Representation Theory (of finite groups) (2019)

Applications received up to the initial deadline of 29^th March will be processed and a first list of selected candidates will be published around 08^th April.However interested candidates who missed the deadline may still apply. Applications will remain open until 20^th April or until capacity is reached, Whichever is earlier.

Convener(s)
Name:	K N Raghavan	Viji Thomas
Mailing Address:	IMSc, Chennai	IISER Thiruvananthapuram
Email:	knr.imsc at gmail.com	vthomas at iisertvm.ac.in

Participants have to arrange for their own travel.

Dates:

Monday, June 3, 2019 - 09:00 to Saturday, June 15, 2019 - 18:00

Venue:

IISER

Venue Address:

IISER Thiruvananthapuram

Venue State:

Kerala

Venue City:

Thiruvananthapuram

PIN:

695551

Chrono Order:

318

Syllabus:

Module A (Viji Thomas, IISER TVM) Group action on sets: Permutation representations: the notion of action of a group: permutation, linear, and other types of representations of a group; relation to the notion of symmetry; examples; induced actions (using one or more given actions to produce new actions); orbits, stabilizers, invariant subsets; transitive actions and homogeneous spaces: structure of an orbit; lots of examples of computations of orders of orbits, centralizers; counting orbits: the Cauchy-Frobenius-Burnside lemma and applications, applications to group theory: e.g., to Sylow theorems.

Module B (Sandeep Varma, TIFR Mumbai) Ordinary representation theory of finite groups via characters: basic results: Notion of a linear representation; examples. Notion of a group ring: why representations are the same as modules over the group ring; invariant subspaces and irreducible representations; Schur’s lemma (various versions); semisimplicity of ordinary representations of a finite group using the idea of averaging; notion of character; irreducible characters form an orthonormal basis for the Hilbert space of class functions; calculations using characters; computation of character tables; matrix coefficients and their orthonormality.

Module C (Geetha T, IISER TVM) Basics of the Wedderburn structure theorem for a finite dimensional semisimple algebra: application to ordinary representation theory of a finite group: Simple and semisimple modules; simple and semisimple rings; Matrix rings as examples of simple finite dimensional algebras; semisimplicity of the group ring (over a field of char. zero) of a finite group; Wedderburn structure theorem for a semisimple finite dimensional algebra over an algebraically closed field; applications to ordinary representation theory of a finite group; structure of a simple ring: Burnside’s lemma (about the map to the endomorphism ring of a simple finite dimensional module being over an algebraically closed field being onto) Module D (K N Raghavan, IMSc) Examples: especially the case of symmetric groups. Tabloid representations and their decomposition. Specht modules. Young tableaux and RSK correspondence.

Module D (K N Raghavan, IMSc) Examples: especially the case of symmetric groups. Tabloid representations and their decomposition. Specht modules. Young tableaux and RSK correspondence.

Speakers
1. K N Raghavan (KNR), IMSc
2. Geetha Thangavelu (GT), IISER TVM
3. Viji Thomas (VT), IISER TVM
4. Sandeep Varma (SV), TIFR Mumbai

Course Associates (tentative)
1. Bhimarthi Ravinder (BR), INSPIRE faculty, CMI
2. Shraddha Srivastava (SS), PDF, IMSc

Time Table:

	9.30 - 11.00 Lecture 1	11.30-1.00 Lecture 2	2.30-3.30 Tutorial 1	4.00-5.00 Tutorial 2
June 03	VT	SV	VT, BR, SS	SV, BR, SS
June 04	VT	SV	VT, BR, SS	SV, BR, SS
June 05	VT	SV	VT, BR, SS	SV, BR, SS
June 06	VT	SV	VT, BR, SS	SV, BR, SS
June 07	VT	SV	VT, BR, SS	SV, BR, SS
June 08	VT	SV	VT, BR, SS	SV, BR, SS
June 10	GT	KNR	GT, BR, SS	KNR, BR, SS
June 11	GT	KNR	GT, BR, SS	KNR, BR, SS
June 12	GT	KNR	GT, BR, SS	KNR, BR, SS
June 13	GT	KNR	GT, BR, SS	KNR, BR, SS
June 14	GT	KNR	GT, BR, SS	KNR, BR, SS
June 15	GT	KNR	GT, BR, SS	KNR, BR, SS

Tea Breaks: 11.00 - 11.30 and 3.30 - 4.00
Lunch Break: 1.00 - 2.30
Snacks: 5.00 - 5.30

Selected Applicants:

Second list is now available

Sr	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	24485	Mr. Mahesh Krishna K	Male	National Institute Of Technology Karnataka (NITK)	Research Scholar	Mangalore University	2014
2	24492	Mr Panneer Selvama	Male	bharathidasan university	guest faculty	bharathidasan university	2016
3	24566	Mr. Ajay Dabral	Male	S.G.T.B Khalsa College	Guest Lecturer	University OF Delhi	2017
4	24684	Mr. Ranadip Gangopadhyay	Male	Banaras Hindu University	PhD	Netaji Subhas Open University	2013
5	24688	Dr. Dinesh C	Male	National College (Autonomous)	Assistant Professor	Jamal Mohamed College	2010	25/10/2017
6	24703	Mr. Promod Sharma	Male	IIT(BHU), Varanasi	PHD SCHOLAR	ASSAM University Silchar	2017
7	24804	Mr. Rahul Arora	Male	Malwa College	Assistant Professor	S.C.D Goverment College	2008
8	25117	Dr. V. Ramanathan	Male	Periyar University	Postdoctoral Fellow	G. Venkataswamy Naidu College, Kovilpatti.	2010	27/10/2017
9	25617	Dr. N. Annamalai	Male	Central University of Tamil Nadu,	Assistant Professor	Bharathidasan University/ M.Sc	2011	26/02/2019
10	26025	Mr Jino Nainan	Male	St. Gregorios College	Assistant Professor	St. Gregorios College, Kottarakara(Affiliated to University of Kerala)	2003	16/11/2018
11	26111	Dr. Nitin Shridhardarkunde	Male	SRTM University, Nanded.	Assistant Professor	Department of Mathematics, Savitribai Phule Pune University, Pune.	2008	04/10/2018
12	26152	Mr. Ayush Udeep	Male	IIT Bhubaneswar	PhD	Central University of South Bihar	2016
13	26462	Ms Harshitha C	Female	Indian Institute of Science Education and Research, Tirupati	Teaching Assistant(Mathematics)	IIT Gandhinagar	2018
14	26472	Mr. Mayavel P	Male	Anna University	PhD	Bishop Heber College (Autonomous)	2013
15	26602	Mr Bindumadhaba Mohanty	Male	Bhima Bhoi Degree College	Lecturer	Sambalpur University	2014
16	26632	Mr. Jomin Kj	Male	M E S College Nedumkandam	Assistant Professor	S B College Changanassery	2017
17	26715	Mr. Sudip Pandit	Male	IIT Gandhinagar	PhD	IIT Gandhinagar	2018
18	26733	Mr Pranjal Srivastava	Male	IIT Gandhinagar	PhD	University of Allahabad
19	26735	Mr. Kamalesh Saha	Male	IIT Gandhinagar	PhD	Aliah University	2017
20	26856	Mr. Deepak Madhukarbakal	Male	JSPM Jayawantrao Sawant College of Engineering	Asst. Prof.	University of Hyderabad	2018
21	26925	Mr. Sanjay Singha	Male	Indian Institute of Information Technology Vadodara	PhD	VISVA-BHARATI	2018
22	26974	Ms. Sehra Sahu	Female	NITK Surathkal	PhD Student	Central University of Karnataka	2016
23	27013	Mr Sumukha S	Male	NITK, Surathkal	PhD Student	Mangalore University	2017
24	27025	Ms. Ranjana Mehta	Female	IIT Gandhinagar	Postdoctoral Fellow	Kumaun University	2008	14/11/2018
25	27032	Ms Chitra Venugopal	Female	Cochin University of Science and Technology	MPhil Student	Cochin University of Science and Technology	2018
26	27106	Mr. Sandeep Malik	Male	IIT DELHI	PhD	IIT DELHI	2017
27	27116	Mr. Kulbir Singh	Male	Institute of Infrastructure Technology Research and Management (IITRAM)	Research Scholar	Ch. Charan Singh University Meerut	2007
28	27170	Dr Loganathan Seenivasan	Male	Sethupathy Government Arts College	Assistant Professor	Gandhigram Rural Institute- Deemed University	2006	22/07/2016
29	27208	Mr. Om Prakash	Male	Indian Institute Of Technology, Gandhinagar	PhD	Maharshi Dayanand University, Rohtak	2016
30	27258	Mr. Manesh Jacob	Male	Mar Thoma College, Tiruvalla	Assistant Professor	Mahathma Gandhi University	2005
31	27395	Mr. Yogesh Bhagwatrokade	Male	New Arts, Commerce & Science College, Shevgaon	Assistant Professor	SPPU	2010
32	27496	Dr Rajesh Kannan M	Male	Indian Institute of Technology Kharagpur,	Assistant Professor	A J College Sivakasi	2008	30/12/2013
33	24784	Mr Anu Souriar	Male	PSG College of Arts & Science, Coimbatore.	MPhil	MG University	2016

Second List

Sr	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	27611	Dr. Sairam Kaliraj Anbareeswaran	Male	Indian Institute of Technology Ropar	Assistant Professor	ANJA College, Sivakasi	2007	18/07/2014
2	27640	Mr R. Palanivel	Male	National Institute of Technology Karnataka, Surathkal	Research Scholar	Bharathidasan University, Trichy, Tamil Nadu.	2015
3	27648	Mr. Harinarayanan G	Male	IISER	PhD Student	Cochin University Of Science And Technology	2018
4	27676	Ms. Dyuti Roy	Female	IISER TIRUPATI	Ph.D Student	VNIT Nagpur	2015
5	27688	Mr. Debasish Sadhukhan	Male	IISER Tirupati	PhD	University Of Hyderabad	2017
6	27704	Mr. Onkar Kamlakar Kale	Male	IISER Tirupati	PhD Fellow	SPPU PUNE	2016
7	27937	Mrs Niza N	Female	T K M College of Arts and Science	Assistant Professor	University of Kerala	2013
8	27973	Ms Anjali Mohanan	Female	MERCY College	Lecturer	Bharathiar University	2017
9	27977	Mr. Susobhan Mazumdar	Male	St. Joseph's College (Autonomous), Bangalore	Assistant Professor	Indian Institute of Technology, Madras/M.sc	2010
10	28106	Mr. Anubhav Tripathi	Male	SHUATS	Asst. Prof.	BHU,Varanasi	2017
11	28135	Ms Julia T Thomas	Female	Baselius College	Guest faculty	Mahatma Gandhi university	2017
12	28163	Mr. Sivashankar B	Male	Ramanujan Institute for Advanced Study in Mathematics, University of Madras	M.Phil Student	Madras Christian College (Autonomous), University of Madras	2017

How to Reach:

To get to the campus from Thampanoor Railway Station(Trivandrum Central)
The main Bus Station(Thampanoor Bus station) is opposite to this railway station. One can visit www.aanavandi.com to know the bus timings, one can also go to the enquiry counter at the bus station. Vithura Bus can be usually found at 4,5 or 6. Bus Fare might be close to INR 50 from Thampanoor Bus station to Vithura.

If you are traveling from the air port, then you can catch a taxi, which might cost approximaltely INR 1800 to reach Vithura campus. You can also catch a taxi from the airport and go to the Thampanoor Bus station, which will be much cheaper, and the cost of doing this wont be more than INR 200.