• Footballs and donuts in four dimensions 

      [SNAP-2016-012-EN] Klee, Steven (Mathematisches Forschungsinstitut Oberwolfach, 2016)
      In this snapshot, we explore connections between the mathematical areas of counting and geometry by studying objects called simplicial complexes. We begin by exploring many familiar objects in our three dimensional world ...
    • Formal adjoints of linear DAE operators and their role in optimal control 

      [OWP-2011-15] Kunkel, Peter; Mehrmann, Volker (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-16)
      For regular strangeness-free linear differential-algebraic equations (DAEs) the definition of an adjoint DAE is straightforward. This definition can be formally extended to general linear DAEs. In this paper, we analyze ...
    • Formal punctured ribbons and two-dimensional local fields 

      [OWP-2008-01] Kurke, Herbert; Osipov, Denis; Zheglov, Alexander (Mathematisches Forschungsinstitut Oberwolfach, 2008-03-05)
      We investigate formal ribbons on curves. Roughly speaking, formal ribbon is a family of locally linearly compact vector spaces on a curve. We establish a one-to-one correspondence between formal ribbons on curves plus some ...
    • Formation Control and Rigidity Theory 

      [SNAP-2019-017-EN] Zelazo, Daniel; Zhao, Shiyu (Mathematisches Forschungsinstitut Oberwolfach, 2019-12-11)
      Formation control is one of the fundamental coordination tasks for teams of autonomous vehicles. Autonomous formations are used in applications ranging from search-and-rescue operations to deep space exploration, with ...
    • 1922 - Foundations and New Horizons for Causal Inference 

      [OWR-2019-25] (2019) - (26 May - 01 Jun 2019)
      While causal inference is established in some disciplines such as econometrics and biostatistics, it is only starting to emerge as a valuable tool in areas such as machine learning and artificial intelligence. The ...
    • 0632 - Four-dimensional Manifolds 

      [OWR-2006-35] (2006) - (06 Aug - 12 Aug 2006)
      This workshop has provided a broad panorama of recent developments in the study of topological, smooth, and symplectic 4-manifolds. Related invariants of knots and 3-manifolds were also discussed.
    • The Fourier Transform on Harmonic Manifolds of Purely Exponential Volume Growth 

      [OWP-2019-12] Biswas, Kingshook; Knieper, Gerhard; Peyerimhoff, Norbert (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-08)
      Let $X$ be a complete, simply connected harmonic manifold of purely exponential volume growth. This class contains all non-flat harmonic manifolds of non-positive curvature and, in particular all known examples of harmonic ...
    • Fourier-Mukai transform on Weierstrass cubics and commuting differential operators 

      [OWP-2016-03] Burban, Igor; Zheglov, Alexander (Mathematisches Forschungsinstitut Oberwolfach, 2016-05-10)
      In this article, we describe the spectral sheaves of algebras of commuting differential operators of genus one and rank two with singular spectral curve, solving a problem posed by Previato and Wilson. We also classify all ...
    • 0513 - Free Probability Theory 

      [OWR-2005-15] (2005) - (27 Mar - 02 Apr 2005)
      Free probability theory is a line of research which parallels aspects of classical probability, in a non-commutative context where tensor products are replaced by free products, and independent random variables are replaced ...
    • 1524 - Free Probability Theory 

      [OWR-2015-28] (2015) - (07 Jun - 13 Jun 2015)
      The workshop brought together leading experts, as well as promising young researchers, in areas related to recent developments in free probability theory. Some particular emphasis was on the relation of free probability ...
    • Freeness of Multi-Reflection Arrangements via Primitive Vector Fields 

      [OWP-2017-10] Hoge, Torsten; Mano, Toshiyuki; Röhrle, Gerhard; Stump, Christian (Mathematisches Forschungsinstitut Oberwolfach, 2017-04-20)
      In 2002, Terao showed that every reflection multi-arrangement of a real reflection group with constant multiplicity is free by providing a basis of the module of derivations. We first generalize Terao's result to ...
    • Friezes and tilings 

      [SNAP-2015-004-EN] Holm, Thorsten (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      Friezes have occured as architectural ornaments for many centuries. In this snapshot, we consider the mathematical analogue of friezes as introduced in the 1970s by Conway and Coxeter. Recently, infinite versions of such ...
    • 1310 - From "Mixed" to "Applied" Mathematics: Tracing an important dimension of mathematics and its history 

      [OWR-2013-12] (2013) - (03 Mar - 09 Mar 2013)
      The workshop investigated historical variations of the ways in which historically boundaries were drawn between ‘pure’ mathematics on the one hand and ‘mixed’ or ‘applied’ mathematics on the other from about 1500 until ...
    • From Betti numbers to ℓ²-Betti numbers 

      [SNAP-2020-001-EN] Kammeyer, Holger; Sauer, Roman (Mathematisches Forschungsinstitut Oberwolfach, 2020-04-15)
      We provide a leisurely introduction to ℓ²-Betti numbers, which are topological invariants, by relating them to their much older cousins, Betti numbers. In the end we present an open research problem about ℓ²-Betti numbers.
    • From computer algorithms to quantum field theory: an introduction to operads 

      [SNAP-2015-017-EN] Krähmer, Ulrich (Mathematisches Forschungsinstitut Oberwolfach, 2015)
      An operad is an abstract mathematical tool encoding operations on specific mathematical structures. It finds applications in many areas of mathematics and related fields. This snapshot explains the concept of an operad and ...
    • 1211 - Frontiers in Nonparametric Statistics 

      [OWR-2012-14] (2012) - (11 Mar - 17 Mar 2012)
      The goal of this workshop was to discuss recent developments of nonparametric statistical inference. A particular focus was on high dimensional statistics, semiparametrics, adaptation, nonparametric bayesian statistics, ...
    • A Function Algebra Providing New Mergelyan Type Theorems in Several Complex Variables 

      [OWP-2019-02] Falcó, Javier; Gauthier, Paul Montpetit; Manolaki, Myrto; Nestoridis, Vassili (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-11)
      For compact sets $K\subset \mathbb C^{d}$, we introduce a subalgebra $A_{D}(K)$ of $A(K)$, which allows us to obtain Mergelyan type theorems for products of planar compact sets as well as for graphs of functions.
    • 0012 - Functional Analysis and Partial Differential Equations 

      [TB-2000-13] (2000) - (19 Mar - 25 Mar 2000)
    • 0237 - Fundamental Groups in Geometry 

      [TB-2002-43] (2002) - (08 Sep - 14 Sep 2002)