Winter School on Arithmetic Algebraic Geometry 23 December 2002 - 1 January 2003

Time Table

Date Day 9.30  11.00  12.00  2.30  4.00  5.30

Arithmetic Geometry

23-12 Mon Ghorpade 1 Cowsik 1  Ghorpade 2 Cowsik 2  Thakur 1 Video 1
24-12 Tue Ghorpade 3 Cowsik 3  Thakur 2 Cowsik 4  Thakur 3 Video 2
25-12 Wed Cowsik 5  Ghorpade 4 Inamdar 1 Ghorpade 5 Biswas 1 Video 3
26-12 Thu Inamdar 2 Dalawat 1 Inamdar 3 Dalawat 2 Biswas 2 Video 4
27-12 Fri Biswas 3  Dalawat 3 Biswas 4  Adhikari 1 Dalawat 4 Video 5
28-12 Sat Biswas 5  Adhikari 2 Patil 1  Inamdar 4 Patil 2  Passi
30-12 Mon Adhikari 3 Patil 3  Ramana 1 Singh 1  Patil 4  Dalawat 5
31-12 Tue Singh 2  Katre 1  Ramana 2 Singh 3  Katre 2  Dalawat 6
1-1  Wed Singh 4  Katre 3  Ramana 3 Prasad 1  Prasad 2

Speaker  Affiliation  Chap. Lects. Title

Arithmetic Geometry: Reference : Bump

S. R. Ghorpade IIT Bombay  1-3,5  5  Review & Local algebra
M. Thakur  HRI, Allahabad  4  3  Dimension and products
R. C. Cowsik  Univ. of Mumbai  5  4  Local algebra
1  Riemann hypothesis for elliptic curves
S. P. Inamdar  ISI Bangalore  6  3  Properties of affine varieties
9  1  Geometry of ramification
C. S. Dalawat  HRI Allahabad  7  4  Varieties
S. D. Adhikari  HRI Allahabad  9  4  Ramification
J. Biswas  ISI Bangalore  8  2  Complete nonsingular curves
J. Biswas  ISI Bangalore  10  3  Completions
D. P. Patil  IISc Bangalore  11  4  Differentials and residues
B. Singh  IIT Bombay  12  4  Riemann-Roch Theorem
D. Surya Ramana HRI Allahabad  13  3  Elliptic curves
S. A. Katre  Univ. of Poona  14  3  Zeta function of a curve

Guest Lectures and Video Shows

R. P. Langlands IAS, Princeton  4  Videos: Practice of mathematics
C. S. Dalawat  HRI, Allahabad  2  Birch-Swinnerton Dyer Conjecture
I. B. S. Passi  HRI, Allahabad  1  Polynomial maps on groups
D. Prasad  TIFR Bombay  2  Weil Conjectures

Winter School on Computational Algebraic Geometry 2 January- 11 January 2003

Time Table

Date Day 9.30  11.00  12.00  2.30  4.00  5.30

Preparatory Lectures

2-1  Thu Mangala 1 Rao 1  Mangala 2 Rao 2  Nagaraj 1 Raghvendra
3-1  Fri Rao 3  Mangala 3 Nagraj 2 Mangala 4 Verma 1 Video 6
4-1  Sat Verma 2 Mangala 5 Rao 4  Verma 3 Nagaraj 3 Video 7
5-1  Sun Verma 4 Nagaraj 4 Decker 1 Local  sights  2.15-6.15
Speaker  Affiliation  No. Title
Wolfram Decker  Univ. of Saarland  1  Open Session
Mangala V. Manohar Mumbai University  5  Groebner Basics
D. S. Nagaraj  Mat Science, Chennai 4  Sheaf Cohomology
R. A. Rao  TIFR Bombay  5  Primary Decomposition
N. Raghvendra  TCS, Hyderabad  1  Elliptic curve cryptography
J. K. Verma  IIT Bombay  4  Invariant Theory

Jan 6-11 Workshop on Computational Algebraic Geometry by

W. Decker, University of Saarland and C. Lossen, Univ. of Kaiserlauten, Germany

Date Day Time  Title
6-1  Mon 9.30-10.45 Introduction to Singular and Macaulay 2 I
11.00-12.15 Introduction to Singular and Macaulay 2 II
2.00- open Lab session 1
7-1  Tue 9.30-10.45 Constructive module theory and homological algebra I
11.00-12.15 Constructive module theory and homological algebra II
2.00-open Lab session 2
8-1  Wed 9.30-10.45 Primary decomposition and normalization
11.00-12.15 Solving systems of polynomial equations
2.00-open Lab session 3
9-1  Thu 9.30-10.45 Algorithms in invariant theory
11.00-12.15 Computing in local rings
2.00-open Lab session 4
10-1 Fri 9.30-10.45 Sheaf cohomology and Beilinson monads
11.00-12.15 Basic Singularity Theory
2.00-open Lab session 5
11-1 Sat 9.30-10.45 Applications to algebraic geometry and singularity theory I
11.00-12.15 Applications to algebraic geometry and singularity theory II
2.00-open Lab session 6