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”.
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.
Prof. Hans Munthe-Kaas
President of the Norwegian Mathematical Society, Institute of Mathematics, Bergen, NORWAY
Title: On structure preservation in computational dynamics
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.
Prof. Volker Mehrmann
President of European Mathematical Society (EMS), Institute for Mathematics, Technical University of Berlin, GermanyTitle: "Hierarchical energy based modeling, simulation and control of multi-physics systems." Author: Volker Mehrmann
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).
Prof. Gang Tian
President, Chineese Mathematical Society, School of Mathematical Sciences, (IMU Executive Committee member). University, Beijing, P.R.China, 100871. CHINA.
Title: "Geometric flows and applications"
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.
Prof. Paolo Piccioni
President Brazilian Mathematical Society, (IMU Executive Committee member), University of Sao Paulo, BRAZIL
To be announced soon
Prof. Dipendra Prasad
President of IMU CDC, School of Mathematics, Tata Institute of Fundamental Research, Colaba, Mumbai, INDIATitle: "Multiplicities for tensor product on special linear groups versus classical groups."
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.
Prof. JongHae Keum
President of Korean Mathematical Society, School of Mathematics, Korea Institute for Advanced Studies (KIAS), SOUTH KOREA
Title: "Algebraic Surfaces : their geomety and topology"
To be announced soon
Prof. Jon Keating
President of the London Mathematical Society, University of Oxford , UK.
Title: "Joint Moments of Characteristic Polynomials of Random Unitary Matrices"
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.
Prof. Eero Saksman
President, Finnish Mathematical Society. Department of Mathematics and Statistics, University of Helsinki, FINLANDTitle: 'Multiplicative chaos and its many connections'
I will explain the notion 'Gaussian multiplicative chaos' and describe its many connections inclöuding statistical physics models and Riemann zeta function'.
Prof. Piermarco Cannarsa
President, Italian Mathematical Union.University of Rome “Tor Vergata”. ITALY
Title: "First order mean field games with state constraints."
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.
Prof. Christophe Ritzenthaler
Next Executive Director of CIMPA from September 1, 2020.
Title: "Rational points on curves over finite fields"
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.
Prof. Maria J. Esteban
CEREMADE (CENTRE DE RECHERCHE EN MATHÉMATIQUES DE LA DÉCISION. Past ICIAM President. FRANCE
Title: Symmetry, symmetry breaking for nonlinear PDEs and nonlinear flows
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.
Prof. Giulia Di Nunno
Department of Mathematics, University of Oslo, NORWEY
Title: On sandwiched stochastic differential equations driven by Volterra noises
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.
Prof. José-Maria P. Balmaceda
Former President of the Southeast Asian Mathematical Society in 2018-2019. Institute of Mathematics, University of the Philippines Diliman. Philippines.
To be announced soon
Prof. Maria Eulália Vares
Institute of Matemetics. Federal University, Rio de Janeiro – BRAZILTitle : "Metastability for stochastic dynamics"
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.
AMU-PACOM 2021 Medal Winner (A)
To be announced soon
AMU-PACOM 2021 Medal Winner (B)
To be announced soon
Prof. WEKE PATRICK GUGE Oloo
Director, School of Mathematics, University of Nairobi, KENYA. (Representing East Africa )
Title: The Landscape of Mathematical Sciences in the East African Region.
To be announced soon
Prof. Eugène OKASSA
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
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.
An African women Mathematician
To be announced
To be announced soon
Prof. Abba Gumel
Foundation Professor of Mathematics, School of Mathematical and Statistical Science, Arizona State UniversityTitle: "Mathematics of the Dynamics and Control of the COVID-19 Pandemic "
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.
Professor Gaston M. N'Guérékata
University Distinguished Professor and Associate Dean at Morgan State University in Baltimore, Maryland, USA.
Title: "Almost Periodic Elliptic Equations: Sub- and Super-Solutions"
The method of sub- and super-solutions is a classical tool in the theory of second order differential equations. It is known that this method does not have a direct extension to almost periodic equations. We show that if an almost periodic second order semi-linear elliptic equation possesses an ordered pair of almost periodic sub- and super-solutions, then very many equations in the envelope have either almost automorphic solutions, or Besicovitch almost periodic solutions. In addition, we provide an application to almost periodically forced pendulum equations.
Prof. Saminathan Ponnusamy
IIT Madras, India, President of the Ramanujan Mathematical Society (RMS), India
Title : Bohr's Inequality: Refinments and generalizations
To be announced soon
Prof. Ngo Viet Trung
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"
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).