NCMW - Intersection Theory (2022)

Speakers and 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

Details available here

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)

Details available here

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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