Konferenzen  >  Mathematik  >  Infinitesimalrechnung, Differentialgleichungen, Integralrechnung

Simulation,    Computerphysik und Numerische Simulation

Hausdorff Research Institute for Mathematics (HIM)

Because of the ubiquity of Fourier analysis, oscillatory integrals are present in many techniques in both harmonic analysis and analytic number theory. Current state-of-the-art methods in both fields are pushing beyond classical methods because of increased importance of understanding the uniformity and stability of the estimates. In addition, researchers are uncovering unifying ideas that span the (traditionally somewhat separated areas) of oscillatory integrals in the setting of analysis, and character sums in number theory. Recent work on estimating oscillatory integrals have even applied model theory, from logic. This summer school will give participants an introduction on the classical methods for estimating oscillatory integrals and explain current cutting-edge developments. Throughout, the lectures will view these problems through a lens of understanding the uniformity and stability of the estimates.

Analysis,    Kurse und Veranstaltungen für Studenten der Mathematik

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

Optimierungsrechnung, Entscheidungsunterstützung,    Komplexe Systeme und Chaos

Banach Center

Kurse und Veranstaltungen für Studenten der Mathematik,    Analysis

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

Institute for Advanced Study in Mathematics (IASM)

There have been vast breakthroughs in the area of PDEs with singular randomness in the past a few years, notably parabolic PDEs with singular random noise, and (deterministic) dispersive PDEs with singular random initial data. A common feature of these two types of problems is that the randomness present is too singular for nonlinear operations in the equation to be well-defined classically, but on the other hand magical cancellations from these randomness also allow treatment of these equations with the help of probabilistic methods. Recent research in these two areas also brings potential interaction with the field of inverse problems from PDEs. This workshop will provide opportunity for senior and young researchers from the above areas to meet, discuss, and inspire each other. We aim to foster collaborations between different communities and inspire new research ideas.

Centro de Ciencias de Benasque Pedro Pascual

The main purpose of this Workshop-Summer School is to build an opportunity to share recent results, ideas and projects related to the theory of Partial Differential Equations (PDE), with particular emphasis on issues related with its numerical approximation, the optimal design and control. This new edition will pay special attention to the interactions with Data Sciences and Machine Learning.

Numerische Analysis,    Kurse und Veranstaltungen für Studenten der Mathematik

American Institute of Mathematics, Pasadena, California

This workshop, sponsored by AIM and the NSF, will be devoted to exploring the geometric and analytic regularity of fully nonlinear partial differential equations (PDE) arising from geometry and physics. Ever since Yau's solution to the Calabi conjecture, geometric PDEs, such as the complex Monge-Ampère equations, have been extensively studied from both the geometric and analytic perspective. These equations have profound applications across many areas of mathematics, including differential geometry, metric geometry and algebraic geometry. Notable advancements have been made in this field, including the sharp L∞ estimates of Kolodziej, and Hölder continuity for complex Monge-Ampère equations. The goal is to bring together experts in this field to explore open problems and develop new techniques which are expected to yield solutions to some of the long-standing questions.

The main topics of the workshop include: Exploration of the geometry of Kähler metrics in the absence of Ricci curvature lower bound, using analytic estimates on Kähler potentials. Analyzing the connection between stability, subsolutions, and the existence of solutions for a specific class of fully nonlinear PDEs. Hölder continuity of solutions for fully nonlinear PDEs, particularly those of the Hessian type. Geometric and analytic estimates for singular metrics on complex varieties.

Stefan Banach Mathematical Center

American Institute of Mathematics, Pasadena, California

This workshop, sponsored by AIM and the NSF, will be devoted to exploring the geometric and analytic regularity of fully nonlinear partial differential equations (PDE) arising from geometry and physics. Ever since Yau's solution to the Calabi conjecture, geometric PDEs, such as the complex Monge-Ampère equations, have been extensively studied from both the geometric and analytic perspective. These equations have profound applications across many areas of mathematics, including differential geometry, metric geometry and algebraic geometry. Notable advancements have been made in this field, including the sharp L∞ estimates of Kolodziej, and Hölder continuity for complex Monge-Ampère equations. The goal is to bring together experts in this field to explore open problems and develop new techniques which are expected to yield solutions to some of the long-standing questions.

Casa Matemática Oaxaca (CMO)

Our society faces various grand challenges that it urgently needs to address over the coming years, such as mitigating climate change, combating environmental damage, and providing effective, affordable healthcare for everyone. Data science and Artificial Intelligence are expected to play a key role in successfully tackling many of these challenges. While recent progress in AI was driven mostly by empirical developments, we are entering now a new phase in which questions of trustworthiness, scalability, fairness, privacy, reproducibility, and explainability emerge as key factors. Fundamentally new ideas and approaches are needed to address these open problems, which will require a close collaboration between mathematicians, statisticians, computer scientists, and engineers. This workshop features an interdisciplinary group of exceptional scientists from across the world to present recent developments, foster new interactions, and create novel ideas for the solution of the aforementioned data science problems.

Mustererkennung und Bildverarbeitung, Maschinelles Sehen,    Wissenschaftliches Rechnen und Datenwissenschaft

The Hausdorff Research Institute for Mathematics (HIM)

This workshop aims at bringing together young and talented mathematicians which work on subjects related to Calculus of Variations and its applications. Examples of interesting topics covered in the conference include regularity in PDEs, machine learning, mechanics, geometric flows, optimal transportation, Riemannian geometry, and quantum mechanics.

The general idea of the workshop is to not limit the interaction between speakers and participants to the bare scientific presentations, but to provide enough space and time between the talks to leave space to potential collaborations and fruitful discussions. We in particular encourage researchers in a young stage of career (Master and PhD students) to participate to the Workshop.

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

The format of this two-weeks event is audience-oriented: Instead of having a sequel of very specialized talks on the speaker's own favorite research theme we plan to design a list of topics and techniques of general interest from which the participants can learn in order to enrich and facilitate their own work. In this spirit, speakers are asked to prepare material suggested by the organizers (but of course coordinated with them) and to present it in an accessible manner enabling a deeper understanding of the main aspects.

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Kurse und Veranstaltungen für Studenten der Mathematik,    Wissenschaftliches Rechnen und Datenwissenschaft

Discover the forefront of research and innovation in the field of Fractional Calculus! The International Conference on Fractional Calculus and Applications is a premier gathering of scholars, researchers, and professionals from around the world, dedicated to advancing knowledge and fostering collaboration in this rapidly evolving discipline.

Fractional Differential Equations, Fractional Partial Differential Equations, Theory of existence and uniqueness of solutions, Stability analysis, Boundary value problems, Inverse problems, Fractional Control Systems, Applications in Physics, Engineering, Biology, and more.

Angewandte Mathematik (allgem.),    Analysis

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

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

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

Analysis,    Numerische Analysis

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

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