Sunder's Page
SUNDER'S HOME-PAGE
This is me.
I do mathematics at my institute.
What follows might give you an idea of the sort of things I will be doing, am doing, and have been doing here.
Advanced Instructional School on Operator Theory/Algebras, at IMSc, February 1-21, 2016.>
Lecture Series on (easy) Quantum Groups, by Moritz Weber, at IMSc, January 5-24, 2015.>
Master-Class in Modular Theory of von Neumann algebras, November 24-December 05, 2014.>
IMSc-ISI Joint
Workshop on Subfactors at IMSc, December 30,2013-January 10, 2014.
Here are a workshop and a conference my colleague Vijay had little choice
`organising' - (the poor chap had me doing some back-seat driving, to boot!) -
because I couldn't possibly be obviously organising them myself:
Instructional
Workshop on Subfactors and Planar Algebras, March 26 - April 3, 2012.
SunderFest 2012, April 4 - April 6, 2012. >
Here are some announcements of conferences/workshops I have conducted in
the past:
ATM Workshop on Operator Algebras, January 30 - February 11, 2012.
Instructional workshop on the Functional
Analysis of Quantum Information Theory, December 26, 2011 - January
6, 2012. >
Satellite Conference on Operator
Algebras, August 9 - 13, 2010.
Instructional workshop on Free
Probability , July 26- August 6, 2010.
Workshop on von Neumann algebras, Ergodic
theory and Geometric Group theory , February 2 - 13, 2009.
My Curriculum Vitae
Here are the pdf files of some talks I have given at assorted places:
- Planar algebras and 1+1-dimensional TQFTs
(lectures given at UBC, Vancouver in September 2006)
- Hopf C^*-algebras and their quantum doubles -
from the point of view of subfactors
(lecture given at Max-Planck Institut in Bonn in August 2007)
- $II_1$ factors and Ergodic Theory
(lecture given at ISI, Bangalore in February 2008)
- Non-crossing partition and 2-cabled Temperley-Lieb
planar algebras
(lecture given at BIRS, Banff in March 2008)
- von Neumann algebras and free probability
(lecture given at the Ramanujan Math. Society at Bangalore in May 2009)
- Catalan numbers
(lecture given at CESCI, Madurai to school students on August 25, 2009.)
- Free probability: classical and free CLTs
(lecture given at ISI, Bengaluru in November 2009)
- On the GJS construction for graphs: I.
Presentation of two categories
(first of two-part lecture given along with Vijay Kodiyalam at Vanderbilt
University in May 2010)
- Hilbert von Neumann modules
(lecture given at ISI, Bengaluru in January 2011)
And here are some talks I have given in Chennai:
- Temperley-Lieb algebras and non-crossing
partitions
(lecture given at the Ramanujan Institute for Advanced Study in Mathematics)
- When is a knot not the unknot?
(lecture given at IMSc)
- Braids
(lecture given at Ethiraj College)
- The Perron Frobenius Theorem
(lecture given at Chennai Mathematical Institute)
- Transfinite considerations
(lecture given to finishing school students at IIT, Madras)
- Self-adjoint operators and their spectra
(lecture given at IIT, Madras in April 2011)
Here are the pdf files of a course of lectures I gave (at IIT Kanpur,
ISI Kolkata and at IISc Bangalore during 2008-'09) as part of the
"Panorama of Mathematics"
series organised by the National Board for Higher Mathematics. The course was
titled "Operator algebras - Stage for non-commutativity",
and consisted of five lectures, as follows:
- $C^*$-algebras: the Gelfand Naimark Theorems
- K-theory of $C^*$-algebras
- von Neumann algebras
- $II_1$ factors and subfactors
- The Jones polynomial invariant of knots
Here are the pdf files of a course of lectures I gave at IIT, Bombay, in
April 2007, on "Temperley-Lieb algebras"
- Temperley-Lieb algebras
- Wenzl's theorem
- von Neumann algebras, II_1 factors and their
subfactors
- The standard invariant of a subfactor
To view a lecture I gave at IIT Bombay on Paul Halmos, click
here for the first part, and
here for the second part.
Here are the pdf files of a course of lectures I gave on
von Neumann algebras
at IISc, Bangalore in March 2006.
Here is an announcement of some lectures a couple of us gave to
beginning undergraduate students in the Chennai area:
Spirit of Enquiry Lectures in Mathematics
More material on the linear algebra course
which I taught.
To see a `.pdf' version of my book Functional Analysis: Spectral
Theory, click
here .
Literary pursuits
(Almost all the contents of this section may also be found in the blog
http://differentstrokes-vss.blogspot.in/)
I have been increasingly mobility challenged of late due to the onset of
a neurological condition known as multiple sclerosis; and perforce, I have
had to notice the different ways that society excludes people like me, not
deliberately, but for want of consciously thinking of the need for a more
inclusive and accessible society.
What started as irritation and unproductive
annoyance changed to a decision to do something about it. For a start, I
thought I might attempt to keep writing small pieces
with the hope of reaching more people's consciousness on this matter. This
`second career ' of mine started with an article called
Stairway to Heaven, or ...
which appeared in Current Science (Sept. 10, 2011), and was
subsequently written about in The Hindu (Bangalore edition, Sept. 12,
2011). I used a preliminary version of this
piece to convince a sympthetic editor of the Times of India to
let me
write a bi-monthly column
titled Different Strokes for Different Folks whose blurb describes
the raison d'etre for this column as my `wish to use this space to
periodically (roughly two Saturdays in a month) remind people
of the concerns of the differently abled'. (This column existed for more than a year until, for seemingly mutually acceptable reasons, this arrangement came to an end.)
I shall keep updating this page as more and more pieces appear.
Questionnaire, ToI, August 20, 2011.
Wheels within wheels, ToI, September 10, 2011.
Role Models, ToI, September 24, 2011.
Kings of the road, ToI, October 8, 2011.
As an off-shoot of this column, I gave my first ever invited
non-mathematical talk, A second career,
on 19/10/2011.
A breath of fresh air, ToI, October 24, 2011.
We talk a good game!, ToI, October 29, 2011.
Places I love to hate, ToI, November 19, 2011.
Oversight, ToI, November 26, 2011.
What they say, ToI, December 3, 2011.
Ingenious hurdles to access, ToI, December 24, 2011.
The Wrights' problem, ToI,
January 07, 2012.
In a world of their own, ToI,
January 21, 2012.
Imply vs. Infer, ToI,
February 4, 2012.
Attention to detail, ToI,
February 18, 2012.
All-Encompassing Inclusion is Possible,
ToI, March 3, 2012.
What Can We Do,
ToI, March 24, 2012.
Spare a thought for the elderly,
ToI, April 7, 2012.
Is it so hard to treat people with dignity?, ToI, April 21, 2012.
Is going legal the only way?, ToI, May 5, 2012.
My great grand-aunt, ToI, May 19, 2012.
Do ATMs have to have steps?, ToI, June 02, 2012.
Let us learn to hear you, ToI, June 16, 2012.
Whither universal design, ToI, June 30, 2012.
Time for some sensitivity, ToI, July 14, 2012.
Two for the price of one.
What is not accessibility, ToI, August 04, 2012.
Who is mad?, ToI, August 18, 2012.
Ingenuity revisited, ToI, September 1, 2012.
Technologically disabled, ToI, September 15, 2012.
My personal Santa, ToI Online, September 29, 2012 (http://www.blogs.timesofindia.indiatimes.com/DifferentStrokes/entry/my-personal-santa).
Knee-jerk denial of reality, ToI Online, October 13, 2012 (http://www.blogs.timesofindia.indiatimes.com/DifferentStrokes/entry/knee-jerk-denial-of-reality).
Short-sighteness, ToI
Online, October 27, 2012 (http://www.blogs.timesofindia.indiatimes.com/DifferentStrokes/entry/Short-sightedness).
Another very special person
Shades of perceptions
My editorial debut
Whiter than white
When Herbie goes flying
Signing away one's rights
Scenes we'd like to see!
Now that the connection with ToI has come completely unhinged, and as all my writing on this theme appears in my blog http://differentstrokes-vss.blogspot.in/
I shall stop duplicating effort of posting them here as well. So, although `my
literary pursuits' still continue, they will no longer be recorded here.
Research
My research interests have centered around Hilbert space and focused on
operators, operator algebras, subfactors, planar algebras, and free
probability.
List of publications
Monographs
- Bounded Integral operators on
$L^2$-spaces, with P.R. Halmos, Ergeb.
der Math., No. 96, Springer-Verlag, Berlin, 1978.
(M.R. 80g:47036 and 87f:47041, Zbl 573.47020, 389.47001).
- An invitation to von Neumann algebras, Universitext,
Springer-Verleg, New York, 1986.
(M.R. 88f:46115, Zbl 616.46052).
- Introduction to Subfactors, with Vaughan Jones, London
Math. Soc. Lect. Note Series, No. 234, Cambridge Univ. Press, Cambridge, 1997.
(M.R.98h:46067 Zbl 903.46062).
- Functional Analysis: Spectral Theory, TRIM Series, No. 13,
Hindustan Book Agency, Delhi, 1997, and Birkhauser Advanced Texts,
Basel, 1997. (M.R. 99h:47001, Zbl 957.47001, 919.46002).
- Topological quantum field theories from subfactors, with
Vijay Kodiyalam, CRC Research Notes in Mathematics Series, 423,
2000 (Zbl 992.07801).
- Measure and Probability, with Siva Athreya, Universities
Press, Hyderabad, 2008. (ISBN:978-81-7371-613-3)
- Functional Analysis of Quantum Information Theory, with Prabha Mandayam and Ved Prakash Gupta, Springer Lecture Noters in Physics No. 902 (to appear), and e-print arXiv 1410-7188 (quant-ph); a blurb of this book may be found at http://www.springer.com/in/book/9783319167176.
- Operators on Hilbert Space, TRIM Series, No. 71,
Hindustan Book Agency, Delhi, 2015; a blurb of this book may be found at http://www.hindbook.com/index.php/operators-on-hilbert-space.
Papers
- Two characterisation theorems for integral operators,
Integral Eqns. and Oper. Theory, 1(1978), 250-269.
(M.R.80d:47079, Zbl 376.47024).
- Absolutely bounded matrices, Indiana Univ Math. J. 27,
(1978),919-927. (M.R. 80d:47052, Zbl 419.47011).
- Algebra of kernels, J of the Indian Math. Soc., 44,
(1979), 143-156. (M.R. 86j:47076, Zbl 621.47031).
- Unitary equivalence to integral operators, Pacific J, of
Math. 92, (1981), 211-215 (M.R. 82f:47045, Zbl 508.47020).
- A non-commutative analogue of $|D X^k| = |k x^{k-1}|$, Lin. Alg.
and Applicns, 44(1982), 87-95, (M.R. 83h:47004, Zbl 486.46050).
- Distance between normal operators, Proc. Amer. Math.
Soc. 84(1982), 483-484, (M.R. 83c:47040, Zbl 486.47015).
- On permutations, convex hulls and normal operators, Lin Alg
and Applicns., 48,(1982),403-411.(M.R.85b:15032, Zbl 537.15014).
- A spectrum modulo operators of rank less than n, Math.
Today , 1,(1983), 81-88. (M.R.85a:47018, Zbl 532.47010).
- On ideals and duals of $C^*$-algebras, Indian J. of Pure and
Appl. Math, 15,(1984),601-608.(M.R.85i:46079, Zbl 588.46039).
- On majorisation and Schur products, with R.B. Bapat, Lin. Alg
and Applicns., 72,(1985), 107-117. (M.R.87c:15018, Zbl 577.15016).
- An extremal property of the determinant and the
permanent, with R.B. Bapat, Lin. Alg. and Applicns, 76, (1986),
153-164.(M.R.87j:15012, Zbl 602.15008).
- Stochastic integration in Fock space, Pac. J. of Math.,
122,(1986), 481-491. (M.R.88c:60126, Zbl 583.60051, 543.60063).
- A model for AF-algebras and a representation of the Jones
projections, J. of Oper. Theory,
18,(1987),289-301.(M.R.89e:46079, Zbl 693.46054).
- N subspaces, Canadian J. of Math., Vol XL, No.1,(1988), 38-54.
(M.R.89i:46023, Zbl 656.46017).
- Monomials in the Jones projections, Proc. Amer. math. Soc., 103,
(1988),761-764. (M.R.89f:46119, Zbl 673.46040).
- Hypergroups and subfactors, Proc. of a symposium on
Operator Theory and
Functional Analysis, Cochin (1989) 49-65. (M.R. 91 m: 46096, Zbl 718.46035).
- The Laplacean spectrum of a graph, with R. Grone and R. Merris,
SIAM J. of Matrix Anal. and Applns., 11 (1990),
218-238.(M.R.91c:05130, Zbl 733.05060).
- Pairs of $II_1$ factors, Proc. of the Indian Acad. of Sci.
(Math. Sci.), Vol. 100, No.2, August 1990, pp. 357-377.
(M.R.:92b:46098, Zbl 727.46039).
- The work of Vaughan Jones - From subfactors to knot
invariants, Current Science,59,(1990),1285-1292.
- On hypergroups of matrices, with R.B. Bapat, J. of Lin.
and Multilin. Alg., 29, (1991), 125-140.(M.R.92k:20137, Zbl 734.20033).
- On commuting squares and subfactors, J. of Functional Anal.
101(1991), 286-311.(M.R.92j:46111, Zbl 739.46042).
- $II_1$ factors, their bimodules and hypergroups, Trans.
of the Amer. Math. Soc. 330(1992), 227-256. (M.R. 92f:46076, Zbl
757.46053).
- Unitary orbits of self-adjoints in some $C^*$-
algebras, with Klaus Thomsen, Houston J. of Math. 18(1992).
127-138, (Special Volume dedicated to
the memory of Domingo Herrero). (M.R. 93e:46071, Zbl 812.46057).
- From hypergroups to subfactors, Operator Algebras and
Operator Theory,
Ed. W. Arveson et al,Proceedings of OATE 2 conference, Romania 1989, Pitman
Research Notes in Mathematics, Longman Scientific, Essex, UK, 1992,
pp. 198-216. (M.R. 93m:46074, Zbl 792.46045).
- On the non-occurrence of the Coxeter graphs
$\beta_{2n+1}, D_{2n+1}$ and $E_7$ as the principal graph invariant of an
inclusion of $II_1$ factors, with A.K. Vijayarajan, Pacific J. of
Math., 161,(1993),185-200.
(M.R.94g:46067, Zbl 798.43005)
- On some convex sets and their extreme points, with A. Rajarama
Bhat and V. Pati, Math. Annalen.,
296,(1993),637-648.(M.R.94f:46076, Zbl 791.46006)
- On principal graphs and weak duality, with Uma Krishnan,
Math. Scand., 74,(1994),49-63.(M.R.95i:46087, Zbl 809.05057).
- On the relation between subfactors and hypergroups,
Applications of hypergroups and related measure algebras, Contemp.
Math., 183, pp. 331-340, 1995. (M.R.96d:46087, Zbl 830.46053).
- On boundedness and $||~||_p$-continuity of second
quantisation, with H. Araki and K.B. Sinha, Publ. R.I.M.S., 31,
(1995), 941-952. (M.R.97j:81166, Zbl 848.47017).
- On some subfactors of integer index arising from vertex models,
with Uma Krishnan and Cherian Varughese, J. Functional
Analysis, 140, (1996), 449-471. (M.R.97j:46066, Zbl 899.46049).
- On biunitary permutation matrices and some
subfactors
of index $9$, with Uma Krishnan, Trans. of the Amer. Math. Soc.,
348, (1996), 4691-4736. (M.R. 97c:46077, Zbl 862.46035).
- Notes on the imprimitivity theorem,
Analysis, Geometry and
Probability, an expository volume brought out in honour of
K.R. Parthasarathy), 299-321, Hindustan Book Agency, Delhi,
1996. (M.R.98k:22027, Zbl 949.22007).
- Exponentials of indicator functions are
total in the Boson Fock space $\Gamma (L^2[0,1])$, with K.R.
Parthasarathy, Quantum Probability
Communications, Vol. X, (1998), 281-284. (M.R.2000j:81136)
- Schrodinger operators with fairly arbitrary spectral features,
with M. Krishna, Rev. Math. Phys., 19, (1997), 343-360.
(M.R.98d:47100, Zbl 879.34081).
- Commuting Squares,
The Mathematics Student, 67, (1998), 65-72. (M.R.2001b:46101).
- Fusion Rule Algebras and Walks on
Graphs,
with N.J. Wildberger, The Proceedings of the Fifth Ramanujan
Symposium on Harmonic Analysis, Ed. K. Parthasarathy, Publ. of
the Ramanujan Inst., No.6, (1999), 53-80.
- The subgroup subfactor,
with Vijay Kodiyalam, Math. Scand., 86, (2000), 45-74.
(M.R.2001b:46103, Zbl 991.60290).
- The algebra of $G$-relations,
with Vijay Kodiyalam and R. Srinivasan,
Proc. of the Indian Acad. Sci. (Math. Sci.), 110,
(2000), 263-292. (MR. 2001k:16019, Zbl 992.06392).
- Flatness and fusion coefficients,
with Vijay Kodiyalam, Pac. J. Math., 201, (2001),
177-204. (M.R. 2002k:46162).
- Spectra of Principal Graphs,
with Vijay Kodiyalam, Internat. J. Math., 12, (2001), 203-210.
(M.R.2002b:46101).
- Discrete series of fusion algebras,
with R. Srinivasan and Norman Wildberger,
J. of Aust. Math. Soc., 72, (2002), 419-425.
(M.R. 2003j:46096).
- Planar depth and planar subalgebras,
with Zeph Landau,
J. of Functional Analysis, 195, (2002), 71-88.(M.R. 2003d:46080).
- On trace zero matrices,
Resonance, 7, No.6, (2002), 14-26.
- Actions of finite hypergroups,
with Norman Wildberger,
J. of Algebraic Combinatorics, 18(2), (2003), 135-151..
(M.R. 2004g:20092).
- The planar algebra associated to a Kac
algebra,
with Vijay Kodiyalam and Zeph Landau, Proc. of the Indian
Acad. Sci. (Math. Sci.), 113, (2003), 15-51. (M.R. 2004d:46075)
- Complete invariants for complex semisimple Hopf
algebras, with Sumant Datt and Vijay Kodiyalam, Math. Res. Lett., 10,
No. 5-6, (2003), 571-587.
- On Jones' planar algebras,
with Vijay Kodiyalam, J. of Knot Theory and its Ramifications,
13, No. 2(March), (2004), 219-248.
- A complete set of numerical invariants for a
subfactor,
with Vijay Kodiyalam, J. of Functional Analysis, 212, (2004), 1-27.
- Hamel bases and measurability, with
M.G. Nadkarni, Mathematics Newsletter, vol. 14, No. 3, (2004).
- The planar algebra of a semisimple
and cosemisimple Hopf algebra, with Vijay Kodiyalam,
Ind. Acad. of Sci., vol. 116
no. 4, (2006), 443-458; and e-print arXiv math.QA/0506153.
- von Neumann Algebras: Introduction, modular theory
and classification theory, Encyclopedia of Math. Physics,
eds. J.-P. Francoise, G.L. Naber and
Tsou S.T., Oxford: Elsevier, 2006 (ISBN 978-0-1251-2666-3), vol 5
pp. 379-385.
- Subfactors and 1+1-dimensional TQFTs,
with Vijay Kodiyalam and Vishwambhar Pati, International
Journal of Mathematics, Vol. 18, No. 1 (2007) 69-112, e-print arXiv
math.QA/0507050.
- Paul Halmos - Expositor par excellence,
Resonance, (2007), 17-28.
- Temperley-Lieb and Non-crossing
Partition planar algebras , with Vijay Kodiyalam,
Noncommutative Rings, Group Rings,
Diagram Algebras and Their Applications Edited by: S. K. Jain, Ohio
University, Athens, OH, and S. Parvathi, University of Madras,
Chennai, India, Contemp. Math., Vol. 456, (2008).
- The Riesz representation theorem ,
Indian J. of Pure and Appl. Math., 39(6), December 2008, 467-481.
- von Neumann Algebras and Ergodic
Theory , in `Perspectives in Mathematical Sciences II, Pure
Mathematics', 199-208, World Scientific, June 2009.
- Kac algebras, quantum doubles and
planar algebras , with S. Jijo,
Contemporary Math. Vol. 490, 97-104, 2009.
- von Neumann algebras and free
probability,
Mathematics Newsletter of the Ramanujan Mathematical Society, Vol. 19,
No. 1, pp. 7-9, June 2009.
- Planar algebras and Kuperberg's
3-manifold invariant, with Vijay Kodiyalam,
Journal of Operator Theory, vol. 63, No. 1, (2010), 101-122,
and e-print arXiv math.OA/0807.3714.
- From subfactor planar algebras to
subfactors, with Vijay Kodiyalam,
Internat. J. Math. vol. 20, No. 10, pp. 1207-1231, 2009, and
e-print arXiv math.OA/0807.3714.
- Guionnet-Jones-Shlyakhtenko
subfactors associated to finite-dimensional Kac algebras,
Journal
of Functional Analysis, Vol. 257, (2009), 3930-3948 and e-print arXiv
math.OA/0901.3180.
- On the Guionnet-Jones-Shlyakhtenko
construction for graphs, with Vijay Kodiyalam, Journal of
Functional
Analysis, 260 (2011) 2635 - 2673; and e-print arXiv math. OA/0911.2047.
- Double cones are intervals,
Operator Theory: Advances and Applications, Vol. 207, 359-362, Birkhauser
Verlag, Basel/Switzerland, 2010.
- Israel Moiseevich Gelfand (1913 - 2009)
, Resonance, Vol. 16, No. 2, (2011), 165-179.
- Hilbert von Neumann modules, with
Panchugopal Bikram, Kunal Mukherjee and R. Srinivasan, (special volume of)
Communications in Stochastic Analysis (in honour of Prof. K. R. Parthasarathy),
vol. 6, no. 1 (March 2012), 49-64, and e-print arXiv math. OA/1102.4663.
- From graphs to free products, with
Madhushree Basu and Vijay Kodiyalam, Proc. (MathSci) of the Indian Acad. of
Sciences, Vol. 122, No. 4, November 2012, 547-560, and e-print arXiv math.
OA/1102.4413.
- On Extendability of Endomorphisms and E_0-semigroups of factors, with
Panchugopal Bikram, Masaki Izumi and and R. Srinivasan, Kyushu Journal of
Mathematics, Vol. 68, No. 1, 165-179, (2014), and a preliminary version as e-print arXiv:1211.2576.
[math. OA].
- Continuous minimax theorems, with
Madhushree Basu, Operator Algebras and Mathematical Physics, 24th International
Workshop in Operator Theory and its Applications, Bangalore, December 2013, Editors: Bhattacharyya, Tirthankar and Dritschel, Michael A., Proc. of
Vol. 247, pp. 37-56, Springer, Basel, (2015), and e-print arXiv:1210.7581
[math. OA].
- Fuglede's theorem, Indian J. of Pure and Applied Math., Vol. 46(4): 415-417, 2015.
- A tensor-analogue of the Schur product, with K. Sumesh, Positivity, October 2015, pp. 1-4, and e-print arXiv:1509.04884[math. OA].
- Operator algebras in India in the last decade, with the help of Vijay Kodiyalam, Partha Sarathi Chakraborty and Arup Pal; and inputs from many others.
Personal Information:
Address (Residence): E1, Block III, Shivani Apartments;
40, East Coast Road;
Thiruvanmiyur;
Chennai 600 041, India.
PHONE(IMSc): (044) 2254 3210,2254 3100
PHONE(Home) : (044) 2451 6082
FAX(IMSc) : (044) 2254 1586
TELEGRAMS : MATSCIENCE, MADRAS 600 113
E-MAIL : sunder@imsc.res.in
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