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:20260404T110657Z UID:GeometryAndAlgebra/1 DESCRIPTION:Title: Homology of moduli spaces of finite rank objects\nby Joachim Jelisiejew (University of Warsaw) as part of Oberseminar "Geometr y and Algebra"\n\n\nAbstract\nAbstract: Deformations of finite rank $k$-al gebras form a very complicated scheme\, called the Hilbert scheme of point s. However the homology and even the motive of this scheme is perfectly be haved\, in fact isomorphic to those of a Grassmannian. It the talk I will explain the proof and related open questions for secant varieties and defo rmations of finite rank modules. This is a joint work with Marc Hoyois\, D enis Nardin\, Burt Totaro and Maria Yakerson.\n LOCATION:https://stable.researchseminars.org/talk/GeometryAndAlgebra/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Mateusz Skomra (LAAS\, Toulouse) DTSTART:20210212T123000Z DTEND:20210212T140000Z DTSTAMP:20260404T110657Z UID:GeometryAndAlgebra/2 DESCRIPTION:Title: Derandomization and absolute reconstruction for sums of powers of linear forms\nby Mateusz Skomra (LAAS\, Toulouse) as part of Oberseminar "Geometry and Algebra"\n\n\nAbstract\nWe study the decomposit ion of multivariate polynomials as sums of powers of linear forms. In this talk\, we focus on the following problem: given a homogeneous polynomial of degree $3$ over a field\, decide whether it can be written as a sum of cubes of linearly independent linear forms over an extension field. This t ask can be equivalently expressed as a decomposition problem for symmetric tensors of order $3$. Even if the input polynomial has rational coefficie nts\, the answer may depend on the choice of the extension field. We study the cases where the extension field is either the real or the complex num bers. Our main result is an algorithm that solves this problem in polynomi al time when implemented in the bit model of computation. Furthermore\, co ntrary to the previous algorithms for the same problem\, our algorithm is algebraic and does not make any appeal to polynomial factorization. We als o discuss how our algorithm can be extended to other tensor decomposition problems. \n\nThis talk is based on a joint work with Pascal Koiran.\n LOCATION:https://stable.researchseminars.org/talk/GeometryAndAlgebra/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Brosch (Tilburg University) DTSTART:20210122T123000Z DTEND:20210122T140000Z DTSTAMP:20260404T110657Z UID:GeometryAndAlgebra/3 DESCRIPTION:Title: More efficient and flexible Flag-Algebras coming from po lynomial optimization\nby Daniel Brosch (Tilburg University) as part o f Oberseminar "Geometry and Algebra"\n\n\nAbstract\nFlag Algebras\, i.e. g luing-algebras of limit operators describing the densities of partially la belled sub-graphs\, were first introduced by Razborov in 2007 as a powerfu l tool for problems in extremal combinatorics. Recently Raymond et al. inv estigated the connections between Flag-SOS and limits of symmetric problem s in polynomial optimization\, describing an alternative way to derive the se algebras. We take a closer look at the symmetry of this problem\, deriv ing a more efficient equivalent hierarchy. We then describe a way to deter mine alternative\, related hierarchies\, which make it possible to calcula te non-trivial bounds for problems where the usual Flag-SOS method fails. These hierarchies we then apply to the rectilinear crossing numbers of gra phs and to distance one maximizing graphs on the Euclidean plane.\n LOCATION:https://stable.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:20260404T110657Z UID:GeometryAndAlgebra/4 DESCRIPTION:Title: Introducing PDEs in the Moment Problem with the heat equ ation as an example\nby Philipp di Dio (https://www.math.tu-berlin.de/ fachgebiete_ag_diskalg/computeralgebra/v_menue/mitarbeiter/dr_philipp_j_di _dio/) as part of Oberseminar "Geometry and Algebra"\n\n\nAbstract\nPartia l differential equations (PDEs) and the theory of moments in real algebrai c geometry (RAG) are two highly developed fields in mathematics. In this t alk we want to show how to combine both fields and hopefully establishing a fruitful interaction enabling the usage of PDEs\, their methods\, and re sults in RAG and the other way around. We demonstrate this attempt with th e heat equation.\n\nZoom Meeting ID: 967 1490 6489\n LOCATION:https://stable.researchseminars.org/talk/GeometryAndAlgebra/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Harm Derksen (Northeastern University) DTSTART:20210702T113000Z DTEND:20210702T130000Z DTSTAMP:20260404T110657Z UID:GeometryAndAlgebra/5 DESCRIPTION:Title: Maximum Likelihood Estimates for Matrix and Tensor Norma l Models\nby Harm Derksen (Northeastern University) as part of Obersem inar "Geometry and Algebra"\n\n\nAbstract\nFor matrix normal models and te nsor normal models we will discuss how many samples are needed such that: (1) the likelihood function is bounded from above\, (2) maximum likelihood estimates (MLEs) exist\, and (3) MLEs exist uniquely. Our techniques are based on invariant theory\, the representation theory of quivers and the c astling transform for tensors. This is joint work with Visu Makam and Mich ael Walter.\n\nMeeting-ID: 979 5651 7630\nKenncode: 519326\n LOCATION:https://stable.researchseminars.org/talk/GeometryAndAlgebra/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Breiding (MPI Leipzig) DTSTART:20220128T123000Z DTEND:20220128T140000Z DTSTAMP:20260404T110657Z UID:GeometryAndAlgebra/6 DESCRIPTION:Title: Facet Volumes of Polytopes\nby Paul Breiding (MPI Le ipzig) as part of Oberseminar "Geometry and Algebra"\n\n\nAbstract\nWe con sider what we call facet volume vectors of polytopes. Every full-dimension al polytope in $\\mathbb R^d$ with $n$ facets defines $n$ positive real nu mbers: the $n$ $(d-1)$-dimensional volumes of its facets. For instance\, e very triangle defines three lenghts\; every tetrahedron defines four areas . We study 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 ve ctors of all $d$-polytopes in $\\mathbb R^d$ with $n$ facets is a full dim ensional cone in $\\mathbb R^n$\, and we describe this cone in terms of in equalities. For tetrahedra this is a cone over a regular octahedron. (Join t work with Pavle Blagojevic and Alexander Heaton.)\n\nMeeting ID: 973 092 6 5791\nPasscode: 593503\n LOCATION:https://stable.researchseminars.org/talk/GeometryAndAlgebra/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonio Lerario (SISSA\, Trieste) DTSTART:20220204T123000Z DTEND:20220204T133000Z DTSTAMP:20260404T110657Z UID:GeometryAndAlgebra/7 DESCRIPTION:Title: The zonoid algebra\nby Antonio Lerario (SISSA\, Trie ste) as part of Oberseminar "Geometry and Algebra"\n\n\nAbstract\nIn this seminar\, I will discuss the so called "zonoid algebra"\, a construction i ntroduced in a recent work (joint with Breiding\, Bürgisser and Mathis) w hich allows to put a ring structure on the set of zonoids (i.e. Hausdorff limits of Minkowski sums of segments). This framework gives a new perspect ive on classical objects in convex geometry\, and it allows to introduce n ew functionals on zonoids\, in particular generalizing the notion of mixed volume. Moreover this algebra plays the role of a probabilistic intersect ion ring for compact homogeneous spaces.\n\nJoint work with P. Breiding\, P. Bürgisser and L. Mathis.\n\nJoin Zoom Meeting\nhttps://zoom.us/j/97309 265791?pwd=aGNmbk1zOC81QzR3WlI3TUxmL3FaZz09\n\nMeeting ID: 973 0926 5791\n Passcode: 593503\n LOCATION:https://stable.researchseminars.org/talk/GeometryAndAlgebra/7/ END:VEVENT END:VCALENDAR