Convener(s)
| Name: | Sudarshan Gurjar | Anand Sawant |
| Mailing Address: |
Assistant Professor, |
Reader, Tata Institute of Fundamental Research, Dr. Homi Bhabha Road, Colaba, Mumbai-400005 |
| Email: | sgurjar at math.iitb.ac.in | asawant at math.tifr.res.in |
The aim of this workshop is to give a detailed account of the basics of Intersection Theory in Algebraic Geometry and discuss some applications. The first part will be devoted to basic properties of Chow groups, construction of characteristic classes, the technique of deformation to the normal cone and the intersection product. The second part will be devoted to the Grothendieck-Riemann-Roch theorem along with a few mini-courses on other advanced topics. The main reference for the workshop will be W. Fulton’s book “Intersection theory”.
The workshop is targeted at advanced graduate students and early career researchers working in related areas. Basic knowledge of algebraic geometry will be assumed.
The workshop will be conducted entirely in the offline mode. In case it is not feasible to hold the workshop in offline mode, we wish to postpone the workshop to a suitable later date.
Dates:
Venue:
Venue Address:
Department of Mathematics,
IIT Bombay
Powai, Mumbai-400076.
Venue State:
Venue City:
PIN:
Chrono Order:
Syllabus:
Speakers and Syllabus:
|
Name of the Speakers with their affiliation. |
No. of Lectures |
Detailed Syllabus |
|
Nitin Nitsure (NN) |
6 |
Basics of intersection theory (Cycles, rational equivalence, functoriality properties, relevant commutative algebra background) Main reference: Fulton, Chapter 1 |
|
Amit Hogadi (AH) |
4 |
Vector bundles and Chern classes (Divisors and line bundles, intersection with divisors, Gysin map for divisors, Segre classes, Chern classes, the projective bundle formula) Main reference: Fulton chapters 2, 3 |
|
Chetan Balwe (CB) |
4 |
Deformation to the normal cone (Segre class of a cone, Segre class of a subscheme, multiplicity along a subvariety, deformation to the normal cone) Main reference: Fulton chapters 4, 5 |
|
Anand Sawant (AS) |
4 |
The intersection product (Construction of the intersection product using reduction to the diagonal, the moving lemma and Serre’s Tor formula) Main reference: Fulton chapters 6, 11 |
|
V. Srinivas (VS) |
6 |
The Grothendieck Riemann-Roch theorem (The Chern character, Todd classes, the Grothendieck group of veector bundles, the Grothendieck Riemann-Roch theorem) |
|
Kapil Paranjape (KP) |
4 |
Overview of connections of intersection theory with Hodge theory |
Time Table:
Tentative time-table, mentioning names of the speakers and tutors with their affiliation:
|
Day |
Date |
Lecture 1 (9.30–11.00) |
Tea (11.–11.30) |
Lecture 2 (11.30–1.00) |
Lunch (1.00–2.30) |
Lecture 3 (2.30–4.00) |
Tea /Snacks (4.00-4.30) |
Lecture 4/Discussion (4.30-5.30) |
|
|
|
(Name of the speaker) |
|
(Name of the speaker) |
|
(Name of the speaker) |
|
(Name of the speaker) |
|
Mon |
02/05 |
NN 1 |
|
AH 1 |
|
NN 2 |
|
Discussion |
|
Tues |
03/05 |
NN 3 |
|
AH 2 |
|
CB 1 |
|
Discussion |
|
Wed |
04/05 |
NN 4 |
|
AH 3 |
|
Discussion |
|
--- |
|
Thu |
05/05 |
NN 5 |
|
AH 4 |
|
CB 2 |
|
Discussion |
|
Fri |
06/05 |
NN 6 |
|
CB 3 |
|
CB 4 |
|
Discussion |
|
Sat |
|
|
|
|
|
|
|
|
|
Sun |
|
|
|
|
|
|
|
|
|
Mon |
09/05 |
AS 1 |
|
AS 2 |
|
VS 1 |
|
Discussion |
|
Tues |
10/05 |
AS 3 |
|
KP 1 |
|
VS 2 |
|
Discussion |
|
Wed |
11/05 |
AS 4 |
|
KP 2 |
|
VS 3 |
|
--- |
|
Thu |
12/05 |
KP 3 |
|
VS 4 |
|
VS 5 |
|
Discussion |
|
Fri |
13/05 |
KP 4 |
|
VS 6 |
|
Discussion |
|
--- |
|
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Selected Applicants:
| Sr.n | SID | Full Name | Gender | Affiliation | Position in College /University | University/ Institute M.Sc./ M.A. | Year of Passing M.Sc. / M.A | Ph.D. Deg date |
| 1 | 37599 | Mr Soumik Ghosh | Male | TIFR, Mumbai | Student | Indian Statistical Institute, Kolkata | 2020 | |
| 2 | 37610 | Ms. Parnashree Ghosh | Female | Indian Statistical Institute, Kolkata | JRF | IIT Kharagpur | 2018 | |
| 3 | 37648 | Ms. Nidhi Gupta | Female | IISER Mohali | PhD | IISER Mohali, M.Sc | 2020 | |
| 4 | 37652 | Mr Pritthijit Biswas | Male | Chennai Mathematical Institute | PhD student | Ramakrishna Mission Vivekananda University | 2017 | |
| 5 | 37657 | Mr Ashutosh Roy Choudhury | Male | TIFR MUMBAI | MSc Student | TIFR MUMBAI | ||
| 6 | 37661 | Mr. Sandip Samanta | Male | Indian Institute of Science Education and Research Kolkata | Integrated PhD | IISER Kolkata | 2021 | |
| 7 | 37687 | Mr Jagadish Pine | Male | CMI | PHD Student SRF | Presidency University, Kolkata | 2015 | |
| 8 | 37724 | Mr. Roktim Mascharak | Male | TIFR | Integrated PhD student | TIFR | Awaiting Result | |
| 9 | 37731 | Mr. Arnab Roy | Male | TIFR | Integrated PhD student | TIFR | Awaiting Result | |
| 10 | 37733 | Ms Shruti Rastogi | Female | IISER | PhD student | IISER | 2020 | |
| 11 | 37734 | Mr. Bidhan Paul | Male | IIT MADRAS | Research Scholar | IIT MADRAS | 2019 | |
| 12 | 37748 | Ms Ananya Pal | Female | Indian Statistical Institute,Kolkata | PhD student | Calcutta University | 2018 | |
| 13 | 37781 | Mr. Arkamouli Debnath | Male | Tata Institute of Fundamental Research, Mumbai | PhD | Indian Statistical Institute Kolkata | 2020 | |
| 14 | 37789 | Mr. Sourayan Banerjee | Male | IISER Bhoplal | Integrated PhD | IISER Bhopal | 2019 | |
| 15 | 37800 | Ms. Diksha Garg | Female | IISER Bhopal | PhD | Panjab University, Chandigarh | 2018 | |
| 16 | 37818 | Mr. Sandeep S | Male | TIFR Mumbai | Ph.D | TIFR Mumbai | 2021 | |
| 17 | 37840 | Mr Jebasingh R | Male | IISER Kolkata | PhD | M.Sc. | 2019 | |
| 18 | 37844 | Mr Supravat Sarkar | Male | Tata Institute of Fundamental Research | PhD | Indian Statistical Institute, Bangalore | 2021 | |
| 19 | 37861 | Ms Meghana Bhat | Female | Indian Institute of Technology Dharwad | PhD | Pondicherry University | 2021 | |
| 20 | 38105 | Mr. Sourav Holme Choudhury | Male | Institute of Mathematical Sciences | PhD | Indian Statistical Institute Kolkata | 2018 | |
| 21 | 37791 | Mr. Sourjya Banerjee | Male | ISI Kolkata | PHD | University of Calcutta | 2016 | |
| 22 | Shivam Vats | Male | IISER Tirupati | PHD | ||||
| 23 | Ashima Bansal | Female | IISER Tirupati | PHD | ||||
| post doc | ||||||||
| 1 | 37668 | Dr. Anantadulal Paul | Male | The International Centre for Theoretical Sciences (ICTS) | Post-doc | PUNE UNIVERSITY | 2015 | 13/12/2021 |
| 2 | 37868 | Dr. Rakesh Pawar | Male | Indian Institute of Science Education and Research (IISER) Pune | Postdoctoral Fellow | Indian Institute of Technology Bombay | 2012 | 18/08/2017 |
| 3 | 37886 | Dr Arusha C | Female | TIFR Mumbai | Visiting Fellow | M.S. University of Baroda | 2015 | 31/03/2021 |
| 4 | 37897 | Dr. Anoop Singh | Male | Tata Institute of fundamental research | Visiting Fellow | University of Allahabad | 2013 | 16/03/2021 |
| 5 | 37988 | Mr. Nilkantha Das | Male | ISI Kolkata | Postdoc | IIT Bombay | 2016 | |
| 6 | 38080 | Mr. Aditya Subramaniam | Male | Tata Institute of Fundamental Research | Postdoctoral Fellow | Savitribai Phule Pune Univeristy | 2015 | 30/07/2021 |
| Faculty Members | ||||||||
| 1 | 37611 | Ms Soumi Tikader | Female | Diamond Harbour Women's University | Assistant Professor | Jadavpur University | 2013 | 30/07/2019 |
| 2 | 38086 | Dr .Vivek Sadhu | Male | IISER Bhopal | Asst. Professor | Jadavpur university | 2007 | |
| Waitlisted Applicants | ||||||||
| 1 | 37717 | Mr. Uttaran Dutta | Male | IISER Mohali | MSc Student | IISER Mohali | 2022 | |
| 2 | 37877 | Ms. Bandna Rani | Female | IISER Mohali | PhD | Punjabi University, Patiala | 2016 | |
| 3 | 37931 | Mr. Raja Kundu | Male | IIT MADRAS | PhD Student | IIT Madras | 2020 | |
| 4 | 37945 | Mr. Abhishek Koparde | Male | IISER Pune | MSc Student | IISER Pune | 2022 | |
| 5 | 37990 | Mr Arka Karmakar | Male | Chennai Mathematical Institute | BSc Student | |||