• 1506 - Geometric and Algebraic Combinatorics 

      [OWR-2015-5] (2015) - (01 Feb - 07 Feb 2015)
      The 2015 Oberwolfach meeting “Geometric and Algebraic Combinatorics” was organized by Gil Kalai (Jerusalem), Isabella Novik (Seattle), Francisco Santos (Santander), and Volkmar Welker (Marburg). It covered a wide variety ...
    • 1935 - Geometric, Algebraic, and Topological Combinatorics 

      [OWR-2019-39] (2019) - (25 Aug - 31 Aug 2019)
      The 2019 Oberwolfach meeting "Geometric, Algebraic and Topological Combinatorics" was organized by Gil Kalai (Jerusalem), Isabella Novik (Seattle), Francisco Santos (Santander), and Volkmar Welker (Marburg). It covered a ...
    • Geometry of Free Loci and Factorization of Noncommutative Polynomials 

      [OWP-2017-23] Helton, J. William; Klep, Igor; Volčič, Jurij; Helton, J. William (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-02)
      The free singularity locus of a noncommutative polynomial f is defined to be the sequence $Z_n(f)=\{X\in M_n^g : \det f(X)=0\}$ of hypersurfaces. The main theorem of this article shows that f is irreducible if and only if ...
    • 0915b - Hilbert Modules and Complex Geometry 

      [OWR-2009-20] (2009) - (05 Apr - 11 Apr 2009)
      The major topics discussed in this workshop were Hilbert modules of analytic functions on domains in ℂn, Toeplitz and Hankel operators, the interplay of commutative algebra, complex analytic geometry and multivariable ...
    • 1607b - Hochschild Cohomology in Algebra, Geometry, and Topology 

      [OWR-2016-10] (2016) - (14 Feb - 20 Feb 2016)
      In 1945 Gerhard Hochschild published "On the cohomology groups of an associative algebra" in the Annals of Mathematics and thereby created what is now called Hochschild theory. In 1963, Murray Gerstenhaber proved that the ...
    • Infeasibility certificates for linear matrix inequalities 

      [OWP-2011-28] Klep, Igor; Schweighofer, Markus (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-25)
      Farkas' lemma is a fundamental result from linear programming providing linear certi cates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly ...
    • 2207a - Interpolation, Approximation, and Algebra 

      [OWR-2022-7] (2022) - (13 Feb - 19 Feb 2022)
      This report involves two concepts of geometric modeling: multi-variate data interpolation by polynomials, and the study of generalized bary\-centric coordinates. These topics are connected to a wide range of of applications, ...
    • 0917 - Kommutative Algebra 

      [OWR-2009-22] (2009) - (19 Apr - 25 Apr 2009)
      The workshop brought together researchers on various areas of Commutative Algebra. New results in combinatorial commutative algebra, homological methods and invariants, characteristic p-methods, and in general commutative ...
    • 0517 - Kommutative Algebra 

      [OWR-2005-19] (2005) - (24 Apr - 30 Apr 2005)
      The lectures of the conference whose participants included a significant group of researchers from affine geometry were devoted to the following areas: characteristic p-methods, combinatorial commutative algebra and effective ...
    • 2040a - Lefschetz Properties in Algebra, Geometry and Combinatorics (hybrid meeting) 

      [OWR-2020-31] (2020) - (27 Sep - 03 Oct 2020)
      The themes of the workshop are the Weak Lefschetz Property - WLP - and the Strong Lefschetz Property - SLP. The name of these properties, referring to Artinian algebras, is motivated by the Lefschetz theory for projective ...
    • Linear Syzygies, Hyperbolic Coxeter Groups and Regularity 

      [OWP-2017-15] Constantinescu, Alexandru; Kahle, Thomas; Varbaro, Matteo (Mathematisches Forschungsinstitut Oberwolfach, 2017-05-24)
      We build a new bridge between geometric group theory and commutative algebra by showing that the virtual cohomological dimension of a Coxeter group is essentially the regularity of the Stanley–Reisner ring of its nerve. ...
    • 2104 - Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (online meeting) 

      [OWR-2021-5] (2021) - (24 Jan - 30 Jan 2021)
      The central topic of the workshop was the notion of logarithmic vector fields along a divisor in a smooth complex analytic or algebraic variety, i.e., the vector fields on the ambient variety tangent to the divisor. ...
    • Matchings and Squarefree Powers of Edge Ideals 

      [OWP-2019-25] Erey, Nursel; Herzog, Jürgen; Hibi, Takayuki; Saeedi Madani, Sara (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-11)
      Squarefree powers of edge ideals are intimately related to matchings of the underlying graph. In this paper we give bounds for the regularity of squarefree powers of edge ideals, and we consider the question of when such ...
    • 1336 - Matrix Factorizations in Algebra, Geometry, and Physics 

      [OWR-2013-44] (2013) - (01 Sep - 07 Sep 2013)
      Let $W$ be a polynomial or power series in several variables, or, more generally, a nonzero element in some regular commutative ring. A matrix factorization of $W$ consists of a pair of square matrices $X$ and $Y$ of the ...
    • A McKay Correspondence for Reflection Groups 

      [OWP-2018-14] Buchweitz, Ragnar-Olaf; Faber, Eleonore; Ingalls, Colin (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-02)
      We construct a noncommutative desingularization of the discriminant of a finite reflection group $G$ as a quotient of the skew group ring $A=S*G$. If $G$ is generated by order two reflections, then this quotient identifies ...
    • 2136b - MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties (hybrid meeting) 

      [OWR-2021-43] (2021) - (05 Sep - 11 Sep 2021)
      The study of symmetry as a structural property of algebraic objects is one of the fundamental pillows of the developments of modern mathematics, most prominently beginning with the work of Abel and Galois. The focus of ...
    • 1050c - Mini-Workshop: Algebraic and Analytic Techniques for Polynomial Vector Fields 

      [OWR-2010-57] (2010) - (12 Dec - 18 Dec 2010)
      Polynomial vector fields are in the focus of research in various areas of mathematics and its applications. As a consequence, researchers from rather different disciplines work with polynomial vector fields. The main goal ...
    • 1609b - Mini-Workshop: Arrangements of Subvarieties, and their Applications in Algebraic Geometry 

      [OWR-2016-14] (2016) - (28 Feb - 05 Mar 2016)
      While arrangements of hyperplanes have been studied in algebra, combinatorics and geometry for a long time, recent discoveries suggest that they (and more generally arrangements of nonlinear subvarieties) play an even more ...
    • 1840b - Mini-Workshop: Asymptotic Invariants of Homogeneous Ideals 

      [OWR-2018-45] (2018) - (30 Sep - 06 Oct 2018)
      Recent decades have witnessed a shift in interest from isolated objects to families of objects and their limit behavior, both in algebraic geometry and in commutative algebra. A series of various invariants have been ...
    • 1810a - Mini-Workshop: Chromatic Phenomena and Duality in Homotopy Theory and Representation Theory 

      [OWR-2018-9] (2018) - (04 Mar - 10 Mar 2018)
      This mini-workshop focused on chromatic phenomena and duality as unifying themes in algebra, geometry, and topology. The overarching goal was to establish a fruitful exchange of ideas between experts from various areas, ...