Blar i forfatter Artikler, rapporter og annet (matematikk og statistikk) "Basu, Saugata"

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    • On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms 

      Basu, Saugata; Riener, Cordian (Journal article; Tidsskriftartikkel; Peer reviewed, 2018-03-02)
      Let R be a real closed field. We prove that for any fixed <i>d</i>, the equivariant rational cohomology groups of closed symmetric semi-algebraic subsets of R<sup><i>k</i></sup> defined by polynomials of degrees bounded by <i>d</i> vanishes in dimensions <i>d</i> and larger. This vanishing result is tight. Using a new geometric approach we also prove an upper bound of [mathematical formula] on the ...

    • On the Isotypic Decomposition of Cohomology Modules of Symmetric Semi-algebraic Sets: Polynomial Bounds on Multiplicities 

      Basu, Saugata; Riener, Cordian (Journal article; Tidsskriftartikkel; Peer reviewed, 2018-04-30)
      We consider symmetric (under the action of products of finite symmetric groups) real algebraic varieties and semi-algebraic sets, as well as symmetric complex varieties in affine and projective spaces, defined by polynomials of degrees bounded by a fixed constant <i>d</i>. We prove that if a Specht module, S<sup>λ</sup>⁠, appears with positive multiplicity in the isotypic decomposition of the ...