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Institute of Mathematics of the Polish Academy of Sciences, Warsaw

The aim of the workshop is to commemorate the 20th anniversary of the death of Professor Stanislaw Łojasiewicz — who played a crucial role in the creation of the Gdańsk-Kraków-Łódź-Warszawa Seminar in Singularity Theory, which is currently held online each month at IMPAN — by bringing together world-class experts in real and complex analytic geometry and in singularity theory — a vast area of research to which S. Łojasiewicz has made a fundamental contribution — as well as other researchers eager to connect with techniques in these domains. In particular, the diffusion of these techniques and their potential in current research problems, especially among young researchers, is one of the objectives of the meeting.

Topics that will be discussed during the workshop include the geometry of semi- and sub- analytic sets, o-minimal structures, Łojasiewicz inequalities and their applications to non-standard and functional analysis, Lipschitz geometry, stratification theory, equisingularity and invariants of singularities.

Operator Theory and particularly Spectral Theory are at the root of several branches in Mathematics and offer a wide range of challenging research problems. The purpose of this conference is to highlight some of the major theoretical advances in the fields of Operator Theory, Spectral Theory and Functional Analysis. The wide scope of the Conference ICOT should provide an excellent opportunity for sharing ideas and problems amongst specialists.

Algèbre,    Calcul infinitésimal, équations différentielles et intégrales

CIRM – Centre International de Rencontres Mathématiques

The Research Institute for Mathematical Sciences (RIMS)

Mathématiques appliquées (en général),    Reconnaissance de formes et traitement d'image, vision par ordinateur

The Research Institute for Mathematical Sciences (RIMS)

The Research Institute for Mathematical Sciences (RIMS)

The Research Institute for Mathematical Sciences (RIMS)

The Research Institute for Mathematical Sciences (RIMS)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

The Research Institute for Mathematical Sciences (RIMS)

Kyoto University, Japan | The Research Institute for Mathematical Sciences (RIMS)

Calcul infinitésimal, équations différentielles et intégrales,    Mathématiques appliquées (en général)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banach Center

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

This proposal focuses on new problems and new methods at the interface of harmonic analysis (taken in a very broad sense) and ergodic theory, with applications focused in number theory. A special emphasis is on equidistribution problems on arithmetic symmetric spaces, effective methods in homogeneous dynamics, periods of automorphic forms, families of L-functions over number fields and functions fields, and applications of Fourier uniqueness.

Théorie des nombres, arithmétique,    Calcul infinitésimal, équations différentielles et intégrales

ICERM

In spite of their omnipresence and importance, a number of questions about knots remain elusive. Addressing them solicits techniques from a range of mathematical disciplines at the interface of algebra, analysis, geometry, modeling, and low-dimensional topology. Some of the most exciting recent avenues of research include optimizing geometry, quantum knot invariants, and applications in material sciences, physics, and molecular biology. This workshop emphasizes bridging the gap between theoretical, computational, and experimental approaches in knot theory and its applications, including artificial intelligence.

Program Staff;     Tél.: [1-401-863-5030];     Email.: programstaff@icerm.brown.edu

Géométrie et topologie,    Algèbre

Institute of Mathematics at the University of Granada (IMAG)

The program's primary objective is to foster new collaborations, both on existing links within the analysis of PDEs and calculus of variations communities, and towards a closer interplay with machine learning and artificial intelligence. We will foster the communication of the latest vanguard results of interest for the above fields, to find a common ground of collaboration and promote cross-pollination of the technical advancements. To this aim, the program will feature both world leading experts in nonlinear diffusion models, nonlocal many-particle systems modelling, kinetic PDEs, and machine learning modelling, together with \normalcolor some of the most promising young researchers in those fields.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Statistique, Théorie des jeux,    Thermodynamique, dynamique des fluides et physique statistique

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to solving open problems regarding the stability of nonlinear waves using computer assisted methods of proof. Some results using computer assisted methods of proof include Hilbert's 18th problem and Smale's 14th problem. Researchers have developed efficient methods for obtaining rigorous error bounds for numerical approximations of heteroclinic and homoclinic connections between fixed points in ODE systems. These rigorous computation methods establish the existence and uniqueness of the solution in addition to providing a tight, completely rigorous error bound. Thus, these rigorous computations can be used to prove Theorems. Similarly, researchers have developed efficient and robust numerical methods for computing quantities that relay information about the spectral stability of one-dimensional traveling wave solutions to PDEs, which in turn yields information regarding the nonlinear stability. This workshop will help researchers identify collaborative opportunities to use rigorous computation to prove theorems regarding open problems in nonlinear wave theory.

Computer assisted proofs for stability analysis of nonlinear waves. Stability of multi-dimensional non-planar traveling waves. Rigorous computation of center manifolds

Mathématiques appliquées (en général),    Démonstration automatique de théorèmes

Banach Center

Mathématiques appliquées (en général),    Calcul infinitésimal, équations différentielles et intégrales

The Fields Institute

Differential equations, in particular evolutionary differential equations, are used to model, often with uncanny effectiveness, a vast number of natural and social phenomena. The study of dynamical behaviors of the underlying models, e.g. their stabilities, robustness, bifurcations, and complexities, has become truly essential to understand the phenomena being modeled. It is precisely because of the modeling effectiveness of evolutionary differential equations that their dynamical study is among the fastest growing and most active multidisciplinary research fields today. Not only is the existing theory of dynamics of evolutionary equations closely intertwined with many areas of mathematics, but also the concepts, methods, and paradigms, introduced in the study have become an indispensible component of a multitude of works of more applied nature, in disciplines including chemistry, physics, material science, mechanics, electrical engineering, as well as in the emerging applications of social sciences, not to mention the explosion during the last several decades of applications related to the biological and life sciences. As we push the boundaries of applicability of the existing theory, we routinely discover that new mathematical and computational tools are needed, often symbiotically. To witness, it is widely accepted that an important factor contributing to the explosive growth in studying dynamics of evolutionary differential equations has been the availability of sophisticated and powerful computational tools. Yet, huge systems, systems with multiple time scales, multi-physics models, stochastic differential equations, non-smooth evolutionary problems, still transcend our collective understanding, and exhibit inherent complexities which are requiring the development of sophisticated new modeling and numerical techniques, and whose validity will need to be validated by rigorous mathematics.

Calcul infinitésimal, équations différentielles et intégrales,    Simulation

Dept. of Mathematics, Stockholm University, SWEDEN

Marcus Wallenberg Symposium in memory of SERGEY NABOKO

Mathématiques appliquées (en général),    Physique mathématique

Casa Matemática Oaxaca (CMO)

Convexity is a branch of classical mathematics and it is located at the confluence of geometry, analysis, topology and combinatorics. Although its origins can be traced back to Archimedes and its systematic study started at the end of the nineteenth century, it was not until the mid-twentieth century that convexity became a well established branch of mathematics. Nowadays, it is an important area that is attracting young researchers and students. Why? Because of its intrinsic beauty, it’s fascinating and intriguing open questions that have an instant intuitive appeal, but also, because of its many relations with other areas of mathematics and its multiple applications, such as in economics, engineering and data science. The purpose of this workshop is to bring together key people working in this area, in order to explore recent progress and to help focus on future research directions.

Renyi Institute

Isaac Newton Institute for Mathematical Sciences (INI)

The "Complex analysis: techniques, applications and computations" (CAT) programme of 2019 brought together participants from diverse geographical and scientific communities to develop and apply complex analysis to a host of problems from areas including pure and applied mathematics, physics, engineering, and medicine. The Follow-On workshop is an opportunity to consolidate the achievements of the CAT programme and enhance its impact. Its first main goal will be to assess the progress that has taken place in the key thematic areas of the programme. The second main goal will be to formulate new open problems for the community to address in subsequent years. Finally, the workshop will also provide an opportunity to establish new collaborations. The workshop will mirror the structure of the original thematic programme and will cover the following three main overlapping areas: (1) Techniques of complex analysis, including, but not limited to, connections with classical, harmonic and asymptotic analysis, new transform methods, advances in the Wiener–Hopf and Riemann–Hilbert problems; (2) Applications of complex analysis, highlighting connections with diverse areas of modern physics and applied sciences as well as engineering; and n(3) computational complex analysis, including a range of topics bridging mathematical foundations of various numerical techniques and their software implementations.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Banach Center

ICMS - International Centre for Mathematical Sciences

The aim of this workshop is to bring together experts from different communities to cover the investigation of diffusive systems from several viewpoints: analytically, combining methods and techniques from Partial Differential Equations (PDEs) and dynamical systems to derive and analyse mathematical models for the applied phenomena; numerically, reviewing the most recent techniques and software for the computation of bifurcation diagrams and continuation with respect to the systems’ parameters; and, last but not least, from the applied — in particular biological — viewpoint: a constant exchange of knowledge between the theoretical investigations and the experimental data is in fact crucial in order to advance the research in this area. Our speakers will illustrate the most recent advancements in these fields, and foster the creation of new research directions with a concluding description of three open research questions aimed at colleagues working in fields different from their own. This will allow researchers with different backgrounds to learn ultimate techniques, connect with experts from various areas, and collaborate with fellow participants to produce new, cutting-edge research.

Mathématiques appliquées (en général),    Calcul infinitésimal, équations différentielles et intégrales

CIRM – Centre International de Rencontres Mathématiques

Banach Center

The conference concerns the broadly understood mathematical analysis, in particular, the so-called geometric analysis (including calculus of variation and partial differential equations of geometric origin, Sobolev spaces theory on manifolds and on metric spaces, and knot theory issues related to curvature energies).

Géométrie et topologie,    Calcul infinitésimal, équations différentielles et intégrales

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Calcul infinitésimal, équations différentielles et intégrales,    Mathématiques numériques

CIRM – Centre International de Rencontres Mathématiques

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics) and Institute of Mathematics of the Polish Academy of Sciences

Many physical, chemical, biomedical, and techni- cal processes can be described by means of partial differential equations or dynamical systems. In recent years, multi-physics and multi-scale prob- lems have become a particular focus of applied mathematical research. A numerical treatment of such problems is usually very time consuming and thus requires the development of efficient discret- ization schemes that are often realized on large parallel computing environments. In addition, these problems often need to be solved repeatedly for many varying parameters, introducing a curse of dimensionality when the solution is also viewed as a function of these parameters. Examples for such situations include design, control, optimiza- tion, inverse problems, uncertainty analysis and statistical sampling.

The seminar takes place at the Mathematical Re- search and Conference Center of the Institute of Mathematics of the Polish Academy of Sciences in Będlewo.

Mathématiques appliquées (en général),    Calcul infinitésimal, équations différentielles et intégrales

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics) and Institute of Mathematics of the Polish Academy of Sciences

Optimal transport theory is a very successful field of mathematics connecting calculus of variations, probability theory, differential geometry, partial differential equations, functional analysis, statis- tics and computer sciences. Going back to Monge around 1780, this theory has deep connections with the earlier work of Euler on Hydrodynamics around 1750. This connection has recently known a strong revival on many different sides, leading to various non trivial generalizations of the con- cept of optimal transport.

The seminar takes place at the Mathematical Re- search and Conference Center of the Institute of Mathematics of the Polish Academy of Sciences in Będlewo.

Mathématiques appliquées (en général),    Calcul infinitésimal, équations différentielles et intégrales

Banach Center

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)