Oberwolfach Reports: Recent submissions

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    • 2248b - Mini-Workshop: A Geometric Fairytale full of Spectral Gaps and Random Fruit 

      [OWR-2022-53] Workshop Report 2022,53 (2022) - (27 Nov - 03 Dec 2022)
      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 ...

    • 2225 - Hilbert Complexes: Analysis, Applications, and Discretizations 

      [OWR-2022-29] Workshop Report 2022,29 (2022) - (19 Jun - 25 Jun 2022)
      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 ...

    • 2248a - Mini-Workshop: Topological and Differential Expansions of o-minimal Structures 

      [OWR-2022-52] Workshop Report 2022,52 (2022) - (27 Nov - 03 Dec 2022)
      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 ...

    • 2249b - History of Mathematics through Collaboration: Toward a Composite Portrait of Oswald Veblen 

      [OWR-2022-56] Workshop Report 2022,56 (2022) - (04 Dec - 10 Dec 2022)
      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 ...

    • 2240b - Mini-Workshop: Quantization of Complex Symplectic Varieties 

      [OWR-2022-45] Workshop Report 2022,45 (2022) - (02 Oct - 08 Oct 2022)
      The mini-workshop featured two main series of lectures: "Functoriality in non-abelian Hodge theory" by Tony Pantev, and "Quantization of the Hitchin system and the analytic Langlands program" by Jörg Teschner. In ...

    • 2248c - Mini-Workshop: Subvarieties in Projective Spaces and Their Projections 

      [OWR-2022-54] Workshop Report 2022,54 (2022) - (27 Nov - 03 Dec 2022)
      The major goals of this workshop are to lay paths for a systematic study of geproci (and related, e.g., projecting to almost complete intersections or full intersections) sets of points in projective spaces, study ...

    • 2240a - Mini-Workshop: Zero-Range and Point-Like Singular Perturbations: For a Spillover to Analysis, PDE and Differential Geometry 

      [OWR-2022-44] Workshop Report 2022,44 (2022) - (02 Oct - 08 Oct 2022)
      The field of contact interactions and perturbations of differential operators supported on subsets with non-trivial co-dimension is an increasingly active mainstream of mathematical physics (in particular, operator and ...

    • 2245 - Analytic Number Theory 

      [OWR-2022-50] Workshop Report 2022,50 (2022) - (06 Nov - 12 Nov 2022)
      Analytic number theory is a subject central to modern mathematics. There are many important unsolved problems which have stimulated a large amount of activity by many talented researchers. At least two of the Millennium ...

    • 2222 - Universality: Random Matrices, Random Geometry and SPDEs 

      [OWR-2022-27] Workshop Report 2022,27 (2022) - (29 May - 04 Jun 2022)
      The postulate that large random systems can be described by limiting objects whose characteristic do not depend on the exact details of the models one started from is central in probability theory, under the name of ...

    • 2239 - At the Interface between Semiclassical Analysis and Numerical Analysis of Wave Scattering Problems 

      [OWR-2022-43] Workshop Report 2022,43 (2022) - (25 Sep - 01 Oct 2022)
      In this context of wave scattering, both semiclassical analysis and numerical analysis share the same goal - that of understanding the behaviour of the scattered wave - but these two fields operate largely in isolation, ...

    • 2218 - Interactions between Algebraic Geometry and Noncommutative Algebra 

      [OWR-2022-23] Workshop Report 2022,23 (2022) - (01 May - 07 May 2022)
      This workshop was on the interactions between noncommutative algebra, representation theory and algebraic geometry. The major objective was to bring together researchers from those areas with the focus on topics and ...

    • 2242 - Arbeitsgemeinschaft: Quantitative Stochastic Homogenization 

      [OWR-2022-48] Workshop Report 2022,48 (2022) - (16 Oct - 22 Oct 2022)
      Homogenization means approximating the effective, i.e. macroscopic, behavior of a heterogeneous medium by a homogeneous one, which amounts to a substantial conceptual and practical reduction of complexity. Stochastic ...

    • 2240c - Mini-Workshop: Mathematical Foundations of Robust and Generalizable Learning 

      [OWR-2022-46] Workshop Report 2022,46 (2022) - (02 Oct - 08 Oct 2022)
      Machine learning has become an highly active field of research, but its mathematical underpinnings are still hardly understood. This workshop identified key challenges, and it discussed potential solutions. Bringing ...

    • 2238 - Multiscale Wave-Turbulence Dynamics in the Atmosphere and Ocean 

      [OWR-2022-42] Workshop Report 2022,42 (2022) - (18 Sep - 24 Sep 2022)
      The atmosphere and oceans present an ongoing first-rate challenge to science and mathematics because they operate on an extremely broad ranges of scales, from molecular to planetary in length and from below seconds ...

    • 2241 - Arbeitsgemeinschaft: Higher Rank Teichmüller Theory 

      [OWR-2022-47] Workshop Report 2022,47 (2022) - (09 Oct - 14 Oct 2022)
      Higher rank Teichmüller theory is the study of certain connected components of character varieties of surface groups in higher rank semisimple Lie groups, with the property that all elements in these components correspond ...

    • 2237 - Large Scale Stochastic Dynamics 

      [OWR-2022-41] Workshop Report 2022,41 (2022) - (11 Sep - 17 Sep 2022)
      The goal of this workshop was to explore the recent advances in the mathematical understanding of the macroscopic properties which emerge on large space-time scales from interacting microscopic particle systems. The ...

    • 2236 - Complex Geometry and Dynamical Systems 

      [OWR-2022-40] Workshop Report 2022,40 (2022) - (04 Sep - 10 Sep 2022)
      The workshop focused on recent developments in holomorphic dynamics, several complex variables and complex geometry. The topics of the talks included dynamics of holomorphic and rational maps, the theory of currents, ...

    • 2235 - Character Theory and Categorification 

      [OWR-2022-39] Workshop Report 2022,39 (2022) - (28 Aug - 03 Sep 2022)
      Over a hundred years after the work of Frobenius and Schur, the sheer enormity of what is not known about the character theory of symmetric and alternating groups continues to surprise and awe the uninitiated. How does ...

    • 2229 - The Renormalization Group 

      [OWR-2022-33] Workshop Report 2022,33 (2022) - (17 Jul - 23 Jul 2022)
      The renormalization group was originally introduced as a multiscale approach to quantum field theory and the theory of critical phenomena, explaining in particular the universality observed e.g. in critical exponents. ...

    • 2234 - Mathematical Imaging and Surface Processing 

      [OWR-2022-38] Workshop Report 2022,38 (2022) - (21 Aug - 27 Aug 2022)
      This workshop was gathering applied mathematicians and computer scientists interested in image and geometry processing. These topics have developed tremendously in the past few years with the rise of artificial ...