Cohen Macaulay simplicial complexes in graph theory (2023)

Convener(s)


Name:	Priyavrat Deshpande	Anurag Singh
Mailing Address:	Assistant Professor, Chennai Mathematical Institute	Assistant Professor, Indian Institute of Technology Bhilai
Email:	pdeshpande at cmi.ac.in	anurags at iitbhilai.ac.in

The main aim of this workshop is to introduce participants with various methods and tools that are used to solve problems at the intersection of topological combinatorics and combinatorial commutative algebra. The
topics that we plan to explore are: Stanley-Reisner ring of a simplicial complex, Cohen-Macaulay conditions, edge and cover ideals of graphs, splitting monomial ideals and Fröberg’s theorem, component-wise linearity, simplicial complexes associated with graphs; like neighborhood complexes, independence complexes, matching complexes and their generalizations etc, discrete Morse theory and its applications. We also plan to discuss topological invariants of above men-tioned graph complexes and their connections to graph theory.

Pre-requisites: First course in commutative algebra and algebraic topology with the understanding of homology and cohomology calculations.

Dates:

Monday, July 10, 2023 - 19:00 to Saturday, July 15, 2023 - 19:00

Venue:

Venue Address:

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

Venue State:

Tamil Nadu

Venue City:

Kelambakkam

PIN:

603103

Syllabus:

Syllabus:

Speaker and affiliation	Number of Lectures	Detailed Syllabus
Manoj Kummini CMI	4	Stanley-Reisner ring of a simplicial complex, Cohen-Macaulay condition, edge and cover ideals of graphs, splitting monomial ideals and Fröberg’s theorem, component-wise linearity.
Priyavrat Deshpande CMI	4	Discrete Morse theory. Cohen-Macaulay, shellable and vertex decomposable complexes from a topological perspective.
Anurag Singh IIT Bhilai	4	Simplicial complexes associated with graphs; neighborhood complexes, independence com- plexes, matching complexes and their generaliza- tions. Topological invariants of these complexes and their connections to graph theory.

Time Table:

Time-table(with names of speakers and tutors):

Day	Date	Lecture 19.30–11.00	Tea	Lecture 2 11.30–1.00	Lunch	Tutorial 2.30–3.30	Tea	Tutorial 4.00-5.00	Snacks
Mon	10/7/2023	AS		PD		AS+1		PD+1
Tue	11/7/2023	AS		PD		AS+1		PD+1
Wed	12/7/2023	MK		AS		AS+1		MK+1
Thu	13/7/2023	MK		PD		PD+1		MK+1
Fri	14/7/2023	MK		AS		PD+1		AS+1
Sat	15/7/2023	MK		PD		AS+1		PD+1

AS: Anurag Singh; MK: Manoj Kummini; PD: Priyavrat Deshpande.

Selected Applicants:

Serial	SID	Full Name	Gender	Affiliation	University/ Institute M.Sc./ M.A.	Year of Passing M.Sc./ M.A	Ph.D. Degree Date
1	45837	Mr. Manohar Kumar	Male	Indian Institute of Technology Kharagpur	Indian Institute of Technology, Kharagpur	2020
2	45349	Dr. Shuchita Goyal	Female	IIT Kanpur	IIT Guwahati	2011	02/23/2019
3	46188	Ms. Siddhi Balu Ambhore	Female	Indian Institute of Technology Gandhinagar	Indian Institute of Technology Gandhinagar	2020
4	46354	Ms Shruti Priya	Female	IIT Kharagpur	NIT Rourkela	2020
5	46882	Ms Paromita Bordoloi	Female	Indian Institute of Technology Jammu	IIT GUWAHATI	2021
6	46931	Ms. Prativa Biswas	Female	Indian Institute of Technology Kharagpur	INDIAN INSTITUTE OF TECHNOLOGY KHARAGPUR	2021
7	47494	Ms. Pratiksha Chauhan	Female	Indian Institute of Technology- Mandi	Central University of Haryana	2020
8	47692	Mrs Priyanka Magar-Sawant	Female	IIT Bombay	Savitribai Phule Pune University	2017
9	48647	Ms. Mansi Mittal	Female	IIT PATNA	Banaras Hindu University	2019
10	49073	Ms. Deblina Dey	Female	IIT Madras	Ramakrishna Mission and Vivekananda Educational and Research Institute	2020
11	48226	Ms Chitra Venugopal	Female	Indian Institute of Technology Hyderabad	Cochin University of Science and Technology	2018
12	48007	Ms Nidhi Gupta	Female	Central University of Jammu	Central University of Jammu	2019
13	47270	Mr Raju Kumar Gupta	Male	Indian Institute of Technology Delhi	Banaras Hindu University	2019
14	45727	Mr. Om Prakash	Male	IIT Gandhinagar	Maharshi Dayanand university Rohtak	2016
15	45731	Mr. Kamalesh Saha	Male	Indian Institute of Technology Gandhinagar	Aliah University	2017	12/19/2022
16	45970	Mr. Anoot Kumar Yadav	Male	Indian Institute of Technology Patna	Ewing Christian College (University of Allahabad)	2018
17	46220	Mr. Ajay P Joseph	Male	NATIONAL INSTITUTE OF TECHNOLOGY KARNATAKA	COCHIN UNIVERSITY OF SCIENCE AND TECHNOLOGY	2021
18	46278	Mr. Vivek Bhabani Lama	Male	Indian Institute of Technology Kharagpur	St.Joseph's College (Autonomous), Bangalore City University	2021
19	46799	Mr. Sourav Sarkar	Male	Indian Institute of Technology Delhi	Indian Institute of Technology Madras	2020
20	47329	Mr Suhith K N	Male	Shiv Nadar Institution of Eminence	St Josephs College	2020
21	47694	Mr. Marie Amalore Nambi P	Male	IIT Hyderabad	Loyola College Chennai	2015
22	47772	Mr. Himanshu Chandrakar	Male	Indian Institute of Technology Bhilai	Visvesvaraya National Institute of Technology, Nagpur	2021
23	48098	Mr. Kanoy Kumar Das	Male	Ramakrishna Mission Vivekananda Educational and Research Institute	Ramakrishna Mission Vidyamandira	2018
24	48101	Mr. Bijender Dharan	Male	Indian Institute of Technology Jammu	Kurukshetra University, Kurukshetra	2015
25	48293	Mr. Pritam Roy	Male	Indian Institute of Technology Kharagpur	The university of Burdwan	2021
26	48358	Dr Samir Shukla	Male	IIT Mandi	IIT Delhi	2011
27	48670	Mr Omkar Deepak Javadekar	Male	IIT Bombay	Indian Institute of Technology, Bombay	2020
28	48678	Mr. Amit Roy	Male	National Institute of Science Education and Research Bhubaneswar	Chennai Mahematical Institute	2015	03/01/2021
29	48729	Dr. Dharm Veer	Male	IIT Ghandhinagar	Chennai Mathematical Institute	2016	04/19/2023
30	48764	Mr. Prajwal Dhondiram Udanshive	Male	University of Western Ontario	University of Western Ontario	2021
31	47470	Mr Vinay Sipani	Male	IIT Madras	IIT Madras (M.Sc.)	2019
32	48177	Mr. Sagar Sudhirkumar Sawant	Male	Indian Institute of Technology, Madras	University of Mumbai	2018
33	48451	Mr. Nirmal Kotal	Male	Chennai Mathematical Institute	IIT Kharagpur	2017
34	48517	Dr. Selvaraja S	Male	Chennai Mathematical Institute	Indian Institute of Technology Kanpur	2013	03/26/2018
35	48646	Mr. Pritam Chandra Pramanik	Male	TCG CREST	Jadavpur University	2022
Wait listed
1	45925	Mr Sirajul Haque	Male	RAMAKRISHNA MISSION VIVEKANANDA EDUCATIONAL AND RESEARCH INSTITUTE	University of Calcutta	2019
2	46121	Mr Pranjal Srivastava	Male	Indian Institute of Technology Gandhinagar	University of Allahabad	2016
3	46775	Mr. Siddhartha Pramanik	Male	IIT Kharagpur	IIT Madras	2022
4	48760	Mr. Tapas Kumar Roy	Male	Indian Institute of Technology Kharagpur (IIT KGP)	Jadavpur University, Kolkata	2019
5	48929	Mr. Praveen Mathil	Male	Birla Institute of Technology and Science Pilani	Indian Institute of Technology, Roorkee	2019
6	46260	Mr Ananthakrishnan Ravi	Male	Indian Institute of technology Delhi	Indian Institute of Technology Madras	2022
7	46016	Mr. Paramhans Kushwaha	Male	IIT JAMMU	IIT DELHI	2020
8	48716	Mr. Dhruv Bhasin	Male	Indian Institute of Science Education and Research, Pune	Indian Institute of Science Education and Research, Pune	2020

How to Reach:

TBA

School Short Name:

cmscigt

Last Date Application:

Monday, August 15, 2022

School Type:

NCMW