Operator Theory (2019) | National Centre for Mathematics

Convener(s)


Name:	Prof. Satyajit Guin	Prof. Sameer Chavan
Mailing Address:	Assistant Professor Department of Mathematics and Statistics Indian Institute of Technology, Kanpur Kanpur 208016, Uttar Pradesh, India	Professor Department of Mathematics and Statistics Indian Institute of Technology, Kanpur Kanpur 208016, Uttar Pradesh, India
Email:	sguin at iitk.ac.in	chavan at iitk.ac.in

Please Note: Participants have to arrange for their own travel.

In this program, we plan to touch upon various classical as well as modern aspects of operator theory. In particular, we focus on topics from function theory, graph theory, spectral theory, representation theory and Quantum groups etc.
The topics are listed as follows:
Positive definiteness, Interpolation problem, operator-theoretic invariants associated with directed graphs, Hilbert space operators in quantum mechanics, representation theory for compact groups, Quantum groups

The treatment of these topics will be self-contained and only the basic knowledge in complex analysis and function analysis will be assumed. In the tutorial session, emphasis will be given on problem solving. The audience will be introduced to some future research directions in operator theory.

Dates:

Monday, December 16, 2019 - 17:45 to Saturday, December 28, 2019 - 17:45

Venue:

IIT Kanpur

Venue Address:

Department of Mathematics and Statistics,
Indian Institute of Technology Kanpur,
Kanpur 208016, Uttar Pradesh, India

Venue State:

Uttar Pradesh

Venue City:

Kanpur

PIN:

208016

Chrono Order:

338

Syllabus:

Name of the Speaker with affiliation	No. of Lectur es	Detailed Syllabus
K. B. Sinha (KBS) J. N. Centre for Advanced Scientific Research, Jakkur, Bangalore560064, India, and Indian Statistical Institute, India	4	Unbounded Operators in Hilbert Space and Applications in Quantum Mechanics: Basic results/examples of unbounded, closed and selfadjoint operators, Sum of two unbounded operators, some results/examples, the spectral theory of such operators, Spectral theorem of Unbounded self-adjoint operators, examples with computation of spectral measure/families, the types of Spectrum, Computation of spectra for differential operators, Dirichlet vs Neumann Operators, Sum of two unbounded self-adjoint operators (if time permits).
B. V. Rajarama Bhat (BVR) Stat-Math Unit, Indian Statistical Institute, Bangalore 560059	4	Completely positive maps and dilation theorems: Positive maps, Examples and basic properties, von Neumann inequality, Fejer-Riesz Lemma and its application to trigonometric moments, Completely Positive maps, Schur product and tensor product, Choi Theorem and its application to numerical range, Stinespring’s Dilation Theorem and its applications (if time permits).
Partha Sarathi Chakraborty (PC) Stat-Math Unit, Indian Statistical Institute, Kolkatta 700 108	4	Introduction to compact Quantum groups: Definition of compact quantum groups and its examples, the Haar state, right regular representations, irreducible unitary representations, the Hopf*- algebra of matrix elements, dual of compact quantum groups, glimpse into locally compact quantum groups.
Shibanand Biswas (SB) Indian Institute of Science Education And Research Kolkata 741 246	4	Operator theory approach to Pick Interpolation problem: Kernels and function spaces, Hardy spaces, Fatou's theorem, Examples of spaces with H-infinity as multiplier algebra, Necessity of positivity of Pick matrix, Szego kernel having Pick property and its uniqueness, realization formula and Pick problem, Characteriztion of kernels with complete pick property and examples.
Satyajit Guin (SG) Department of Mathematics and Statistics Indian Institute of Technology Kanpur Kanpur 208016 Uttar Pradesh, India	4	Representation theory for compact groups: Compact and locally compact groups, the Haar measure, Fourier transform, C-algebra, spectrum, Unitization, the Gelfand-Naimark theorem, continuous Functional Calculus, The dual group, C-algebra of an LCA group, Pontryagin duality, representations of compact groups.
Sameer Chavan (SC) Department of Mathematics and Statistics Indian Institute of Technology Kanpur Kanpur 208016 Uttar Pradesh, India	4	Introduction to graph-theoretic operator theory: Directed graphs/trees, examples and basic properties, weighted shifts on directed trees, motivation, examples and basic properties (boundedness, adjoint, circularity, kernel and cokernel), reproducing kernel Hilbert spaces of holomorphic functions associated with directed trees, bounded point evaluation, spectral theory (if time permits).

References*:

1. Barry Simon, Operator theory. A Comprehensive Course in Analysis, Part 4. American Mathematical Society, Providence, RI, 2015. xviii+749 pp.
Vern Paulsen, Completely bounded maps and operator algebras. Cambridge Studies in Advanced Mathematics, 78. Cambridge University Press, Cambridge, 2002. xii+300 pp.
Jim Agler, J. E. McCarthy, Pick interpolation and Hilbert function spaces. (English summary) Graduate Studies in Mathematics, 44. American Mathematical Society, Providence, RI, 2002. xx+308 pp.
Z. Jablonski, Il Bong Jung, Jan Stochel, Weighted shifts on directed trees. Mem. Amer. Math. Soc. 216 (2012), no. 1017, viii+106 pp.
S. L. Woronowicz, Compact quantum groups. Symétries quantiques (Les Houches, 1995), 845–884, North-Holland, Amsterdam, 1998.
Folland, Gerald B. A course in abstract harmonic analysis. Second edition. Textbooks in Mathematics. CRC Press, Boca Raton, FL, 2016. xiii+305 pp

*Lecture notes from the speakers will be distributed.

Tutorial Assistants:

Sr.n	Name	Affiliation
1	Rajeev Gupta (RG)	IIT Kanpur
2	Shailesh Trivedi (ST)	IIT Kanpur
3	Ankit Bhojak (AB)	IIT Kanpur

Time Table:

Time-Table (with names of speakers and course associates/tutors):

Day	Date	Lecture 1 (9.30–11.00)	Tea (11.05 – 11.25)	Lecture 2 (11.30–1.00)	Lunch (1.05–2.25)	Tutorial (2.30–3.30)	Tea (3.35-3.55)	Tutorial (4.00-5.00)	Snacks 5.05-5.30
		(name of the speaker )		(name of the speaker)		(name of the speaker + tutors)		(name of the speaker + tutors)
Mon	16/12/19	SB		SC		SB+RG		SC+ST
Tues	17/12/19	SB		SC		SB+RG		SC+ST
Wed	18/12/19	SB		SC		SB+RG		SC+AB
Thu	19/12/19	SB		SC		SB+RG		SC+AB
Fri	20/12/19	PC		SG		PC+ST		SG+AB
Sat	21/12/19	PC		SG		PC+ST		SG+AB
SUNDAY : OFF
Mon	23/12/19	PC		SG		PC+RG		SG+ST
Tues	24/12/19	PC		SG		PC+RG		SG+ST
Wed	25/12/19	KBS		BVR		KBS+RG		BVR+AB
Thu	26/12/19	KBS		BVR		KBS+RG		BVR+AB
Fri	27/12/19	KBS		BVR		KBS+ST		BVR+AB
Sat	28/12/19	KBS		BVR		KBS+ST		BVR+AB

Selected Applicants:

Sr.n	SID	Full Name	Gender	Affilation	Position in College/ University	University/ Institute M.Sc./ M.A.	Year of Passing M.Sc./ M.A	Ph.D. Degree Date
1	28149	Mr. Shesh Kumar Pandey	Male	University of Delhi, Delhi	PhD	University of Delhi, Delhi	2014
2	28238	Mr Sushant Pokhriyal	Male	Shiv Nadar University	PhD	University of Delhi/Ramjas College M.Sc	2014
3	28632	Mr. Vikas Laxmikant Shukla	Male	IISER Pune	Bs-Ms student	IISER Pune
4	28832	Mr. Sagar Naganath Shinde	Male	IISER Bhopal	Integrated PhD
5	28856	Mr. Chaitanya Janardan Kulkarni	Male	IISER Bhopal	PhD	Department of Mathematics Savitribai Phule Pune University	2017
6	28944	Mr. Sushil Singla	Male	Shiv Nadar University	PhD	Shiv Nadar University	2016
7	29016	Mr Shubhankar Mandal	Male	Indian Institute of Technology Bhilai	PhD	National Institute of Technology Rourkela	2016
8	29094	Mr. Mohammad Irshad Khan	Male	Banaras Hindu University	Ph.D. Student	IIT Delhi	2017
9	29095	Mr Anurag Kumar Patel	Male	Banaras Hindu University	Ph.D. Student	Banaras Hindu University	2018
10	29100	Mr. Vivek Kumar	Male	Central University of Jammu	PhD	University of Jammu	2017
11	29114	Mr. Ashish Naudiyal	Male	Banaras Hindu University Varanasi	PhD Student	H N B Garhwal University	2017
12	29135	Mr Samir Panja	Male	IIT Bombay	PhD	IIT Kanpur	2016
13	29244	Mr. Sayan Dutta	Male	Indian Institute of Technology Bombay	Ph.D.	Indian Institute of Technology Bombay	2018
14	29257	Mr. Rashid A.	Male	Nationali Institute Of Technology Calicut	PhD. Scholar.	National Institute of Technology Calicut	2015
15	29298	Mr. Bappa Ghosh	Male	Indian Statistical Institute	Mmath Student	Indian Statistical Institute
16	29316	Mrs. Reshmi Mn	Female	IIT Bombay	Ph.D. Student	NIT Calicut	2016
17	29327	Mr. Rahul Ghosh	Male	Indian Statistical Institute , Kolkata	M.Math 1st Year Student	ISI Kolkata
18	29368	Ms. Aastha Malhotra	Female	Faculty Of Mathematical Sciences, University Of Delhi	PhD Student	Miranda House, University Of Delhi	2016
19	29396	Mr Sarathkumar N S	Male	Cochin University of Science And Technology	Project Assistant	Mahatma Gandhi University, Kottayam	2017
20	29442	Ms Prajakta Satish Sahasrabuddhe	Female	IIT Bombay	PhD	IITMadras	2015
21	29457	Mr. Pankaj Dey	Male	IISER TVM	Integrated Phd	IISER TVM	2017
22	29467	Mr. Bharat Talwar	Male	University of Delhi	Ph.D. Student	University of Delhi	2016
23	29471	Mr. Kousik Dhara	Male	I. I. T. Madras	PhD	IIT Madras	2014
24	29505	Mr. Lav Kumar Singh	Male	School of physical sciences , JNU	PhD	Dr. Harisingh Gour Central university	2016
25	29512	Ms. Jyoti Sharma	Female	Department of Mathematics, University of Delhi	Research Scholar	University of Delhi	2015
26	29521	Mr Malay Mandal	Male	Chennai Mathematical Institute	PhD	IIT Guwahati	2017
27	29541	Mr Ritaman Ghosh	Male	Chennai Mathematical Institute	MSc Student
28	29567	Mr. Arindam Ghosh	Male	Indian Institute of Technology Hyderabad.	PhD	Presidency University, Kolkata	2017
29	29671	Mr. Uttaran Choudhurry	Male	TIFR Centre for Applicable Mathematics	MSc Student	TIFR Centre for Applicable Mathematics
30	29711	Dr. Shankar P	Male	Indian Statistical Institute	NBHM - Post Doctoral Fellow	PONDICHERRY UNIVERSITY	2012	10/10/2018
31	29726	Ms. Anshu Singh	Female	IISER	IPhD student	IISER	2017
32	29815	Ms. Arushi Agarwal	Female	IISER Mohali	BS-MS Integrated Student
33	29831	Mr. Suman Das	Male	Indian Institute of Technology Ropar	PhD	IISER Kolkata (BS-MS Dual Degree)	2018
34	29840	Dr. Muthukumar P	Male	Indian Statistical Institute	NBHM Post Doctoral Fellow	IIT Madras	2012	26/03/2019
35	29855	Mr. Arghya Pratihar	Male	Ramakrishna Mission Vivekananda Educational And Research Institute	MSc Student	Ramakrishna Mission Vivekananda Educational And Research Institute	Appeared
36	29897	Ms. Shanola Smitha Sequeira	Female	IIT, Hyderabad	PhD	Pondicherry University	2017
37	29904	Ms Poongothai K	Female	Ramanujan Institute for Advanced Study in Mathematics, University of Madras	PhD Scholar-IV year	University of Madras	2014
38	29919	Ms Apurva Seth	Female	IISER Bhopal.	PhD	9.8	2017
39	29929	Mr Manuj Verma	Male	IIT Delhi	PhD	Banaras Hindu University	2018
40	29974	Mr. Sreejith Siju	Male	IIT Pkd	PhD Student	CMC college Kottayam	2015
	Waiting
1	29820	Mr Sayan Chattopadhyay	Male	IISER Mohali	BS-MS Integrated Student
2	29441	Mr. Bappa Bisai	Male	Indian institute of technology Bombay	Phd	IIT Bombay	2016
3	28984	Mr. Dimple Saini	Male	The LNM Institute of Information Technology	Ph.D Student	University Of Delhi	2017
4	28331	Mr. Dipendranath Mahato	Male	Tezpur University	M.Sc. Student	Tezpur University	Appeared / Awaiting Result
5	29413	Mr. Vidya Sagar	Male	IIT DELHI	PhD	IIT Jodhpur, Karwar, Rajasthan	2018
6	29548	Mr Rahul Maurya	Male	IIITA Allahabad	Ph.D.	Banaras Hindu University	2014
7	29941	Mr. Debabrota Mondal	Male	IIT Bhubaneswar	MSc Student	IIT Bhubaneswar	Appeared / Awaiting Result
8	29752	Ms. Ritika Singhal	Female	IIT Delhi	PhD	IIT Delhi
9	29938	Mr. Kapil Jaglan	Male	IIT ropar	phd student	dav college chandigarh	2017

How to Reach:

TBA

School Short Name:

Last Date Application:

Saturday, August 31, 2019

School Type:

AIS