http://publications.mfo.de/handle/mfo/3923 Oberwolfach Reports Volume 19 (2022) Mon, 06 Apr 2026 23:30:20 GMT 2026-04-06T23:30:20Z http://publications.mfo.de/handle/mfo/4038 Heat Kernels, Stochastic Processes and Functional Inequalities The workshop provided a forum for recent progress on a wide array of topics at the nexus of Analysis (elliptic, subelliptic and parabolic differential equations), Geometry (Riemannian and sub-Riemannian geometries, metric measure spaces, geometric analysis and curvature), and Probability Theory (Brownian motion, Dirichlet spaces, stochastic calculus and random media). The workshop provides a unique opportunity to encourage and foster interactions between mathematicians who share some common interests but might use different research tools or work in different mathematical settings. Sat, 01 Jan 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/4038 2022-01-01T00:00:00Z The workshop provided a forum for recent progress on a wide array of topics at the nexus of Analysis (elliptic, subelliptic and parabolic differential equations), Geometry (Riemannian and sub-Riemannian geometries, metric measure spaces, geometric analysis and curvature), and Probability Theory (Brownian motion, Dirichlet spaces, stochastic calculus and random media). The workshop provides a unique opportunity to encourage and foster interactions between mathematicians who share some common interests but might use different research tools or work in different mathematical settings. http://publications.mfo.de/handle/mfo/4024 Mathematical Advances in Geophysical Fluid Dynamics The workshop "Mathematical Advances in Geophysical Fluid Dynamics" addressed recent advances in modeling, analytical, computational and stochastical studies of geophysical flows. Of particular interest were contributions concerning modeling and analysis of sea ice models, well-posedness results for the primitive equations and boundary layers, stratified flows and models for moist atmospheric dynamics including phase transitions. Sat, 01 Jan 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/4024 2022-01-01T00:00:00Z The workshop "Mathematical Advances in Geophysical Fluid Dynamics" addressed recent advances in modeling, analytical, computational and stochastical studies of geophysical flows. Of particular interest were contributions concerning modeling and analysis of sea ice models, well-posedness results for the primitive equations and boundary layers, stratified flows and models for moist atmospheric dynamics including phase transitions. http://publications.mfo.de/handle/mfo/4019 Enumerative Combinatorics Enumerative Combinatorics focuses on the exact and asymptotic counting of combinatorial objects. It has fruitful connections to several disciplines, including statistical physics, algebraic combinatorics, probability theory, graph theory and computer science. This workshop brought together experts from all these various fields with the goal of promoting cooperation and interaction among researchers with largely varying backgrounds. It was the third workshop on this topic (the first two editions dating back to 2014 and 2018) and this time the main focus was on interactions with algebraic combinatorics. Sat, 01 Jan 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/4019 2022-01-01T00:00:00Z Enumerative Combinatorics focuses on the exact and asymptotic counting of combinatorial objects. It has fruitful connections to several disciplines, including statistical physics, algebraic combinatorics, probability theory, graph theory and computer science. This workshop brought together experts from all these various fields with the goal of promoting cooperation and interaction among researchers with largely varying backgrounds. It was the third workshop on this topic (the first two editions dating back to 2014 and 2018) and this time the main focus was on interactions with algebraic combinatorics. http://publications.mfo.de/handle/mfo/4016 Algebraic Structures in Statistical Methodology Algebraic structures arise naturally in a broad variety of statistical problems, and numerous fruitful connections have been made between algebra and discrete mathematics and research on statistical methodology. The workshop took up this theme with a particular focus on algebraic approaches to graphical models, causality, axiomatic systems for independence and non-parametric models. Sat, 01 Jan 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/4016 2022-01-01T00:00:00Z Algebraic structures arise naturally in a broad variety of statistical problems, and numerous fruitful connections have been made between algebra and discrete mathematics and research on statistical methodology. The workshop took up this theme with a particular focus on algebraic approaches to graphical models, causality, axiomatic systems for independence and non-parametric models. http://publications.mfo.de/handle/mfo/4013 Real Analysis, Harmonic Analysis and Applications The workshop focused on important developments within the last few years in real and harmonic analysis including nonlinear Carleson theorems and singular integral theory, Fourier restriction theory and spherical maximal functions as well as concurrent progress in the application of these for example to partial differential equations. Sat, 01 Jan 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/4013 2022-01-01T00:00:00Z The workshop focused on important developments within the last few years in real and harmonic analysis including nonlinear Carleson theorems and singular integral theory, Fourier restriction theory and spherical maximal functions as well as concurrent progress in the application of these for example to partial differential equations. http://publications.mfo.de/handle/mfo/4010 Geometrie The workshop Geometrie, organized by Aaron Naber (Evanston), André Neves (Chicago) and Burkhard Wilking (Münster) was well attended with over 42 participants (35 in person and 7 online) with broad geographic representation from all continents, and held in a very active atmosphere. During the meeting, various interesting topics in geometry were discussed, such as geometric flows, Einstein manifolds and spaces with sectional curvature bounds. Sat, 01 Jan 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/4010 2022-01-01T00:00:00Z The workshop Geometrie, organized by Aaron Naber (Evanston), André Neves (Chicago) and Burkhard Wilking (Münster) was well attended with over 42 participants (35 in person and 7 online) with broad geographic representation from all continents, and held in a very active atmosphere. During the meeting, various interesting topics in geometry were discussed, such as geometric flows, Einstein manifolds and spaces with sectional curvature bounds. http://publications.mfo.de/handle/mfo/4009 Mini-Workshop: A Geometric Fairytale full of Spectral Gaps and Random Fruit In many situations, most prominently in quantum mechanics, it is important to understand well the eigenvalues and associated eigenfunctions of certain self-adjoint differential operators. The goal of this workshop was to study the strong link between spectral properties of such operators and the underlying geometry which might be randomly generated. By combining ideas and methods from spectral geometry and probability theory, we hope to stimulate new research including important topics such as Bose--Einstein condensation in random environments. Sat, 01 Jan 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/4009 2022-01-01T00:00:00Z In many situations, most prominently in quantum mechanics, it is important to understand well the eigenvalues and associated eigenfunctions of certain self-adjoint differential operators. The goal of this workshop was to study the strong link between spectral properties of such operators and the underlying geometry which might be randomly generated. By combining ideas and methods from spectral geometry and probability theory, we hope to stimulate new research including important topics such as Bose--Einstein condensation in random environments. http://publications.mfo.de/handle/mfo/4008 Hilbert Complexes: Analysis, Applications, and Discretizations In this workshop 70 (43 at MFO, 27 online) leading mathematicians from Europe, United States, China, and Australia met at the MFO to discuss and present new developments in the mathematical and numerical analysis including discretizations of Hilbert complexes related to systems of partial differential equations, in particular the well known de Rham complex and the complexes of elasticity and the biharmonic equations. The report at hand offers the extended abstracts of their talks. Sat, 01 Jan 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/4008 2022-01-01T00:00:00Z In this workshop 70 (43 at MFO, 27 online) leading mathematicians from Europe, United States, China, and Australia met at the MFO to discuss and present new developments in the mathematical and numerical analysis including discretizations of Hilbert complexes related to systems of partial differential equations, in particular the well known de Rham complex and the complexes of elasticity and the biharmonic equations. The report at hand offers the extended abstracts of their talks. http://publications.mfo.de/handle/mfo/4007 Mini-Workshop: Topological and Differential Expansions of o-minimal Structures The workshop brought together researchers with expertise in areas of mathematics where model theory has had interesting applications. The areas of expertise spanned from expansions of o-minimal structures preserving tame geometric properties to expansions of specified fields by classical operators that preserve neo-stability properties. There were presentations and discussions on recent developments in definable groups and decompositions in relatively tame setups, the interplay of different notions of dimension and closure operators, and applications of the model theory of differential fields to diophantine geometry. Sat, 01 Jan 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/4007 2022-01-01T00:00:00Z The workshop brought together researchers with expertise in areas of mathematics where model theory has had interesting applications. The areas of expertise spanned from expansions of o-minimal structures preserving tame geometric properties to expansions of specified fields by classical operators that preserve neo-stability properties. There were presentations and discussions on recent developments in definable groups and decompositions in relatively tame setups, the interplay of different notions of dimension and closure operators, and applications of the model theory of differential fields to diophantine geometry. http://publications.mfo.de/handle/mfo/4006 History of Mathematics through Collaboration: Toward a Composite Portrait of Oswald Veblen Oswald Veblen played a pivotal role in the history of American mathematics in the twentieth century. His life, however, remains largely unstudied. This conference was designed to redress this issue by exploring Oswald Veblen and his contributions to the history of American and international mathematics in an interactive workshop that used the Veblen Papers from the US Library of Congress as a foundational and shared resource. With this frame, the conference raised queries and discussed issues related to Veblen, his mathematical contributions, and his collaborative initiatives, including his critical work aiding refugee mathematicians in WWII that helped establish long standing programs at American institutions that continue to advance mathematics at the highest level. The workshop echoed Veblen's collaborative focus and brought together historians of mathematics and mathematicians to work alongside one another during the conference. This content and collaborative approach combined to advance our understanding of Veblen's collaborations and the history of twentieth-century mathematics more broadly. Sat, 01 Jan 2022 00:00:00 GMT http://publications.mfo.de/handle/mfo/4006 2022-01-01T00:00:00Z Oswald Veblen played a pivotal role in the history of American mathematics in the twentieth century. His life, however, remains largely unstudied. This conference was designed to redress this issue by exploring Oswald Veblen and his contributions to the history of American and international mathematics in an interactive workshop that used the Veblen Papers from the US Library of Congress as a foundational and shared resource. With this frame, the conference raised queries and discussed issues related to Veblen, his mathematical contributions, and his collaborative initiatives, including his critical work aiding refugee mathematicians in WWII that helped establish long standing programs at American institutions that continue to advance mathematics at the highest level. The workshop echoed Veblen's collaborative focus and brought together historians of mathematics and mathematicians to work alongside one another during the conference. This content and collaborative approach combined to advance our understanding of Veblen's collaborations and the history of twentieth-century mathematics more broadly.