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Category: List of Bases 2010 2010 ICTP activities in Trieste ICTP activities in Trieste
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lecture

Start Time:

31 May 2010 at 08:00

Ends On:

11 June 2010

Location:

Trieste - Italy

Venue:

LB (Main Lecture Hall)

Organizer(s):

Directors: C. Huneke, M.-E. Rossi, Le D.T., Ngo Viet Trung. Local Organizer: R. Ramakrishnan

Description:



FIRST WEEK (31 May - 4 June)
--------------------------------------------
An Advanced School with four instructional courses on fundamental techniques in Commutative Algebra and related fields:
1. A. Conca (University of Genova, Italy): Hilbert function and multiplicity
2. S. Goto (Meiji University, Japan): Numerical invariants of local rings
3. I. Swanson (Reed College, USA): Integral closures of ideals, rings and modules
4. B. Ulrich (Purdue University, USA): Blow-up algebras

SECOND WEEK (7 - 11 June)
------------------------------------------
An International Workshop on Commutative algebra. The aim of the workshop is to summarize recent developments of the theory of local rings and related fields and to set up new directions for future investigations. Young Mathematicians are encouraged to participate.

DEADLINE for APPLICATIONS EXPIRED (on 5 February)

Material:

Advanced School - day 1

Room: Leonardo da Vinci Building Main Lecture Hall

31 May 2010
08:00
09:30
-- Registration --
01h30'
Room: Leonardo da Vinci Building, Lobby
09:30
10:20
Rees algebras of modules from the point of view of equisingularity theory - I
50'
B. Ulrich
Purdue University, USA
10:20
11:00
Coffee break
40'
11:00
11:50
Integral closures of ideals, rings, and modules - I
50'
I. Swanson
Reed College,USA
11:50
14:30
Lunch break
02h40'
14:30
15:20
Homological Degrees and the Hilbert Coefficients of Parameters in Local Rings - I
50'
S. Goto
Meiji University, Japan
15:20
16:00
Coffee break
40'
16:00
16:50
Generic initial ideals, Hilbert functions and Betti numbers - I
50'
C. Caviglia
Purdue University, USA
Advanced School - day 2

Room: Leonardo da Vinci Building Main Lecture Hall

1 June 2010
09:30
10:20
Generic initial ideals, Hilbert functions and Betti numbers - II
50'
C. Caviglia
Purdue University, USA
10:20
11:00
Coffee break
40'
11:00
11:50
Rees algebras of modules from the point of view of equisingularity theory - II
50'
B. Ulrich
Purdue University, USA
11:50
14:30
Lunch break
02h40'
14:30
15:20
Integral closures of ideals, rings, and modules - II
50'
I. Swanson
Reed College,USA
15:20
16:00
Coffee break
40'
16:00
16:50
Homological Degrees and the Hilbert Coefficients of Parameters in Local Rings - II
50'
S. Goto
Meiji University, Japan
Advanced School - day 3 (Republic's Day)

Room: Leonardo da Vinci Building Main Lecture Hall

2 June 2010
09:30
10:20
Homological Degrees and the Hilbert Coefficients of Parameters in Local Rings - III
50'
S. Goto
Meiji University, Japan
10:20
11:00
Coffee break
40'
11:00
11:50
Generic initial ideals, Hilbert functions and Betti numbers - III
50'
C. Caviglia
Purdue University, USA
11:50
14:30
Lunch break
02h40'
14:30
15:20
Rees algebras of modules from the point of view of equisingularity theory - III
50'
B. Ulrich
Purdue University, USA
15:20
16:00
Coffee break
40'
16:00
16:50
Integral closures of ideals, rings, and modules - III
50'
I. Swanson
Reed College,USA
Advanced School - day 4

Room: Leonardo da Vinci Building Main Lecture Hall

3 June 2010
09:30
10:20
Integral closures of ideals, rings, and modules - IV
50'
I. Swanson
Reed College,USA
10:20
11:00
Coffee break
40'
11:00
11:50
Homological Degrees and the Hilbert Coefficients of Parameters in Local Rings - IV
50'
S. Goto
Meiji University, Japan
11:50
14:30
Lunch break
02h40'
14:30
15:20
Generic initial ideals, Hilbert functions and Betti numbers - IV
50'
C. Caviglia
Purdue University, USA
15:20
16:00
Coffee break
40'
16:00
16:50
Rees algebras of modules from the point of view of equisingularity theory - IV
50'
B. Ulrich
Purdue University, USA
Advanced School - day 5

Room: Leonardo da Vinci Building Main Lecture Hall

4 June 2010
09:30
10:20
Rees algebras of modules from the point of view of equisingularity theory - V
50'
B. Ulrich
Purdue University, USA
10:20
11:00
Coffee break
40'
11:00
11:50
Integral closures of ideals, rings, and modules - V
50'
I. Swanson
Reed College,USA
11:50
14:30
Lunch break
02h40'
14:30
15:20
Homological Degrees and the Hilbert Coefficients of Parameters in Local Rings - V
50'
S. Goto
Meiji University, Japan
15:20
16:00
Coffee break
40'
16:00
16:50
Generic initial ideals, Hilbert functions and Betti numbers - V
50'
C. Caviglia
Purdue University, USA
Workshop - day 1

Room: Leonardo da Vinci Building Main Lecture Hall

7 June 2010
08:45
09:00
Opening
15'
R. Ramakrishnan
ICTP Local Organizer - Acting Head, ICTP Mathematics Group -
09:00
10:00
Finite free resolutions
01h00'
J. Herzog
10:10
10:50
Cohomology of powers of ideals
40'
M. Chardin
11:00
11:30
Coffee break
30'
11:30
12:10
Sharp upper bounds of total betti numbers for given Hilbert polynomials
40'
C. Caviglia
Purdue University, USA
12:10
14:30
Lunch break
02h20'
14:30
15:10
Maps on local cohomology induced by Galois extensions of prime characteristic
40'
A. Singh
University of Utah, USA
15:20
16:00
Some topics on F-thresholds
40'
K. Watanabe
Nihon University, Japan
16:00
16:45
Coffee break
45'
16:45
17:25
Castelnuovo-Mumford regularity of Ext modules and homological degree
40'
L.T. Hoa
Vietnam Academy of Science and Technology, Vietnam
Workshop - day 2 MORNING Leonardo da Vinci Main Lecture Hall

Room: Leonardo da Vinci Building Main Lecture Hall

8 June 2010
09:00
10:00
Hilbert functions of local rings and the classifiation of local Artin Gorenstein algebras
01h00'
J. Elias
Univerity of Barcelona, Spain
10:10
10:50
Smoothability of Artinian Rings
40'
D. Ermann
University of California, USA
11:00
11:30
Coffee break
30'
11:30
12:10
Invariants and Normal Forms of Singularities in Positive Characteristic
40'
G.M. Greuel
Universitaet Kaiserslautern, Germany
12:10
14:30
Lunch break
02h20'
Workshop - day 2 AFTERNOON SISSA Main Lecture Hall

Location: SISSA Main Lecture Hall

8 June 2010
14:30
15:10
On positivity and vanishing of the coefficients of normal Hilbert polynomial
40'
J. Verma
Indian Institute of Technology Bombay, India
15:20
16:00
Asymptotic behaviour of Castelnuovo-Mumford regularity, Artin-Rees numbers and Hilbert coefficients
40'
N.T. Cuong
Academy of Science and Technology of Vietnam, Vietnam
16:00
16:30
Coffee break
30'
16:30
17:10
The first Hilbert coefficient of parameter ideals
40'
L. Ghezzi
The City University of New York, USA
Workshop - day 3

Room: Leonardo da Vinci Building Main Lecture Hall

9 June 2010
09:00
10:00
Hilbert functions
01h00'
I. Peeva
Cornell University, USA
10:10
10:50
Groebner bases of linked ideals
40'
E. Gorla
Universitat Basel, Switzerland
11:00
11:30
Coffee break
30'
11:30
12:10
About Almost Complete Intersections
40'
A. Ragusa
University of Catania, Italy
Workshop - day 4

Room: Leonardo da Vinci Building Main Lecture Hall

10 June 2010
09:00
10:00
The number of defining equations of an algebraic set: a survey
01h00'
G. Lyubeznik
University of Minnesota, USA
10:10
10:50
Complete Intersections and Rational Normal Scrolls
40'
L. Badescu
University of Genova, Italy
11:00
11:30
Coffee break
30'
11:30
12:10
The singularities of a rational plane curve of even degree
40'
C. Polini
University of Notre Dame, USA
12:10
15:00
Lunch break
02h50'
15:00
15:40
Finite dimensionality in the categories of motives
40'
C. Pedrini
University of Genova, Italy
15:50
16:30
The canonical module of a Cox ring
40'
K. Kurano
Meiji University, Japan
20:00
23:00
Social dinner at the Hotel Restaurant Greif
03h00'
Workshop - day 5

Room: Leonardo da Vinci Building Main Lecture Hall

11 June 2010
09:00
10:00
A Life-long Stream of Polynomial Equations
01h00'
L. Robbiano
University of Genova, Italy
10:10
10:50
Stanley decompositions and Hilbert depth in the Koszul complex
40'
W. Bruns
Universität Osnabrueck, Germany
11:00
11:30
Coffee break
30'
11:30
12:10
Groebner bases of cogenerated Pfaffian ideals
40'
E. De Negri
University of Genova, Italy
12:10
14:30
Lunch break
02h20'
14:30
15:10
Computing the depth of the Rees algebra of a module
40'
S. Zarzuela
Univerity of Barcelona, Spain
15:20
16:00
On implicitization and equations in low dimension
40'
A. Simis
Universidade Federal de Pernambuco, Brazil
16:10
16:20
Conclusions
10'
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