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The Hausdorff Research Institute for Mathematics (HIM)

Analytic questions of a discrete nature are ubiquitous in many areas of mathematics and theoretical computer science. The purpose of this conference is to bring together a diverse group of experts working, broadly, on Discrete Analysis with particular emphasis on questions having a geometric component. The topics will include Boolean analysis, vector-valued harmonic analysis, metric embeddings, geometry of graphs and groups, and aspects of discrete probability and theoretical computer science.

Hausdorff Research Institute for Mathematics (HIM)

CIRM – Centre International de Rencontres Mathématiques

The main goal of these Etats de la recherche is to review some of the most recent spectacular developments in algebraic, analytic and arithmetic dynamics. Covered themes will include a variety of problems related to the iteration of rational maps on algebraic varieties as well as the study of their dynamical moduli spaces. Depending on the structure of the ambient field over which these maps are defined, methods may vary drastically. Over the field of complex numbers, one speaks of holomorphic dynamics in which quasi-conformal deformations play a key role. The case of maps defined over general metrized fields have led to the developments of dynamics over Berkovich spaces. One can also consider maps over number fields whose study lies at the core of arithmetic dynamics. Interactions between these various fields have deepened in the recent years. Complex pluripotential theory combined with tools from arithmetic geometry has been used to prove equidistribution results with applications to problems of unlikely intersection, and to explore dynamical moduli spaces and their special varieties. Methods in p-adic analysis and from the minimal model program have revolutionized our understanding of groups of birational transformations. Non-archimedean dynamics has been turned into a very efficient tool to analyze degeneration problems in holomorphic dynamics.

Kurse und Veranstaltungen für Studenten der Mathematik,    Algebra

CIRM – Centre International de Rencontres Mathématiques

Solving time-harmonic wave equations with iterative methods is very challenging because they combine multiple difficulties like e.g. highly oscillatory solutions and complex non-Hermitian and indefinite discrete operators. In addition, the wave number associated to the numerical solution is different from the one of the exact solution thus leading to so-called numerical dispersion which requires very fine mesh to be controlled. There exists numerical schemes designed to reduce the dispersion error where the most used technique to build them relies on stencils involving free parameters that are next obtained by numerically minimizing the dispersion error. In the past few years, we develop an alternative approach called asymptotic dispersion correction. The latter is based on the introduction of a perturbation of the wavenumber (the shift) in the numerical scheme. We then explicitly compute the shift that minimizes the dispersion error for small enough meshsize. In addition, we show that our method can be applied to any finite difference scheme and reduces the relative error. We emphasize that most of works dealing with dispersion reducing methods consider the Helmholtz equation. The goal of the Research in Residence is to extend the asymptotic dispersion correction to the convected Helmholtz equation that can be used to model time-harmonic wave propagation in a moving flow.

Kurse und Veranstaltungen für Studenten der Mathematik,    Infinitesimalrechnung, Differentialgleichungen, Integralrechnung

Banach Center

The SCGAS is an annual conference on geometric analysis and related fields hosted jointly by UC Irvine and UC San Diego.

The 2025 SCGAS conference will feature the following speakers:

Simon Brendle (Columbia University)

Alice Chang (Princeton University)

Pengfei Guan (McGill University)

Lan-Hsuan Huang (University of Connecticut)

Christos Mantoulidis (Rice University)

Valentino Tosatti (New York University)

Ryan Unger (Stanford University)

Differential Geometry, Geometric Analysis

Geometrie und Topologie,    Infinitesimalrechnung, Differentialgleichungen, Integralrechnung

University of Potsdam

The meeting is part of a series of meetings initiated by Professor Schulze devoted to micro-local, singular and global analysis and their interactions with geometry and mathematical physics.

Mathematische Physik,    Geometrie und Topologie

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Partial differential equations are a fundamental tool for modeling various physical phenomena and engineering problems. For example, oil flows in rock grains, turbulent filtration processes, groundwater flows, shallow water waves, phase changes of materials, and traffic congestion problems. The relevant PDEs are non-linear, and present certain degenerate and/or singular nature. Important examples include but are not limited to the porous medium equation, the p-Laplace equation, the total variation flow, the Stefan problem, doubly non-linear parabolic equations, widely degenerate equations, as well as related non-local equations.

Topics of the workshop include: (1) ​Gradient regularity for the porous medium/fast diffusion equation, (2) Wiener's criterion for non-linear parabolic equations, (3) Boundary Harnack estimates, (4) Regularity theory for Stefan-type problems, (5) Regularity theory for widely degenerate equations.

Kurse und Veranstaltungen für Studenten der Mathematik,    Infinitesimalrechnung, Differentialgleichungen, Integralrechnung

The mathematical modeling, simulation and analysis of wave phenomena entail a plethora of fascinating and challenging problems both in analysis and numerical mathematics. During the past decades, these challenges have inspired a number of important approaches, developments and results about wave-type equations in both fields of mathematics. In this conference we want to bring together international experts with different background to stimulate the transfer of ideas, results, and techniques within this exciting area.

Mathematische Physik,    Angewandte Mathematik (allgem.)

CIRM – Centre International de Rencontres Mathématiques

Starting in the 2011 Annals of Mathematics paper of Foreman, Rudolph and Weiss there have many results showing that classical problems in dynamical systems are unsolvable using inherently countable resources. The initial results were for abstract measure preserving systems, but more recent work has focussed on smooth systems on compact manifolds. Gerber and Kunde have made very significant contributions for smooth transformations that are weakly mixing and for Kautomorphisms. They also showed that the Kakutani equivalence relation is not Borel. These results raise more questions than they solve! The proposed Research inResidence is to bring the four researchers together to share knowledge and techniques and hopefully make progress on the open problems.

Faculty of Mathematics at the Universität Regensburg

Algebra,    Geometrie und Topologie

Simons Laufer Mathematical Sciences Institute (SLMath)

Many exciting breakthroughs in combinatorics involve innovative applications of techniques from a wide range of areas such as harmonic analysis, polynomial and linear algebraic methods, spectral graph theory, and representation theory. This workshop will present recent developments in this area and facilitate discussions of research problems.

extremal combinatorics, extremal graph theory, probabilistic combinatorics, discrete geometry, additive combinatorics, combinatorial geometry, incidence geometry, arithmetic progressions, Discrete analysis

Graphentheorie und Kombinatorik,    Algebra

Harmonic analysis on homogeneous spaces is a fundamental area of research that simultaneously generalizes classical harmonic analysis on groups and on Riemannian symmetric spaces. It naturally relates to many areas of mathematics, playing a central role in representation theory and the theory of automorphic forms.

Representation Theory and Noncommutative Geometry

Algebra,    Infinitesimalrechnung, Differentialgleichungen, Integralrechnung

Simons Laufer Mathematical Sciences Institute (SLMath)

In recent years techniques from harmonic analysis viz. projection theorems have found striking applications in finitary analysis on homogenous spaces. Such quantitative results have many potential applications to analytic number theory. This workshop will bring together researchers in these areas to further explore these connections.

University of Bristol / Heilbronn Institute for Mathematical Research

Colloquium-style talks from leading researchers about significant research developments in a range of topics in probability, analysis and dynamical systems.

Email: pad25-conference@bristol.ac.uk

Probability, Analysis, Dynamical Systems, Ergodic Theory

CIRM – Centre International de Rencontres Mathématiques

Kathmandu University, Nepal

We are delighted to announce the International Conference on Non-linear Analysis and Optimization (ICAN-OPT_NEPAL_2025), from May 08 to 10, 2025, at Kathmandu University, Dhulikhel, Nepal including a Workshop on Fixed Point Theory and Applications. This event is organized by Kathmandu University in collaboration with Tribhuvan University, Nepal Sanskrit University, and Nepal Mathematical Society.

This conference will cover diverse topics like Non-linear Analysis, Fixed Point Theory, Operator Theory, Complex Analysis, Harmonic Analysis, Wavelet Analysis, Special Functions, Functional Analysis, Fourier Analysis, Numerical Analysis, Convex Analysis, Optimization Theory, Queueing Theory, Finance & Economics, Differential Equations, Mathematical Biology, Mathematical Modelling, Data Science, and Machine Learning.

CIRM – Centre International de Rencontres Mathématiques

The question of whether or not a collection of equations has a solution in the integers is notoriously challenging, with the answer depending heavily on the geometry of the constituent equations. An important reduction is localization – looking at the equations modulo a prime or over the real numbers. Having solutions locally is a key necessary condition for the equations to have an integral solution and much more tractable to determine explicitly. The proposed research involves determining explicit and exact expressions for how often certain families of equations have local solutions, which can sometimes yield explicit results for how often an equation has an integral solution. In particular, we propose an approach to determine how often a degree 3 polynomial in n+1 variables has an integral zero, by reducing to the local probabilities (via recent work of Browning, Le Boudec, and Sawin) and determining them by a careful recursive argument.

Vanderbilt University

The conference will focus on several aspects of constructive function theory, including orthogonal polynomials, potential theory, discrete and continuous energy problems, special functions, polynomial inequalities, as well as various problems relating to optimization and efficiency. The aim is to stimulate collaboration and the exchange of ideas. The conference will be held in conjunction with the 37th Annual Shanks Lecture, to be given by Professor Doron Lubinsky (Georgia Institute of Technology).

Infinitesimalrechnung, Differentialgleichungen, Integralrechnung,    Kurse und Veranstaltungen für Studenten der Mathematik

Banach Center

University of Helsinki

Conference Quasiweekend III - Twenty years on collects together experts, from all fields of mathematics, using quasiconformal methods, especially in complex dynamics, geometric function theory, geometric group theory, analysis on metric spaces. Previous conferences in this series, Quasiweekend and Quasiweekend II – Ten years after, took place in 2005 and 2015, respectively, in Helsinki. With Quasiweekend III we celebrate mathematical legacy of Juha Heinonen -- initiator of this conference series -- in the broad field of quasiconformal analysis.

Email: quasiweekend@gmail.com

Qusiconformal maps, complex dynamics, geometric function theory, geometric group theory, analysis on metric spaces

Geometrie und Topologie,    Infinitesimalrechnung, Differentialgleichungen, Integralrechnung

Banach Center

The conference will explore the Yang-Baxter equation (YBE), a central topic in pure mathematics with connections to particle physics, statistical mechanics, and various mathematical fields like algebra, knot theory, tensor categories, and Hopf–Galois theory. Introduced in the 1960s by Yang and Baxter, the YBE has evolved into a rich and profound area of study. Drinfel'd's combinatorial version of the YBE, proposed in 1992, unveiled deep connections to numerous mathematical structures, including skew polynomial algebras, Bieberbach and Garside groups, and self-distributive structures such as racks and quandles. New algebraic concepts such as cycle sets, braces, and trusses were developed to address YBE-related problems and have found applications in other areas of mathematics.

Banach Center

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

Numerische Analysis,    Infinitesimalrechnung, Differentialgleichungen, Integralrechnung

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

Banach Center

Banach Center

Geometrie und Topologie,    Statistik, Spieltheorie

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

CIRM – Centre International de Rencontres Mathématiques

The abstract foundation of the book concerning functional analysis, special issues on Sobolev type function scales, and elliptic and parabolic regularity in case of non-smooth data, is already solid. However, the culminating last part of the book is still under discussion and editing. There, it is intended, using the theory established before, to give a condensed and unified treatment of wellposedness for several real-world problems, namely the thermistor problem, the Keller-Segel chemotaxis model, and the macroscopic semiconductor equations (Van Roosbroeck system) in case of Avalanche generation, all for the case of non-smooth spatial domains. These problems were open for decades and solved only recently by the authors and collaborators in journal articles.

Infinitesimalrechnung, Differentialgleichungen, Integralrechnung,    Angewandte Mathematik (allgem.)

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

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