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| 1 | Is the Gröbner basis ideal for a sparse polynomial description where degrees of variables in monomials are either zero or one? | |
| 2 | ||
| 3 | Current Research outlined in (July 2015 Current Trends on Gröbner Bases — The 50th Anniversary of Gröbner Bases, http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/). I number the outlining below by the factors found on the websites. | |
| 4 | ||
| 5 | Outlining the 2015 Conference Contributed Talks | |
| 6 | ||
| 7 | (1) algebraic geometry community (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/01-ruriko-yoshida.pdf) | |
| 8 | ||
| 9 | (2) applied mathematicians such as factor analysis, Bayesian analysis and inverse problems (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/02-richards.pdf) | |
| 10 | ||
| 11 | (3) applied mathematicians using Monte Carlo but found it hard to use Markov basis or Gröbner basis (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/03-satoshi-aoki.pdf) | |
| 12 | ||
| 13 | (7) GreenGroebner package in Mathematica with boundary value problems for Mechanical Engineering, Kirchhoff Circular Plates problem, differential equations (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/07-Jane-Lue.pdf) | |
| 14 | ||
| 15 | (8) Hypergeometric polynomials aka Jacobi polynomials (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/08-nobuki-takayama.pdf) | |
| 16 | ||
| 17 | (9) GR cells, extensions, extension algebras, affine varities, monomial ideals -- looks algebraically demanding (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/09-alexandru-constantinescu.pdf) | |
| 18 | ||
| 19 | (11) !!!!! GR basis, polytopes, adjacency matrices and graph theory (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/11-ohsugi.pdf) | |
| 20 | ||
| 21 | (12) !!!!! GR basis, toric ideals, polytopes (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/12_akihiro_higashitani.pdf) | |
| 22 | ||
| 23 | (13) !!!!! Neural codes, toric ideals, GRs (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/13_Gross.pdf) | |
| 24 | ||
| 25 | (14) !!!!! Many Toric ideals generated by quadratic binomials posess no quadratic Grobner bases (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/14_akihiro_shikama.pdf) | |
| 26 | ||
| 27 | (16) !!!!!! Polyomino ideals, tiling problems (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/16_ayesha_qureshi.pdf) | |
| 28 | ||
| 29 | (18) !!!!!! Cover ideal of very well covered graph http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/18-kyouko-kimura.pdf | |
| 30 | ||
| 31 | (20) Ehrhart polynomials (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/20-akiyoshi-tsuchiya.pdf) | |
| 32 | ||
| 33 | (24) ??? F-thresholds and GR (hard to see to which area related, http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/contributed_talks/24-kazunori-matsuda.pdf) | |
| 34 | ||
| 35 | Outlining the 2015 Conference Invited Talks (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/) | |
| 36 | ||
| 37 | (I) !!!!!! Cocoa Software, GR, multivariate polynomials (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/bigatti.pdf) | |
| 38 | ||
| 39 | (II) !!!!! Acyclic digraph, graph theory, covariance matrix, matrix algebra, vanishing ideal, GR basis (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/drton.pdf) | |
| 40 | ||
| 41 | (III) !!!!! Tropicalisation: Pattern extraction, geometric to combinatorial, objects defined as ideals, GR basis, tropical varieties, Chan's algorithm (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/jensen.pdf) | |
| 42 | ||
| 43 | (IV) !!!!!! Detecting binomality: matrix algebra, easy to undertand <3 (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/kahle.pdf) | |
| 44 | ||
| 45 | (V) Non-commutative algebras (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/levadovskyy.pdf) | |
| 46 | ||
| 47 | (VI) Equivariant GR (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/leykin.pdf) | |
| 48 | ||
| 49 | (VII) Quadratic GR, Matroids, ... (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/michalek.pdf) | |
| 50 | ||
| 51 | (VIII) ... | |
| 52 | ||
| 53 | (IX) !!! Bouquet algebra and Toric ideals -- looks well presented with colours/annotation (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/petrovic.pdf) | |
| 54 | ||
| 55 | (X) !!!!! "The NBM [1] and LDP [2] algorithms are variants of the Buchberger-M¨oller algorithm for zero-dimensional ideals when the point coordinates are known up to a certain precision." -- Buchberger-M¨oller algorithm, vandermonde matrices, symbolic numeric approach, Newton like method to get f from NBM, Matlab code, algebraic statistics, Mahalanobis distance, -- http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/riccomagno.pdf -- applications contain robotics, image analysis. | |
| 56 | ||
| 57 | (XI) !!!! Algebraic geometry to understand supersymmeric spaces in Physics: many Lagrangians optimizatons in Grobner bases: Mike Stillman, Bjarke Roune, software Macaulay2 "The code works for ideals in polynomial rings over finite prime fields. The result is not stashed in the ideal object. groebnerBasis(I, Strategy=>"MGB") -- or groebnerBasis(I, Strategy=>"F4")" -- open questions and looks intriquing! http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/stillman.pdf | |
| 58 | ||
| 59 | (XII) Tensors: maximal minors form the GR basis (http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/sturmfels.pdf) | |
| 60 | ||
| 61 | (XIII) Algebraic and geometric perspective on exponential families: http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/uhler.pdf | |
| 62 | ||
| 63 | (XIIII) Diffferential equations, wishart distribution .... http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/vidunas.pdf | |
| 64 | ||
| 65 | (H) http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/wang.pdf | |
| 66 | ||
| 67 | (HI) !!!!! Monomial ideal method in tree percolation, reliability of system, probabilities -- applied mathematics: http://www.math.sci.osaka-u.ac.jp/~msj-si-2015/invited_talks_slides/wynn.pdf | |
| 68 | ||
| 69 | ||
| 70 | where I have bolded ideas looking relevant from Index of /~msj-si-2015/invited_talks_slides. |
