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SUMMARY:Prof. BV Rajarama Bhat (ISI Bangalore)
DTSTART;VALUE=DATE-TIME:20200819T103000Z
DTEND;VALUE=DATE-TIME:20200819T113000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103410Z
UID:WOTOA/1
DESCRIPTION:Title: A caricature of dilation theory\nby Prof. BV Rajarama B
hat (ISI Bangalore) as part of Webinars on Operator Theory and Operator Al
gebras\n\n\nAbstract\nWe present a set-theoretic version of some basic dil
ation results of operator theory. The results we have considered are Wold
decomposition\, Halmos dilation\, Sz. Nagy dilation\, inter-twining liftin
g\, commuting and non-commuting dilations\, BCL theorem etc. We point out
some natural generalizations and variations. This is a joint work with S
andipan De and Narayan Rakshit.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sameer Chavan (IIT Kanpur)
DTSTART;VALUE=DATE-TIME:20200909T113000Z
DTEND;VALUE=DATE-TIME:20200909T130000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103410Z
UID:WOTOA/3
DESCRIPTION:Title: Dirichlet-type spaces on the unit ball and joint 2-isom
etries\nby Sameer Chavan (IIT Kanpur) as part of Webinars on Operator Theo
ry and Operator Algebras\n\n\nAbstract\nWe discuss a formula that relates
the spherical moments of the multiplication tuple on a Dirichlet-type spac
e to a complex moment problem in several variables. This can be seen as th
e ball-analogue of a formula originally invented by Richter. One may capit
alize on this formula to study Dirichlet-type spaces on the unit ball and
joint 2-isometries. This talk is based on a joint work with Rajeev Gupta a
nd Md Ramiz Reza.\n
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BEGIN:VEVENT
SUMMARY:Sutanu Roy (NISER)
DTSTART;VALUE=DATE-TIME:20200916T113000Z
DTEND;VALUE=DATE-TIME:20200916T130000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103410Z
UID:WOTOA/4
DESCRIPTION:Title: Quantum group contraction and bosonisation\nby Sutanu R
oy (NISER) as part of Webinars on Operator Theory and Operator Algebras\n\
n\nAbstract\nAbstract: In 1953 İnönü and Wigner introduced group contr
action: a systematic (limiting) process to obtain from a given Lie group a
non-isomorphic Lie group. For example\, the contraction of SU(2) group (w
ith respect to its closed subgroup T) is isomorphic to the double cover of
E(2) group. The q-deformed C*-algebraic analogue of this example was intr
oduced and investigated by Woronowicz during the mid '80s to early '90s. M
ore precisely\, the C*-algebraic deformations of SU(2) and (the double cov
er of) E(2) with respect to real deformation parameters 0<|q|<1 become com
pact (denoted by SUq(2)) and non-compact locally compact (denoted by Eq(2)
) quantum groups\, respectively. Furthermore\, the contraction of SUq(2) g
roups becomes (isomorphic) to Eq(2) groups. However\, for complex deformat
ion parameters 0<|q|<1\, the objects SUq(2) and Eq(2) are not ordinary but
braided quantum groups. More generally\, the quantum analogue of the norm
al subgroup of a semidirect product group becomes a braided quantum group
and the reconstruction process of the semidirect product quantum group fr
om a braided quantum group is called bosonisation. In this talk\, we shall
present a braided version of the contraction procedure between SUq(2) and
Eq(2) groups (for complex deformation parameters 0<|q|<1) and address its
compatibility with bosonisation. This is based on a joint work with Atibu
r Rahaman.\n
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BEGIN:VEVENT
SUMMARY:Jyotishman Bhowmick (ISI Kolkata)
DTSTART;VALUE=DATE-TIME:20200923T113000Z
DTEND;VALUE=DATE-TIME:20200923T130000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103410Z
UID:WOTOA/5
DESCRIPTION:Title: Metric-compatible connections in noncommutative geometr
y\nby Jyotishman Bhowmick (ISI Kolkata) as part of Webinars on Operator Th
eory and Operator Algebras\n\n\nAbstract\nLevi-Civita's theorem in Riemann
ian geometry states that if $(M\, g)$ is a Riemannian manifold\, then ther
e exists a unique connection on $M$ which is torsionless and compatible wi
th $g$. The curvature of the manifold is then computed from this particula
r connection. \n\nWe will try to explain the notions to state and prove Le
vi-Civita's theorem in the context of a noncommutative differential calcul
us. In particular\, we will describe two notions of metric-compatibility
of a connection. The talk will be based on joint works with D. Goswami\, S
. Joardar\, G. Landi and S. Mukhopadhyay.\n\nThe geometric notions appeari
ng in the lecture will be defined and explained in the beginning.\n
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BEGIN:VEVENT
SUMMARY:Tirthankar Bhattacharyya (IISc Bangalore)
DTSTART;VALUE=DATE-TIME:20200930T113000Z
DTEND;VALUE=DATE-TIME:20200930T130000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103410Z
UID:WOTOA/6
DESCRIPTION:Title: On the geometry of the symmetrized bidisc\nby Tirthanka
r Bhattacharyya (IISc Bangalore) as part of Webinars on Operator Theory an
d Operator Algebras\n\n\nAbstract\nWe study the action of the automorphism
group of the $2$ complex dimensional manifold symmetrized bidisc $\\mathb
b G$ on itself. The automorphism group is $3$ real dimensional. It foliate
s $\\mathbb G$ into leaves all of which are $3$ real dimensional hypersurf
aces except one\, viz.\, the royal variety. This leads us to investigate I
saev's classification of all Kobayashi-hyperbolic $2$ complex dimensional
manifolds for which the group of holomorphic automorphisms has real dimen
sion $3$ studied by Isaev. Indeed\, we produce a biholomorphism between th
e symmetrized bidisc and the domain\n\n \\[\\{(z_1\,z_2)\\in \\mathbb{C} ^
2 : 1+|z_1|^2-|z_2|^2>|1+ z_1 ^2 -z_2 ^2|\, Im(z_1 (1+\\overline{z_2}))>0\
\}\\]\n\nin Isaev's list. Isaev calls it $\\mathcal D_1$. The road to the
biholomorphism is paved with various geometric insights about $\\mathbb G$
. \n\nSeveral consequences of the biholomorphism follow including two new
characterizations of the symmetrized bidisc and several new characterizati
ons of $\\mathcal D_1$. Among the results on $\\mathcal D_1$\, of particul
ar interest is the fact that $\\mathcal D_1$ is a ``symmetrization''. When
we symmetrize (appropriately defined in the context) either $\\Omega_1$ o
r $\\mathcal{D}^{(2)} _1$ (Isaev's notation)\, we get $\\mathcal D_1$. Th
ese two domains $\\Omega_1$ and $\\mathcal{D}^{(2)} _1$ are in Isaev's lis
t and he mentioned that these are biholomorphic to $\\mathbb D \\times \\m
athbb D$. We produce explicit biholomorphisms between these domains and $\
\D \\times \\D$.\n
END:VEVENT
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SUMMARY:Mizanur Rahaman (BITS Pilani Goa campus)
DTSTART;VALUE=DATE-TIME:20201007T113000Z
DTEND;VALUE=DATE-TIME:20201007T130000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103410Z
UID:WOTOA/7
DESCRIPTION:Title: Bisynchronous Games\nby Mizanur Rahaman (BITS Pilani Go
a campus) as part of Webinars on Operator Theory and Operator Algebras\n\n
\nAbstract\nFor some games played by two cooperating but non-communicating
players\, the players can use entanglement as a resource to improve their
outcomes beyond what is possible classically. Graph colouring game\, grap
h homomorphism game and graph isomorphism game are a few examples of these
games. Over the last few years\, a remarkable progress has been taken pla
ce in the theory of these non-local games. One significant aspect of this
development is its connection with many challenging problems in operator a
lgebras.\n\nIn this talk\, I will review the theory of these games and exp
lain the relevant connection with operator algebras. In particular\, I wil
l introduce a new class of games which is called bisynchronous and will sh
ow a close connection between bisynchronous games and the theory of quantu
m groups. Moreover\, when the number of inputs is equal to the number of o
utputs\, each bisynchronous correlation gives rise to a completely positiv
e map which will be shown to be factorable in the sense of Haagerup and Mu
sat. This is a joint work with Vern Paulsen. No background in quantum theo
ry is needed for this talk.\n
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SUMMARY:Soumyashant Nayak (ISI Bangalore)
DTSTART;VALUE=DATE-TIME:20201014T113000Z
DTEND;VALUE=DATE-TIME:20201014T130000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103410Z
UID:WOTOA/8
DESCRIPTION:Title: What is a Murray-von Neumann algebra?\nby Soumyashant N
ayak (ISI Bangalore) as part of Webinars on Operator Theory and Operator A
lgebras\n\n\nAbstract\nIt was observed by Murray and von Neumann in their
seminal paper on rings of operators (1936) that the set of closed\, densel
y-defined operators affiliated with a finite von Neumann algebra has the s
tructure of a *-algebra. The algebra of affiliated operators naturally app
ears in many contexts\; for instance\, in the setting of group von Neumann
algebras in the study of non-compact spaces and infinite group actions. I
n this talk\, we will give an intrinsic description of Murray-von Neumann
algebras avoiding reference to a Hilbert space\, thus\, revealing the intr
insic nature of various notions associated with such affiliated operators.
In fact\, we will view Murray-von Neumann algebras as ordered complex top
ological *-algebras arising from a functorial construction over finite von
Neumann algebras.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:S Sundar (IMSc Chennai)
DTSTART;VALUE=DATE-TIME:20201021T113000Z
DTEND;VALUE=DATE-TIME:20201021T130000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103410Z
UID:WOTOA/9
DESCRIPTION:Title: An asymmetric multiparameter CCR flow\nby S Sundar (IMS
c Chennai) as part of Webinars on Operator Theory and Operator Algebras\n\
n\nAbstract\nThe theory of E_0-semigroups initiated by R.T. Powers and dev
eloped extensively by Arveson has been an active area of research for well
over thirty years. An E_0-semigroup is a 1-parameter semigroup of unital
normal *-endomorphisms of B(H) where H is a Hilbert space.\n\nHowever\, no
thing prevents us from considering semigroups of endomorphisms indexed by
more general semigroups. This was analysed in collaboration with Anbu Ar
junan\, S.P. Murugan and R. Srinivasan. \n\nI will explain a few similari
ties between the one parameter theory and the multiparameter theory. Also
\, there are significant differences. I will attempt to illustrate one dif
ference by explaining that a multiparameter CCR flow need not be symmetric
.\n
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BEGIN:VEVENT
SUMMARY:Soumalya Joardar (IISER Kolkata)
DTSTART;VALUE=DATE-TIME:20201104T113000Z
DTEND;VALUE=DATE-TIME:20201104T130000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103410Z
UID:WOTOA/11
DESCRIPTION:Title: Quantum symmetry of graph C* -algebras\nby Soumalya Joa
rdar (IISER Kolkata) as part of Webinars on Operator Theory and Operator A
lgebras\n\n\nAbstract\nGraph C*-algebras are examples of C*-algebras gener
ated by partial isometries. The notion of quantum symmetry of graph C*-alg
ebras will be discussed. Emphasis will be given on the invariance of KMS s
tates of graph C*-algebras at critical inverse temperature under such quan
tum symmetry. The richness of quantum symmetry will be exhibited by a part
icular consideration. Also a unitary easy quantum group will be shown to a
ppear as the quantum symmetry of a particular graph C*-algebra. The talk i
s based on a joint project with Arnab Mandal.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Devarshi Mukherjee (University of Goettingen)
DTSTART;VALUE=DATE-TIME:20201111T113000Z
DTEND;VALUE=DATE-TIME:20201111T130000Z
DTSTAMP;VALUE=DATE-TIME:20201029T103410Z
UID:WOTOA/12
DESCRIPTION:Title: Isoradial embeddings and non-commutative geometry\nby D
evarshi Mukherjee (University of Goettingen) as part of Webinars on Operat
or Theory and Operator Algebras\n\n\nAbstract\nIn this talk\, we describe
a framework to study non-commutative geometry as a relative version of dif
ferential geometry. More precisely\, given a C*-algebra A\, we would like
to make sense of a "smooth" subalgebra $A^\\infty \\subseteq A$\, and dedu
ce properties about A using such a subalgebra. Such a smooth subalgebra s
hould be analogous to the Frechet algebra $C^\\infty(M) \\subseteq C(M)$ f
or a smooth manifold M\, in the world of commutative C*-algebras. We shal
l review the fundamental properties and applications of such embeddings\,
called $\\textit{isoradial embeddings}$\, due to Ralf Meyer. If time permi
ts\, I will mention an ongoing research program with Meyer\, Corti\\~nas a
nd Cuntz\, that uses such embeddings to develop noncommutative geometry ov
er finite fields. \n\nI will not assume that the audience has any backgro
und beyond familiar examples of C*-algebras. A lot of the motivation would
however be clearer to those familiar with cyclic homology or operator alg
ebraic K-theory.\n
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