BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joachim Jelisiejew (University of Warsaw) DTSTART:20201218T123000Z DTEND:20201218T140000Z DTSTAMP:20260422T225702Z UID:GeometryAndAlgebra/1 DESCRIPTION:Title: Homology of moduli spaces of finite rank objects\nby Joachi m Jelisiejew (University of Warsaw) as part of Oberseminar "Geometry and A lgebra"\n\n\nAbstract\nAbstract: Deformations of finite rank $k$-algebras form a very complicated scheme\, called the Hilbert scheme of points. Howe ver the homology and even the motive of this scheme is perfectly behaved\, in fact isomorphic to those of a Grassmannian. It the talk I will explain the proof and related open questions for secant varieties and deformation s of finite rank modules. This is a joint work with Marc Hoyois\, Denis Na rdin\, Burt Totaro and Maria Yakerson.\n LOCATION:https://researchseminars.org/talk/GeometryAndAlgebra/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Mateusz Skomra (LAAS\, Toulouse) DTSTART:20210212T123000Z DTEND:20210212T140000Z DTSTAMP:20260422T225702Z UID:GeometryAndAlgebra/2 DESCRIPTION:Title: Derandomization and absolute reconstruction for sums of powers of linear forms\nby Mateusz Skomra (LAAS\, Toulouse) as part of Oberse minar "Geometry and Algebra"\n\n\nAbstract\nWe study the decomposition of multivariate polynomials as sums of powers of linear forms. In this talk\, we focus on the following problem: given a homogeneous polynomial of degr ee $3$ over a field\, decide whether it can be written as a sum of cubes o f linearly independent linear forms over an extension field. This task can be equivalently expressed as a decomposition problem for symmetric tensor s of order $3$. Even if the input polynomial has rational coefficients\, t he answer may depend on the choice of the extension field. We study the ca ses where the extension field is either the real or the complex numbers. O ur main result is an algorithm that solves this problem in polynomial time when implemented in the bit model of computation. Furthermore\, contrary to the previous algorithms for the same problem\, our algorithm is algebra ic and does not make any appeal to polynomial factorization. We also discu ss how our algorithm can be extended to other tensor decomposition problem s. \n\nThis talk is based on a joint work with Pascal Koiran.\n LOCATION:https://researchseminars.org/talk/GeometryAndAlgebra/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Brosch (Tilburg University) DTSTART:20210122T123000Z DTEND:20210122T140000Z DTSTAMP:20260422T225702Z UID:GeometryAndAlgebra/3 DESCRIPTION:Title: More efficient and flexible Flag-Algebras coming from polynomia l optimization\nby Daniel Brosch (Tilburg University) as part of Obers eminar "Geometry and Algebra"\n\n\nAbstract\nFlag Algebras\, i.e. gluing-a lgebras of limit operators describing the densities of partially labelled sub-graphs\, were first introduced by Razborov in 2007 as a powerful tool for problems in extremal combinatorics. Recently Raymond et al. investigat ed the connections between Flag-SOS and limits of symmetric problems in po lynomial optimization\, describing an alternative way to derive these alge bras. We take a closer look at the symmetry of this problem\, deriving a m ore efficient equivalent hierarchy. We then describe a way to determine al ternative\, related hierarchies\, which make it possible to calculate non- trivial bounds for problems where the usual Flag-SOS method fails. These h ierarchies we then apply to the rectilinear crossing numbers of graphs and to distance one maximizing graphs on the Euclidean plane.\n LOCATION:https://researchseminars.org/talk/GeometryAndAlgebra/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Philipp di Dio (https://www.math.tu-berlin.de/fachgebiete_ag_diska lg/computeralgebra/v_menue/mitarbeiter/dr_philipp_j_di_dio/) DTSTART:20210416T113000Z DTEND:20210416T130000Z DTSTAMP:20260422T225702Z UID:GeometryAndAlgebra/4 DESCRIPTION:Title: Introducing PDEs in the Moment Problem with the heat equation a s an example\nby Philipp di Dio (https://www.math.tu-berlin.de/fachgeb iete_ag_diskalg/computeralgebra/v_menue/mitarbeiter/dr_philipp_j_di_dio/) as part of Oberseminar "Geometry and Algebra"\n\n\nAbstract\nPartial diffe rential equations (PDEs) and the theory of moments in real algebraic geome try (RAG) are two highly developed fields in mathematics. In this talk we want to show how to combine both fields and hopefully establishing a fruit ful interaction enabling the usage of PDEs\, their methods\, and results i n RAG and the other way around. We demonstrate this attempt with the heat equation.\n\nZoom Meeting ID: 967 1490 6489\n LOCATION:https://researchseminars.org/talk/GeometryAndAlgebra/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Harm Derksen (Northeastern University) DTSTART:20210702T113000Z DTEND:20210702T130000Z DTSTAMP:20260422T225702Z UID:GeometryAndAlgebra/5 DESCRIPTION:Title: Maximum Likelihood Estimates for Matrix and Tensor Normal Model s\nby Harm Derksen (Northeastern University) as part of Oberseminar "G eometry and Algebra"\n\n\nAbstract\nFor matrix normal models and tensor no rmal models we will discuss how many samples are needed such that: (1) the likelihood function is bounded from above\, (2) maximum likelihood estima tes (MLEs) exist\, and (3) MLEs exist uniquely. Our techniques are based o n invariant theory\, the representation theory of quivers and the castling transform for tensors. This is joint work with Visu Makam and Michael Wal ter.\n\nMeeting-ID: 979 5651 7630\nKenncode: 519326\n LOCATION:https://researchseminars.org/talk/GeometryAndAlgebra/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Breiding (MPI Leipzig) DTSTART:20220128T123000Z DTEND:20220128T140000Z DTSTAMP:20260422T225702Z UID:GeometryAndAlgebra/6 DESCRIPTION:Title: Facet Volumes of Polytopes\nby Paul Breiding (MPI Leipzig) as part of Oberseminar "Geometry and Algebra"\n\n\nAbstract\nWe consider w hat we call facet volume vectors of polytopes. Every full-dimensional poly tope in $\\mathbb R^d$ with $n$ facets defines $n$ positive real numbers: the $n$ $(d-1)$-dimensional volumes of its facets. For instance\, every tr iangle defines three lenghts\; every tetrahedron defines four areas. We st udy the space of all such vectors. We show that for fixed integers $d\\geq 2$ and $n\\geq d+1$ the configuration space of all facet volume vectors o f all $d$-polytopes in $\\mathbb R^d$ with $n$ facets is a full dimensiona l cone in $\\mathbb R^n$\, and we describe this cone in terms of inequalit ies. For tetrahedra this is a cone over a regular octahedron. (Joint work with Pavle Blagojevic and Alexander Heaton.)\n\nMeeting ID: 973 0926 5791\ nPasscode: 593503\n LOCATION:https://researchseminars.org/talk/GeometryAndAlgebra/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonio Lerario (SISSA\, Trieste) DTSTART:20220204T123000Z DTEND:20220204T133000Z DTSTAMP:20260422T225702Z UID:GeometryAndAlgebra/7 DESCRIPTION:Title: The zonoid algebra\nby Antonio Lerario (SISSA\, Trieste) as part of Oberseminar "Geometry and Algebra"\n\n\nAbstract\nIn this seminar \, I will discuss the so called "zonoid algebra"\, a construction introduc ed in a recent work (joint with Breiding\, Bürgisser and Mathis) which al lows to put a ring structure on the set of zonoids (i.e. Hausdorff limits of Minkowski sums of segments). This framework gives a new perspective on classical objects in convex geometry\, and it allows to introduce new func tionals on zonoids\, in particular generalizing the notion of mixed volume . Moreover this algebra plays the role of a probabilistic intersection rin g for compact homogeneous spaces.\n\nJoint work with P. Breiding\, P. Bür gisser and L. Mathis.\n\nJoin Zoom Meeting\nhttps://zoom.us/j/97309265791? pwd=aGNmbk1zOC81QzR3WlI3TUxmL3FaZz09\n\nMeeting ID: 973 0926 5791\nPasscod e: 593503\n LOCATION:https://researchseminars.org/talk/GeometryAndAlgebra/7/ END:VEVENT END:VCALENDAR