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School on Commutative Algebra and Interactions with Algebraic Geometry and Combinatorics | (smr 1563)
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  • Monday, 24 May 2004
    • 08:30 - 10:00 Registration
      Location: Adriatico Guest House (Lower Level 1)
      • 08:30 Registration 1h30'
    • 14:00 - 14:15 Opening
      • 14:00 Opening 15'
    • 14:15 - 15:15 Toric ring and discrete convex geometry (1)
      • 14:15 Toric ring and discrete convex geometry (1) 1h0'
        Speaker: W. Bruns (Universität Osnabrück, Germany)
        Material: lecture notes
    • 15:15 - 15:45 Break
      • 15:15 Break 30'
    • 15:45 - 16:45 Finite free resolutions of modules (1)
      • 15:45 Finite free resolutions of modules (1) 1h0'
        Speaker: J. Herzog (Universität-GHS Essen, Germany)
        Material: lecture notes
  • Tuesday, 25 May 2004
    • 09:00 - 10:00 Toric ring and discrete convex geometry (2)
      • 09:00 Toric ring and discrete convex geometry (2) 1h0'
        Speaker: W. Bruns (Universität Osnabrück, Germany)
        Material: lecture notes
    • 10:00 - 10:30 Break
      • 10:00 Break 30'
    • 10:30 - 11:30 Finite free resolutions of modules (2)
      • 10:30 Finite free resolutions of modules (2) 1h0'
        Speaker: J. Herzog (Universität-GHS Essen, Germany)
        Material: lecture notes
    • 12:00 - 14:00 Lunch Break
      • 12:00 Lunch Break 2h0'
    • 14:00 - 15:00 Singularity theory (1)
      • 14:00 Singularity theory (1) 1h0'
        Speaker: G.-M. Greuel (Universität Kaiserslautern, Germany)
        Material: lecture notes
    • 15:00 - 15:30 Break
      • 15:00 Break 30'
    • 15:30 - 16:30 Topics from Algebraic Geometry (1)
      • 15:30 Topics from Algebraic Geometry (1) 1h0'
        Speaker: L.S. Badescu (Università di Genova, Italy)
        Material: lecture notes
  • Wednesday, 26 May 2004
    • 09:00 - 10:00 Toric ring and discrete convex geometry (3)
      • 09:00 Toric ring and discrete convex geometry (3) 1h0'
        Speaker: W. Bruns (Universität Osnabrück, Germany)
        Material: lecture notes
    • 10:00 - 10:30 Break
      • 10:00 Break 30'
    • 10:30 - 11:30 Finite free resolutions of modules (3)
      • 10:30 Finite free resolutions of modules (3) 1h0'
        Speaker: J. Herzog (Universität-GHS Essen, Germany)
        Material: lecture notes
    • 12:00 - 14:00 Lunch Break
      • 12:00 Lunch Break 2h0'
    • 14:00 - 15:00 Singularity theory (2)
      • 14:00 Singularity theory (2) 1h0'
        Speaker: G.-M. Greuel (Universität Kaiserslautern, Germany)
        Material: lecture notes
    • 15:00 - 15:30 Break
      • 15:00 Break 30'
    • 15:30 - 16:30 Groebner basis (1)
      • 15:30 Groebner basis (1) 1h0'
        Speaker: L. Robbiano (Università di Genova, Italy)
        Material: lecture notes
  • Thursday, 27 May 2004
    • 09:00 - 10:00 Singularity theory (3)
      • 09:00 Singularity theory (3) 1h0'
        Speaker: G.-M. Greuel (Universität Kaiserslautern, Germany)
        Material: lecture notes
    • 10:00 - 10:30 Break
      • 10:00 Break 30'
    • 10:30 - 11:30 Topics from Algebraic Geometry (2)
      • 10:30 Topics from Algebraic Geometry (2) 1h0'
        Speaker: L.S. Badescu (Università di Genova, Italy)
        Material: lecture notes
    • 12:00 - 14:00 Lunch Break
      • 12:00 Lunch Break 2h0'
    • 14:00 - 15:00 Groebner basis (2)
      • 14:00 Groebner basis (2) 1h0'
        Speaker: L. Robbiano (Università di Genova, Italy)
        Material: lecture notes
    • 16:00 - 17:00 ICTP Prize Ceremony - An efficient characterization of prime numbers
      Location: Main Building Main Lecture Hall
      • 16:00 ICTP Prize Ceremony - An efficient characterization of prime numbers 1h0'
        Speaker: M. Agrawal (IIT, Kanpur, India)
  • Friday, 28 May 2004
    • 09:00 - 10:00 Toric ring and discrete convex geometry (4)
      • 09:00 Toric ring and discrete convex geometry (4) 1h0'
        Speaker: W. Bruns (Universität Osnabrück, Germany)
        Material: lecture notes
    • 10:00 - 10:30 Break
      • 10:00 Break 30'
    • 10:30 - 11:30 Finite free resolutions of modules (4)
      • 10:30 Finite free resolutions of modules (4) 1h0'
        Speaker: J. Herzog (Universität-GHS Essen, Germany)
        Material: lecture notes
    • 12:00 - 14:00 Lunch Break
      • 12:00 Lunch Break 2h0'
    • 14:00 - 15:00 Groebner basis (3)
      • 14:00 Groebner basis (3) 1h0'
        Speaker: L. Robbiano (Università di Genova, Italy)
        Material: lecture notes
    • 15:00 - 15:30 Break
      • 15:00 Break 30'
    • 15:30 - 16:30 Topics from Algebraic Geometry (3)
      • 15:30 Topics from Algebraic Geometry (3) 1h0'
        Speaker: L.S. Badescu (Università di Genova, Italy)
        Material: lecture notes
  • Monday, 31 May 2004
    • 09:00 - 10:00 Local cohomology (1)
      • 09:00 Local cohomology (1) 1h0'
        Speaker: P. Schenzel (Martin-Luther-Universität, Germany)
        Material: lecture notes
    • 10:00 - 10:30 Break
      • 10:00 Break 30'
    • 10:30 - 11:30 Characteristic p methods and tight closure (1)
      • 10:30 Characteristic p methods and tight closure (1) 1h0'
        Speaker: A.K. Singh (Georgia Institute of Technology, Atlanta, USA)
        Material: lecture notes
    • 12:00 - 14:00 Lunch Break
      • 12:00 Lunch Break 2h0'
    • 14:00 - 15:00 Combinatorial Commutative Algebra (1)
      • 14:00 Combinatorial Commutative Algebra (1) 1h0'
        Speaker: E. Miller (University of Minnesota, Minneapolis, USA)
        Material: lecture notes
    • 15:00 - 15:30 Break
      • 15:00 Break 30'
    • 15:30 - 16:30 Cohomology rings of finite groups (1)
      • 15:30 Cohomology rings of finite groups (1) 1h0'
        Speaker: D.J. Benson (University of Georgia at Athens, USA)
        Material: lecture notes
  • Tuesday, 1 June 2004
    • 09:00 - 10:00 Local cohomology (2)
      • 09:00 Local cohomology (2) 1h0'
        Speaker: P. Schenzel (Martin-Luther-Universität, Germany)
        Material: lecture notes
    • 10:00 - 10:30 Break
      • 10:00 Break 30'
    • 10:30 - 11:30 Characteristic p methods and tight closure (2)
      • 10:30 Characteristic p methods and tight closure (2) 1h0'
        Speaker: A.K. Singh (Georgia Institute of Technology, Atlanta, USA)
        Material: lecture notes
    • 12:00 - 14:00 Lunch Break
      • 12:00 Lunch Break 2h0'
    • 14:00 - 15:00 Blow-up rings (1)
      • 14:00 Blow-up rings (1) 1h0'
        Speaker: W. Vasconcelos (Rutgers University, Piscataway, USA)
        Material: lecture notes
    • 15:00 - 15:30 Break
      • 15:00 Break 30'
    • 15:30 - 16:30 Cohomology rings of finite groups (2)
      • 15:30 Cohomology rings of finite groups (2) 1h0'
        Speaker: D.J. Benson (University of Georgia at Athens, USA)
        Material: lecture notes
  • Wednesday, 2 June 2004
    • 09:00 - 10:00 Blow-up rings (2)
      • 09:00 Blow-up rings (2) 1h0'
        Speaker: W. Vasconcelos (Rutgers University, Piscataway, USA)
        Material: lecture notes
    • 10:00 - 10:30 Break
      • 10:00 Break 30'
    • 10:30 - 11:30 Combinatorial Commutative Algebra (2)
      • 10:30 Combinatorial Commutative Algebra (2) 1h0'
        Speaker: E. Miller (University of Minnesota, Minneapolis, USA)
        Material: lecture notes
    • 12:00 - 14:00 Lunch Break
      • 12:00 Lunch Break 2h0'
    • 14:00 - 14:00 Local cohomology (3)
      • 14:00 Local cohomology (3)
        Speaker: P. Schenzel (Martin-Luther-Universität, Germany)
        Material: lecture notes
    • 14:30 - 15:30 Characteristic p methods and tight closure (3)
      • 14:30 Characteristic p methods and tight closure (3) 1h0'
        Speaker: A.K. Singh (Georgia Institute of Technology, Atlanta, USA)
        Material: lecture notes
  • Thursday, 3 June 2004
    • 09:00 - 10:00 Blow-up rings (3)
      • 09:00 Blow-up rings (3) 1h0'
        Speaker: W. Vasconcelos (Rutgers University, Piscataway, USA)
        Material: lecture notes
    • 10:00 - 10:30 Break
      • 10:00 Break 30'
    • 10:30 - 11:30 Local cohomology (4)
      • 10:30 Local cohomology (4) 1h0'
        Speaker: P. Schenzel (Martin-Luther-Universität, Germany)
        Material: lecture notes
    • 12:00 - 14:00 Lunch Break
      • 12:00 Lunch Break 2h0'
    • 14:00 - 15:00 Cohomology rings of finite groups (3)
      • 14:00 Cohomology rings of finite groups (3) 1h0'
        Speaker: D.J. Benson (University of Georgia at Athens, USA)
        Material: lecture notes
    • 15:00 - 15:30 Break
      • 15:00 Break 30'
    • 15:30 - 16:30 Combinatorial Commutative Algebra (3)
      • 15:30 Combinatorial Commutative Algebra (3) 1h0'
        Speaker: E. Miller (University of Minnesota, Minneapolis, USA)
        Material: lecture notes
  • Friday, 4 June 2004
    • 09:00 - 10:00 Blow-up rings (4)
      • 09:00 Blow-up rings (4) 1h0'
        Speaker: W. Vasconcelos (Rutgers University, Piscataway, USA)
        Material: lecture notes
    • 10:00 - 10:30 Break
      • 10:00 Break 30'
    • 10:30 - 11:30 Cohomology rings of finite groups (4)
      • 10:30 Cohomology rings of finite groups (4) 1h0'
        Speaker: D.J. Benson (University of Georgia at Athens, USA)
        Material: lecture notes
    • 12:00 - 14:00 Lunch Break
      • 12:00 Lunch Break 2h0'
    • 14:00 - 15:00 Characteristic p methods and tight closure (4)
      • 14:00 Characteristic p methods and tight closure (4) 1h0'
        Speaker: A.K. Singh (Georgia Institute of Technology, Atlanta, USA)
        Material: lecture notes
    • 15:00 - 15:30 Break
      • 15:00 Break 30'
    • 15:30 - 16:30 Combinatorial Commutative Algebra (4)
      • 15:30 Combinatorial Commutative Algebra (4) 1h0'
        Speaker: E. Miller (University of Minnesota, Minneapolis, USA)
        Material: lecture notes
  • Monday, 7 June 2004
    • 09:00 - 09:05 Opening
      • 09:00 Opening 5'
    • 09:05 - 09:50 Nested sets and homology of hyperplane arrangements
      • 09:05 Nested sets and homology of hyperplane arrangements 45'
        Speaker: C. Procesi (Università di Roma "La Sapienza", Italy)
    • 09:50 - 10:05 Break
      • 09:50 Break 15'
    • 10:05 - 10:50 Associated primes of local cohomology modules and of Frobenius powers
      • 10:05 Associated primes of local cohomology modules and of Frobenius powers 45'
        Speaker: I. Swanson (New Mexico State University, USA)
    • 10:50 - 11:05 The Suslin matrices
      • 10:50 The Suslin matrices 15'
        Speaker: R.A. Rao (T.I.F.R., Mumbai, India)
    • 11:05 - 11:20 Break
      • 11:05 Break 15'
    • 11:20 - 12:05 Regularity of ideal and their powers
      • 11:20 Regularity of ideal and their powers 45'
        Speaker: M. Chardin (Université Paris 6, France)
    • 12:05 - 14:00 Lunch Break
      • 12:05 Lunch Break 1h55'
    • 14:00 - 14:45 Generic initial ideals and distractions
      • 14:00 Generic initial ideals and distractions 45'
        Speaker: A. Conca (Università di Genova, Italy)
    • 14:45 - 15:00 On the Betti numbers of shifted complexes of stable simplicial complexes
      • 14:45 On the Betti numbers of shifted complexes of stable simplicial complexes 15'
        Speaker: Z. Tang (Suzhou University, P.R. China)
    • 15:00 - 15:15 Break
      • 15:00 Break 15'
    • 15:15 - 16:00 Finiteness of Hilbert functions and bounds for the Castelnuovo-Mumford regularity of initial ideals
      • 15:15 Finiteness of Hilbert functions and bounds for the Castelnuovo-Mumford regularity of initial ideals 45'
        Speaker: Le Tuan Hoa (Institute of Mathematics, Hanoi, Vietnam)
    • 16:00 - 16:15 Weakly stable ideals and bounds for the Castelnuovo Mumford regularity
      • 16:00 Weakly stable ideals and bounds for the Castelnuovo Mumford regularity 15'
        Speaker: G. Caviglia (University of Kansas, Lawrence, USA)
    • 16:15 - 16:30 Break
      • 16:15 Break 15'
    • 16:30 - 17:15 Endomorphism rings of finite global dimension
      • 16:30 Endomorphism rings of finite global dimension 45'
        Speaker: G. Leuschke (University of Toronto, Canada)
  • Tuesday, 8 June 2004
    • 08:45 - 09:30 A surprising fact about D-modules in characteristics p>0
      • 08:45 A surprising fact about D-modules in characteristics p>0 45'
        Speaker: G. Lyubeznik (University of Minnesota, Minneapolis, USA)
    • 09:30 - 09:45 Hilbert coefficients of the canonical module
      • 09:30 Hilbert coefficients of the canonical module 15'
        Speaker: T. Puthenpurakal (Indian Institute of Technology, Mumbai, India)
    • 09:45 - 10:00 Break
      • 09:45 Break 15'
    • 10:00 - 10:45 Relatively compressed algebras
      • 10:00 Relatively compressed algebras 45'
        Speaker: J. Migliore (University of Notre Dame, USA)
    • 10:45 - 11:00 Graded rings associated with contracted ideals
      • 10:45 Graded rings associated with contracted ideals 15'
        Speaker: J.V. Aryampillimana (T.I.F.R., Mumbai, India)
    • 11:00 - 11:15 Break
      • 11:00 Break 15'
    • 11:15 - 12:00 Blow up algebras and filtrations
      • 11:15 Blow up algebras and filtrations 45'
        Speaker: M. Rossi (Università di Genova, Italy)
    • 12:00 - 14:00 Lunch Break
      • 12:00 Lunch Break 2h0'
    • 14:00 - 14:45 Arithmetic properties of the Rees algebra of a module
      • 14:00 Arithmetic properties of the Rees algebra of a module 45'
        Speaker: S. Zarzuela (Universitat de Barcelona, Spain)
    • 14:45 - 15:00 Integral closedness for mI finitely supported complete ideals
      • 14:45 Integral closedness for mI finitely supported complete ideals 15'
        Speaker: C. D'Cruz (Chennai Mathematical Institute, India)
    • 15:00 - 15:15 Break
      • 15:00 Break 15'
    • 15:15 - 16:00 Normalization of ideals
      • 15:15 Normalization of ideals 45'
        Speaker: C. Polini (University of Notre Dame, USA)
    • 16:00 - 16:15 Normalization of modules
      • 16:00 Normalization of modules 15'
        Speaker: J. Hong (Purdue University, West Lafayette, USA)
    • 16:15 - 16:30 Break
      • 16:15 Break 15'
    • 16:30 - 17:15 Differential simplicity in polynomial rings and algebraic independence of power series
      • 16:30 Differential simplicity in polynomial rings and algebraic independence of power series 45'
        Speaker: Y. Lequain (IMPA, Rio de Janeiro, Brazil)
  • Wednesday, 9 June 2004
    • 08:45 - 09:30 Minimality of Hilbert-Kunz multiplicity
      • 08:45 Minimality of Hilbert-Kunz multiplicity 45'
        Speaker: K. Watanabe (Nihon University, Japan)
    • 09:30 - 09:45 Bounds for multiplicity
      • 09:30 Bounds for multiplicity 15'
        Speaker: T. Roemer (Universität Osnabrück, Germany)
    • 09:45 - 10:00 Break
      • 09:45 Break 15'
    • 10:00 - 10:45 Singularities of moduli spaces of vector bundles in characteristic 0 and p
      • 10:00 Singularities of moduli spaces of vector bundles in characteristic 0 and p 45'
        Speaker: V. Mehta (T.I.F.R., Mumbai, India)
    • 10:45 - 11:00 Sharp upper bound for the regularity index of zero-schemes
      • 10:45 Sharp upper bound for the regularity index of zero-schemes 15'
        Speaker: Phan Van Thien (Hue University, Vietnam)
    • 11:00 - 11:15 Break
      • 11:00 Break 15'
    • 11:15 - 12:00 The Hilbert-Kunz function in graded dimension two
      • 11:15 The Hilbert-Kunz function in graded dimension two 45'
        Speaker: H. Brenner (Ruhr-Universität Bochum, Germany)
    • 12:00 - 14:00 Lunch Break
      • 12:00 Lunch Break 2h0'
  • Thursday, 10 June 2004
    • 08:45 - 09:30 Toroidalization of morphisms of projective 3-folds
      • 08:45 Toroidalization of morphisms of projective 3-folds 45'
        Speaker: D. Cutkosky (University of Missouri, Columbia, USA)
    • 09:30 - 09:45 The geometry of the cone and the arithmetical rank of affine toric varieties
      • 09:30 The geometry of the cone and the arithmetical rank of affine toric varieties 15'
        Speaker: A. Thoma (University of Ioannina, Greece)
    • 09:45 - 10:00 Break
      • 09:45 Break 15'
    • 10:00 - 10:45 Rees rings, fiber ring of codimension two lattices ideals
      • 10:00 Rees rings, fiber ring of codimension two lattices ideals 45'
        Speaker: M. Morales (Universit‚ de Grenoble I, St. Martin d'Hères, France)
    • 10:45 - 11:00 Lexicographic generic initial ideals of of complete intersection space curves
      • 10:45 Lexicographic generic initial ideals of of complete intersection space curves 15'
        Speaker: J. Sidman (Mount Holyoke College, South Hadley, USA)
    • 11:00 - 11:15 Break
      • 11:00 Break 15'
    • 11:15 - 12:00 Toric varieties and hypergeometric functions
      • 11:15 Toric varieties and hypergeometric functions 45'
        Speaker: A. Dickenstein (Universidad de Buenos Aires, Argentina)
    • 12:00 - 14:00 Lunch Break
      • 12:00 Lunch Break 2h0'
    • 14:00 - 14:45 An Eakin-Sathaye theorem for complete and joint reductions
      • 14:00 An Eakin-Sathaye theorem for complete and joint reductions 45'
        Speaker: L. O'Carroll (University of Edinburgh, U.K.)
        Material: lecture notes
    • 14:45 - 15:00 Uniform bounds for the relation type
      • 14:45 Uniform bounds for the relation type 15'
        Speaker: F. Planas (Universitat Politecnica de Catalunya, Barcelona, Spain)
    • 15:00 - 15:15 Break
      • 15:00 Break 15'
    • 15:15 - 16:00 Finite generations of subalgebras of a finitely generated algebra
      • 15:15 Finite generations of subalgebras of a finitely generated algebra 45'
        Speaker: M. Hashimoto (Nagoya University, Japan)
    • 16:00 - 16:15 Characterization of Gorenstein rings via Gorenstein injective dimension
      • 16:00 Characterization of Gorenstein rings via Gorenstein injective dimension 15'
        Speaker: S. Yassemi (University of Tehran, Iran)
    • 16:15 - 16:30 Break
      • 16:15 Break 15'
    • 16:30 - 17:15 Separating invariants
      • 16:30 Separating invariants 45'
        Speaker: G. Kemper (Technische Universität München, Germany)
  • Friday, 11 June 2004
    • 08:45 - 09:30 Uniform behaviour of the Frobenius closures of ideals generated by regular sequences
      • 08:45 Uniform behaviour of the Frobenius closures of ideals generated by regular sequences 45'
        Speaker: R. Sharp (University of Sheffield, U.K.)
    • 09:30 - 09:45 Homology multipliers and the relation-type of parameter ideals
      • 09:30 Homology multipliers and the relation-type of parameter ideals 15'
        Speaker: L. Ghezzi (University of Missouri, Columbia, USA)
    • 09:45 - 10:00 Break
      • 09:45 Break 15'
    • 10:00 - 10:45 Lefschetz theorems for the divisor class group
      • 10:00 Lefschetz theorems for the divisor class group 45'
        Speaker: V. Srinivas (T.I.F.R., Mumbai, India)
    • 10:45 - 11:00 Modules of generalized fractions and local cohomology modules
      • 10:45 Modules of generalized fractions and local cohomology modules 15'
        Speaker: H. Zakeri (University for Teachers Education, Tehran, Iran)
    • 11:00 - 11:15 Break
      • 11:00 Break 15'
    • 11:15 - 12:00 On sequentially Cohen-Macauley modules
      • 11:15 On sequentially Cohen-Macauley modules 45'
        Speaker: Nguyen Tu Cuong (Academy of Sciences of Vietnam, Hanoi)
    • 12:00 - 14:00 Lunch Break
      • 12:00 Lunch Break 2h0'
    • 14:00 - 14:45 On the asymptotic behaviour of cohomology
      • 14:00 On the asymptotic behaviour of cohomology 45'
        Speaker: M. Brodmann (Universität Zürich, Switzerland)
    • 14:45 - 15:00 Associated primes of local cohomology modules
      • 14:45 Associated primes of local cohomology modules 15'
        Speaker: K. Divaani-Aazar (Az-Zahra University, Tehran, Iran)
    • 15:00 - 15:15 Break
      • 15:00 Break 15'
    • 15:15 - 15:30 A criterion for regular sequences
      • 15:15 A criterion for regular sequences 15'
        Speaker: D. Patil (Indian Institute of Science, Bangalore, India)
    • 15:30 - 16:15 The index of reducibility of parameter ideals in FLC rings
      • 15:30 The index of reducibility of parameter ideals in FLC rings 45'
        Speaker: S. Goto (Meiji University, Kawasaki-shi, Japan)
    • 23:55 - 23:55 photo album