School and Workshop on Local Rings and Local Study of Algebraic Varieties

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Abstracts Week I Abstracts Week II Final List of Participants Lecture Notes Photos Poster group picture

School and Workshop on Local Rings and Local Study of Algebraic Varieties | (smr 2147)

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Monday, 31 May 2010

08:00 - 09:30 -- Registration --

Location: Leonardo da Vinci Building, Lobby
- 08:00 -- Registration -- 1h30'
09:30 - 10:20 Rees algebras of modules from the point of view of equisingularity theory - I
- 09:30 Rees algebras of modules from the point of view of equisingularity theory - I 50'
  
  Speaker: B. Ulrich (Purdue University, USA)
10:20 - 11:00 Coffee break
- 10:20 Coffee break 40'

11:00 - 11:50 Integral closures of ideals, rings, and modules - I

11:00 Integral closures of ideals, rings, and modules - I 50'

Speaker:	I. Swanson (Reed College,USA)
Material:	lecture notes

11:50 - 14:30 Lunch break
- 11:50 Lunch break 2h40'

14:30 - 15:20 Homological Degrees and the Hilbert Coefficients of Parameters in Local Rings - I

14:30 Homological Degrees and the Hilbert Coefficients of Parameters in Local Rings - I 50'

Speaker:	S. Goto (Meiji University, Japan)
Material:	lecture notes

15:20 - 16:00 Coffee break
- 15:20 Coffee break 40'
16:00 - 16:50 Generic initial ideals, Hilbert functions and Betti numbers - I
- 16:00 Generic initial ideals, Hilbert functions and Betti numbers - I 50'
  
  Speaker: C. Caviglia (Purdue University, USA)

Tuesday, 1 June 2010

09:30 - 10:20 Generic initial ideals, Hilbert functions and Betti numbers - II
- 09:30 Generic initial ideals, Hilbert functions and Betti numbers - II 50'
  
  Speaker: C. Caviglia (Purdue University, USA)
10:20 - 11:00 Coffee break
- 10:20 Coffee break 40'
11:00 - 11:50 Rees algebras of modules from the point of view of equisingularity theory - II
- 11:00 Rees algebras of modules from the point of view of equisingularity theory - II 50'
  
  Speaker: B. Ulrich (Purdue University, USA)
11:50 - 14:30 Lunch break
- 11:50 Lunch break 2h40'

14:30 - 15:20 Integral closures of ideals, rings, and modules - II

14:30 Integral closures of ideals, rings, and modules - II 50'

Speaker:	I. Swanson (Reed College,USA)
Material:	lecture notes

15:20 - 16:00 Coffee break
- 15:20 Coffee break 40'

16:00 - 16:50 Homological Degrees and the Hilbert Coefficients of Parameters in Local Rings - II

16:00 Homological Degrees and the Hilbert Coefficients of Parameters in Local Rings - II 50'

Speaker:	S. Goto (Meiji University, Japan)
Material:	lecture notes

Wednesday, 2 June 2010

09:30 - 10:20 Homological Degrees and the Hilbert Coefficients of Parameters in Local Rings - III

09:30 Homological Degrees and the Hilbert Coefficients of Parameters in Local Rings - III 50'

Speaker:	S. Goto (Meiji University, Japan)
Material:	lecture notes

10:20 - 11:00 Coffee break
- 10:20 Coffee break 40'
11:00 - 11:50 Generic initial ideals, Hilbert functions and Betti numbers - III
- 11:00 Generic initial ideals, Hilbert functions and Betti numbers - III 50'
  
  Speaker: C. Caviglia (Purdue University, USA)
11:50 - 14:30 Lunch break
- 11:50 Lunch break 2h40'
14:30 - 15:20 Rees algebras of modules from the point of view of equisingularity theory - III
- 14:30 Rees algebras of modules from the point of view of equisingularity theory - III 50'
  
  Speaker: B. Ulrich (Purdue University, USA)
15:20 - 16:00 Coffee break
- 15:20 Coffee break 40'

16:00 - 16:50 Integral closures of ideals, rings, and modules - III

16:00 Integral closures of ideals, rings, and modules - III 50'

Speaker:	I. Swanson (Reed College,USA)
Material:	lecture notes

Thursday, 3 June 2010

09:30 - 10:20 Integral closures of ideals, rings, and modules - IV

09:30 Integral closures of ideals, rings, and modules - IV 50'

Speaker:	I. Swanson (Reed College,USA)
Material:	lecture notes

10:20 - 11:00 Coffee break
- 10:20 Coffee break 40'

11:00 - 11:50 Homological Degrees and the Hilbert Coefficients of Parameters in Local Rings - IV

11:00 Homological Degrees and the Hilbert Coefficients of Parameters in Local Rings - IV 50'

Speaker:	S. Goto (Meiji University, Japan)
Material:	lecture notes

11:50 - 14:30 Lunch break
- 11:50 Lunch break 2h40'
14:30 - 15:20 Generic initial ideals, Hilbert functions and Betti numbers - IV
- 14:30 Generic initial ideals, Hilbert functions and Betti numbers - IV 50'
  
  Speaker: C. Caviglia (Purdue University, USA)
15:20 - 16:00 Coffee break
- 15:20 Coffee break 40'
16:00 - 16:50 Rees algebras of modules from the point of view of equisingularity theory - IV
- 16:00 Rees algebras of modules from the point of view of equisingularity theory - IV 50'
  
  Speaker: B. Ulrich (Purdue University, USA)

Friday, 4 June 2010

09:30 - 10:20 Rees algebras of modules from the point of view of equisingularity theory - V
- 09:30 Rees algebras of modules from the point of view of equisingularity theory - V 50'
  
  Speaker: B. Ulrich (Purdue University, USA)
10:20 - 11:00 Coffee break
- 10:20 Coffee break 40'

11:00 - 11:50 Integral closures of ideals, rings, and modules - V

11:00 Integral closures of ideals, rings, and modules - V 50'

Speaker:	I. Swanson (Reed College,USA)
Material:	lecture notes

11:50 - 14:30 Lunch break
- 11:50 Lunch break 2h40'

14:30 - 15:20 Homological Degrees and the Hilbert Coefficients of Parameters in Local Rings - V

14:30 Homological Degrees and the Hilbert Coefficients of Parameters in Local Rings - V 50'

Speaker:	S. Goto (Meiji University, Japan)
Material:	lecture notes

15:20 - 16:00 Coffee break
- 15:20 Coffee break 40'
16:00 - 16:50 Generic initial ideals, Hilbert functions and Betti numbers - V
- 16:00 Generic initial ideals, Hilbert functions and Betti numbers - V 50'
  
  Speaker: C. Caviglia (Purdue University, USA)

Monday, 7 June 2010
- 08:45 - 09:00 Opening
  - 08:45 Opening 15'
    
    Speaker: R. Ramakrishnan (ICTP Local Organizer - Acting Head, ICTP Mathematics Group -)
- 09:00 - 10:00 Finite free resolutions
  - 09:00 Finite free resolutions 1h0'
    
    Speaker: J. Herzog
- 10:10 - 10:50 Cohomology of powers of ideals
  - 10:10 Cohomology of powers of ideals 40'
    
    Speaker: M. Chardin
- 11:00 - 11:30 Coffee break
  - 11:00 Coffee break 30'
- 11:30 - 12:10 Sharp upper bounds of total betti numbers for given Hilbert polynomials
  - 11:30 Sharp upper bounds of total betti numbers for given Hilbert polynomials 40'
    
    Speaker: C. Caviglia (Purdue University, USA)
- 12:10 - 14:30 Lunch break
  - 12:10 Lunch break 2h20'
- 14:30 - 15:10 Maps on local cohomology induced by Galois extensions of prime characteristic
  - 14:30 Maps on local cohomology induced by Galois extensions of prime characteristic 40'
    
    Speaker: A. Singh (University of Utah, USA)
- 15:20 - 16:00 Some topics on F-thresholds
  - 15:20 Some topics on F-thresholds 40'
    
    Speaker: K. Watanabe (Nihon University, Japan)
- 16:00 - 16:45 Coffee break
  - 16:00 Coffee break 45'
- 16:45 - 17:25 Castelnuovo-Mumford regularity of Ext modules and homological degree
  - 16:45 Castelnuovo-Mumford regularity of Ext modules and homological degree 40'
    
    Speaker: L.T. Hoa (Vietnam Academy of Science and Technology, Vietnam)
Tuesday, 8 June 2010
- 09:00 - 10:00 Hilbert functions of local rings and the classifiation of local Artin Gorenstein algebras
  - 09:00 Hilbert functions of local rings and the classifiation of local Artin Gorenstein algebras 1h0'
    
    Speaker: J. Elias (Univerity of Barcelona, Spain)
- 10:10 - 10:50 Smoothability of Artinian Rings
  - 10:10 Smoothability of Artinian Rings 40'
    
    Speaker: D. Ermann (University of California, USA)
- 11:00 - 11:30 Coffee break
  - 11:00 Coffee break 30'
- 11:30 - 12:10 Invariants and Normal Forms of Singularities in Positive Characteristic
  - 11:30 Invariants and Normal Forms of Singularities in Positive Characteristic 40'
    
    Speaker: G.M. Greuel (Universitaet Kaiserslautern, Germany)
- 12:10 - 14:30 Lunch break
  - 12:10 Lunch break 2h20'
- 14:30 - 15:10 On positivity and vanishing of the coefficients of normal Hilbert polynomial
  - 14:30 On positivity and vanishing of the coefficients of normal Hilbert polynomial 40'
    
    Speaker: J. Verma (Indian Institute of Technology Bombay, India)
- 15:20 - 16:00 Asymptotic behaviour of Castelnuovo-Mumford regularity, Artin-Rees numbers and Hilbert coefficients
  - 15:20 Asymptotic behaviour of Castelnuovo-Mumford regularity, Artin-Rees numbers and Hilbert coefficients 40'
    
    Speaker: N.T. Cuong (Academy of Science and Technology of Vietnam, Vietnam)
- 16:00 - 16:30 Coffee break
  - 16:00 Coffee break 30'
- 16:30 - 17:10 The first Hilbert coefficient of parameter ideals
  - 16:30 The first Hilbert coefficient of parameter ideals 40'
    
    Speaker: L. Ghezzi (The City University of New York, USA)
Wednesday, 9 June 2010
- 09:00 - 10:00 Hilbert functions
  - 09:00 Hilbert functions 1h0'
    
    Speaker: I. Peeva (Cornell University, USA)
- 10:10 - 10:50 Groebner bases of linked ideals
  - 10:10 Groebner bases of linked ideals 40'
    
    Speaker: E. Gorla (Universitat Basel, Switzerland)
- 11:00 - 11:30 Coffee break
  - 11:00 Coffee break 30'
- 11:30 - 12:10 About Almost Complete Intersections
  - 11:30 About Almost Complete Intersections 40'
    
    Speaker: A. Ragusa (University of Catania, Italy)
Thursday, 10 June 2010
- 09:00 - 10:00 The number of defining equations of an algebraic set: a survey
  - 09:00 The number of defining equations of an algebraic set: a survey 1h0'
    
    Speaker: G. Lyubeznik (University of Minnesota, USA)
- 10:10 - 10:50 Complete Intersections and Rational Normal Scrolls
  - 10:10 Complete Intersections and Rational Normal Scrolls 40'
    
    Speaker: L. Badescu (University of Genova, Italy)
- 11:00 - 11:30 Coffee break
  - 11:00 Coffee break 30'
- 11:30 - 12:10 The singularities of a rational plane curve of even degree
  - 11:30 The singularities of a rational plane curve of even degree 40'
    
    Speaker: C. Polini (University of Notre Dame, USA)
- 12:10 - 15:00 Lunch break
  - 12:10 Lunch break 2h50'
- 15:00 - 15:40 Finite dimensionality in the categories of motives
  - 15:00 Finite dimensionality in the categories of motives 40'
    
    Speaker: C. Pedrini (University of Genova, Italy)
- 15:50 - 16:30 The canonical module of a Cox ring
  - 15:50 The canonical module of a Cox ring 40'
    
    Speaker: K. Kurano (Meiji University, Japan)
- 20:00 - 23:00 Social dinner at the Hotel Restaurant Greif
  - 20:00 Social dinner at the Hotel Restaurant Greif 3h0'
Friday, 11 June 2010
- 09:00 - 10:00 A Life-long Stream of Polynomial Equations
  - 09:00 A Life-long Stream of Polynomial Equations 1h0'
    
    Speaker: L. Robbiano (University of Genova, Italy)
- 10:10 - 10:50 Stanley decompositions and Hilbert depth in the Koszul complex
  - 10:10 Stanley decompositions and Hilbert depth in the Koszul complex 40'
    
    Speaker: W. Bruns (Universität Osnabrueck, Germany)
- 11:00 - 11:30 Coffee break
  - 11:00 Coffee break 30'
- 11:30 - 12:10 Groebner bases of cogenerated Pfaffian ideals
  - 11:30 Groebner bases of cogenerated Pfaffian ideals 40'
    
    Speaker: E. De Negri (University of Genova, Italy)
- 12:10 - 14:30 Lunch break
  - 12:10 Lunch break 2h20'
- 14:30 - 15:10 Computing the depth of the Rees algebra of a module
  - 14:30 Computing the depth of the Rees algebra of a module 40'
    
    Speaker: S. Zarzuela (Univerity of Barcelona, Spain)
- 15:20 - 16:00 On implicitization and equations in low dimension
  - 15:20 On implicitization and equations in low dimension 40'
    
    Speaker: A. Simis (Universidade Federal de Pernambuco, Brazil)
- 16:10 - 16:20 Conclusions
  - 16:10 Conclusions 10'