The Grothendieck Riemann Roch Theorem is widely regarded as the defining work in Grothendieck's theory of schemes. The theorem has influenced many areas of mathematics, most notably algebraic geometry and number theory. The main aim of the workshop is to study the Grothendieck Riemann Roch theorem for smooth quasi projective schemes.
In a series of lectures, comprising five modules (each module consists of five lectures with each lecture of duration 1.5 hour), we discuss the following topics in detail: The Riemann Roch theorems for curves and complex algebraic varieties, Chow groups, Intersection theory, Chern classes, and Todd Classes.
Furthermore, we have a series of survey talks on the complex analytic aspects of the Grothendieck Riemann Roch theorem, and its influences on other areas of mathematics.
The workshop is designed for graduate students working in Algebraic Geometry, and young postdoctoral fellows who work in related areas.
Syllabus to be covered in terms of modules of 6 lectures each:
|Name of the Speakers with their affiliation, who will cover each module of 6 lectures.||No. of Lectures||Detailed Syllabus|
|1 Dr. Ananyo Dan, Humboldt University||5 lectures of 1.5 hours each + 5 tutorials||Introduction to Scheme Theory - Hilbert Polynomials, Bezout's Theorem and Divisors.|
|2 Dr. Alok Maharana, IISER, Mohali||5 lectures of 1.5 hours each + 5 tutorials||Introduction to Sheaf Theory - Differentials, Line Bundles and the Riemann-Roch Theorem for Curves.|
|3 Prof. Vijayalaxmi Trivedi TIFR Mumbai||5 lectures of 1.5 hours each||Sheaf Cohomology|
|4. Prof. D. S. Nagaraj, IMSC, Chennai||5 lectures of 1.5 hours each||Chow Groups and Intersection Theory|
|5. Prof. V. Srinivas, TIFR Mumbai||5 lectures of 1.5 hours each||Chern classes, Todd classes, Gorthendieck Riemann-Roch Theorem|
|6. Prof. R. R. Simha, TIFR, Mumbai (retired)||5 lectures of 1.5 hours each||Survey Lectures on the Complex Analytic aspects of Gorthendieck Riemann-Roch theorem|
1. Algebraic geometry by R. Harthsorne,
2. Intersection Theory by W. Fulton
3. Riemann-Roch Algebra by W. Fulton, S. Lang
4. Lecture notes on Algebraic geometry by A. Gathmann
Names of the Tutors / Course associate with their affiliation:
1. Dr. Ananyo Dan and Dr. Anilatmaja Aryasomayajula (Introduction to Scheme Ttheory, and Sheaf Cohomology)
2. Dr. Alok Maharana and Dr. Tathagata sengupta (Introdcution to sheaf theory, Chow groups and Intersection Theory, and Chern classes, Todd classes, Gorthendieck Riemann-Roch theorem)
Tentative time-table mentioning the names of speakers with their affiliation:
|Day||Date||Lecture 1 (9.30–11.00)||Tea (11.05–11. 25)||Lecture 2 (11.30–1.00)||Lunch (1.00–2.00)||Lecture 3 (2.00–3.30)||Tea (3.35-3.55)||Discussion/ Tutorial (4.00-5.00)|
|(name of the speaker )||(name of the speaker )||(name of the speaker )||(Name of the tutor)|
|Mon||07.12.2015||A. Dan||A. Maharana||A. Maharana||A. Dan|
|Tues||08.12.2015||A. Dan||A. Maharana||A. Maharana||A. Dan|
|Wed||09.12.2015||A. Dan||A. Maharana||V. Trivedi||A. Dan|
|Thu||10.12.2015||A. Dan||V. Trivedi||V. Trivedi||A. Maharana|
|Fri||11.12.2015||A. Dan||V. Trivedi||V. Trivedi||A. Maharana|
|Mon||14.12.2015||D. S. Nagaraj||R. R. Simha||R. R. Simha||A. Dan|
|Tues||15.12.2015||D. S. Nagaraj||R. R. Simha||R. R. Simha||D. S. Nagraj|
|Wed||16.12.2015||D. S. Nagaraj||R. R. Simha||V. Srinivas||A. Maharana|
|Thu||17.12.2015||D. S. Nagaraj||V. Srinivas||V. Srinivas||A. Maharana|
|Fri||18.12.2015||V. Srinivas||V. Srinivas||A. Dan||A. Maharana|