Representation theory and syzygies (2023)

Convener(s)

 
Name: Mandira Mondal  Manoj Kummini
Mailing Address: INSPIRE Faculty Fellow, Indian Institute of Technology Jodhpur Professor, Chennai Mathematical Institute
Email: mandira at iitj.ac.in mkummini at cmi.ac.in

This workshop introduces representation-theoretic methods in the study of syzygies. One of the earliest milestones in this area is Lascoux’ description of the syzygies of the determinantal variety. This method (now of- ten called the ‘Kempf-Lascoux-Weyman technique’) was later expanded and used to provide the syzygies in many instances of geometric significance. An exposition of the technique and the pre-requisites needed from representation theory for proving Lascoux’ theorem forms the major part of this workshop.
In the mid 2000’s Boij and Soederberg proposed some conjectures on the numerical nature of free resolutions. Eisenbud-Floystad-Weyman proved one of these conjectures, by constructing free resolutions using Pieri maps between irreducible representations. A discussion of this construction forms the minor part of this workshop.

Pre-requisites: Free resolutions, Koszul complexes, depth, Auslander-Buchsbaum theorem,Hilbert syzygy theorem, divisors and line bundles, sheaf cohomology, higher direct image.

Dates: 

Monday, December 18, 2023 - 19:00 to Saturday, December 23, 2023 - 19:00

Venue: 

Venue Address: 

Chennai Mathematical Institute,
H1 SIPCOT IT Park Siruseri,
Kelambakkam Tamilnadu 603 103.

 

Venue State: 

Venue City: 

PIN: 

603103

Chrono Order: 

461

Syllabus: 

 Syllabus to be covered in terms of modules of 6 lectures each :

Speaker and affiliation Number ofLectures Detailed Syllabus
Manoj Kummini CMI 4 Pure resolutions and Boij-Soederberg conjec- tures. Lascoux resolution.
K. N. Raghavan IMSc 4 Schur functors, Cauchy formula and Pieri formula in char 0. Equivariant pure resolutions in charac- teristic 0.
K. V. Subrahmanyam CMI 4 Grassmannians and flag varieties, tautological bundles. Borel-Weyl-Bott theorem.

 

 References

  1. [EFW11]D. Eisenbud, G. Fløystad, and J. Weyman. The existence of equivariant pure free resolutions. Ann. Inst. Fourier (Grenoble), 61(3):905–926, 2011.
  2. [FH91] W. Fulton and J. Harris. Representation theory, volume 129 of Graduate Texts in Mathematics. Springer-Verlag, New York,1991. A first course, Readings in Mathematics.
  3. [Wey03] J. Weyman. Cohomology of vector bundles and syzygies, volume 149 of Cambridge Tracts in Mathematics. Cambridge Uni-versity Press, Cambridge, 2003.

Time Table: 

Day Date Lecture 1
9.30–11.00

T

E

A

 

 Lecture 2
11.30–1.00

L

U

N

C

H
 

 Tutorial
2.30–3.30

T

E

A

 Tutorial
4.00-5.00

S

N

A

C

K

S
Mon 18/12/2023 MK KNR MK, T1, T2 KNR, T1, T3
Tue 19/12/2023 KVS KNR KVS, T2, T3 KNR, T1, T2
Wed 20/12/2023 MK KVS MK, T1, T3 KVS, T2, T3
Thu 21/12/2023 MK KVS MK, T1, T2 KVS, T1, T3
Fri 22/12/2023 KVS KNR KVS, T2, T3 KNR, T1, T2
Sat 23/12/2023 MK KNR MK, T1, T3 KNR, T2, T3
Tutorial Assistants
S. No. Name Affiliation
1 Dr. Mandira Mondal IIT Jodhpur
2 TBD  
3 TBD  

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. Degree Date
1 51403 Mr. Subham De Male IIT Delhi Graduate Student IIT Delhi Appeared  
2 51680 Mr. Subham Garai Male IIT Kanpur PhD IIT Kanpur 2023  
3 52019 Mr. Paramhans Kushwaha Male IIT JAMMU PhD IIT DELHI 2020  
4 52111 Ms. Divyasree C R Female Indian Institute of Science Education and Research Pune PhD student IISER BHOPAL 2021  
5 52314 Mr. Ganapathy K Male Indian Institute of Technology Madras PhD student IIT Madras    
6 52618 Mr. Nirmal Kotal Male Chennai Mathematical Institute PhD IIT Kharagpur 2017  
7 52629 Mr. Kanoy Kumar Das Male Ramakrishna Mission Vivekananda Educational and Research Institute PhD Ramakrishna Mission Vidyamandira 2018  
8 52722 Dr. Om Prakash Male Indian Institute of Technology Bombay, Powai Institute Post Doctoral Fellow Maharshi Dayanand university Rohtak 2016 29 Jul 23
9 52736 Mr. Abhiram Subramanian Male Chennai Mathematical Institute PhD Student Chennai Mathematical Institute 2022  
10 52755 Mr. Bijender Dharan Male Indian Institute of Technology, Jammu PhD Kurukshetra University, Kurukshetra 2015  
11 53069 Mr. Srinath Guhaprasad Male Indian Institute of Technology, Palakkad PhD Indian Institute of Technology, Palakkad 2022  
12 53107 Mr. Sathish Kumar V Male The Institute of Mathematical Sciences PhD Student Ramanujan Institute for Advanced Study in Mathematics 2018  
13 53191 Mr Omkar Deepak Javadekar Male IIT Bombay MSc & PhD Dual Degree Student Indian Institute of Technology, Bombay 2020  
14 53277 Dr. Suprajo Das Male Indian Institute of Technology, Bombay Postdoctoral Fellow Chennai Mathematical Institute 2014 15 May 20
15 53279 Dr. Sudeshna Roy Female Tata Institute of Fundamental Research, Mumbai Visiting Fellow Jadavpur University 2013 4 Jun 20
16 53538 Mr Aditya Das Male IIT Palakkad PhD University of Delhi 2020  
17 53542 Ms. Saipriya Dubey Female IIT Dharwad Research Associate The Maharaja Sayajirao University of Baroda 2016 25 Feb 23
18 53670 Mr. Kamalesh Saha Male Chennai Mathematical Institute Postdoctoral fellow Aliah University 2017 29 Jul 23
19 53700 Mr. Manohar Kumar Male Indian Institute of Technology Kharagpur PhD Indian Institute of Technology, Kharagpur 2020  
20 53738 Mr. Suraj Rajendra Kulkarni Male The Institute of Mathematical Sciences. Integrated PhD Student IMSc, Chennai Appeared  
21 53800 Mr Rahul Singh Karki Male IIT BOMBAY PhD IIT KHARAGPUR 2018  

 

 

How to Reach: 

TBA

School Short Name: 

rts

Last Date Application: 

Saturday, November 18, 2023

School Type: 

NCMW

Separate faculty form: 

0