM President. FRANCE

*Title: Symmetry, symmetry breaking for nonlinear PDEs and nonlinear flows***Abstract:**In this talk I will address various examples of nonlinear elliptic PDEs related to the optimal functions for some functional inequalities where the use of well-adapted nonlinear flows can, or cannot, help us understand the symmetry and other qualitative properties of the solutions. This is a transversal topic which has connections in analysis and PDEs, but also in global analysis, differential geometry and mathematical physics.

International School for Advanced Studies SISSA, Via Bonomea, 265 34136 Trieste, ITALY

*Title: "**Regularity of the free boundary for the two-phase Bernoulli problem."***Abstract:**

I will brielfy introduce some free boundaries. problems and their applications. Then I will review some of the known regularity results. Eventually I will illustrate a recent result obtained in collaboration with L. Spolaor and B. Velichkov concerning the regularity of the free boundaries in the two phase Bernoulli problems. The new main point is the analysis of the free boundary close to branch points, where we show that it is given by the union of two C^1 graphs. This complete the analysis started by Alt Caffarelli Friedman in the 80’s.

I will brielfy introduce some free boundaries. problems and their applications. Then I will review some of the known regularity results. Eventually I will illustrate a recent result obtained in collaboration with L. Spolaor and B. Velichkov concerning the regularity of the free boundaries in the two phase Bernoulli problems. The new main point is the analysis of the free boundary close to branch points, where we show that it is given by the union of two C^1 graphs. This complete the analysis started by Alt Caffarelli Friedman in the 80’s.

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.

Vice President African Sciences (AAS). Mathematics Department, Faculty of Science, Sohag University, EGYPT. (Representing North Africa)

*Title: "**Quantum Search Algorithm with Dissipation"***Abstract:**

In this communication we discuss Designing an efficient search algorithms is a key challenge in multi-qubit quantum systems. We propose a dynamic multi-qubit quantum search algorithm, which is a generalization of Grover algorithm. This algorithm is distinguished by accuracy in obtaining high probability of finding any marked state in a shorter time than Grover algorithm time. The algorithm performance can be improved with respect to the different values of the controlled phase. A new technique is used to generate the dynamical quantum gates that helps in implementing the current algorithm.

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 COVID-19 Dynamics"***Abstract:***To be announced soon*

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

*Title: "Sous et Super solutions d'équations elliptiques presque périodiques"*

**Abstract:***To be announced soon*

Mathematics Institute (An ERCE of the European Mathematical Society (EMS))

African University of Science and Technology, Abuja, Nigeria.

**Abstract:***Given the complexity, contested, ambiguous and elusive nature of the concept of development, this talk will focus primarily on mathematics and the challenges of the African **human** and economic developments.*

African University of Science and Technology, Abuja, Nigeria.

IIT Madras, India, President of the Ramanujan Mathematical Society (RMS), India

*Title : Bohr's Inequality: Refinments and generalizations***Abstract:***To be announced soon*

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).