Algebry operatorów i ich zastosowania w fizyce
2006/2007 | 2007/2008 | 2008/2009 | 2009/2010 | 2010/2011 | 2011/2012 | 2012/2013 | 2013/2014 | 2014/2015 | 2015/2016 | 2016/2017 | 2017/2018 | 2018/2019 | 2019/2020 | 2020/2021 | 2021/2022 | 2022/2023 | 2023/2024
2015-06-11 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15 
Stanisław Lech Woronowicz (KMMF)G-products for non-regular quantum groups and their Landstad algebras
In the seventies of the last century Magnus Landstad investigated crossed product of C∗-algebra D by an action of abelian locally compact group. He found three conditions that localise a C∗-algebra D inside the multiplier algebra of the crossed product. We shall show, how to formulate these conditions for non-regular locally compact quantum groups.
2015-05-28 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Paweł Kasprzak (KMMF)Quantum families of quantum groups homomorphisms
The notion of quantum family of maps has been introduced in the framework of C*-algebras. As in the classical case, one may consider a quantum family of maps preserving additional structures (e.g. quantum family of maps preserving a state). In this talk I will define a quantum family of homomorphisms of locally compact quantum groups. I will show that, roughly speaking, such a family is classical. The purely algebraic counterpart of the discussed notion, i.e. a quantum family of homomorphisms of Hopf algebras will be introduced and the algebraic counterpart of the aforementioned result will be proved. If time permits I will discuss the cases when the quantum group of inner automorphisms of a locally compact quantum group G acts on the dual of G by classical automorphisms. Joint work with Mariusz Budziński.
2015-05-14 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Simeon Wang (IMPAN)Sidon sets for compact quantum groups
Department of Mathematical Methods in Physics In this talk I will present several recent results on Sidon sets for (quantum) groups. I will establish the equivalence between several different characterizations of Sidon sets for compact quantum groups, and in particular prove that in a discrete group the notions of Sidon sets and strong Sidon sets in the sense of Picardello coincide. I will also prove that any Sidon set for a compact quantum group is a \Lambda(p)-set for a finite p, generalizing previous results of Blendek and Michalicek. Some basic properties of central lacunarity will be also discussed - I will show that in the contrast to the classical SU(2) case one can exhibit a central \Lambda(4)-set for the quantum group SU_q(2). Finally on the other hand I will also prove that the Drinfeld-Jimbo deformations of simply connected compact semi-simple Lie groups (so for example SU_q(2)) do not admit infinite Sidon sets.
In this talk I will present several recent results on Sidon sets for (quantum) groups. I will establish the equivalence between several different characterizations of Sidon sets for compact quantum groups, and in particular prove that in a discrete group the notions of Sidon sets and strong Sidon sets in the sense of Picardello coincide. I will also prove that any Sidon set for a compact quantum group is a \Lambda(p)-set for a finite p, generalizing previous results of Blendek and Michalicek. Some basic properties of central lacunarity will be also discussed - I will show that in the contrast to the classical SU(2) case one can exhibit a central \Lambda(4)-set for the quantum group SU_q(2). Finally on the other hand I will also prove that the Drinfeld-Jimbo deformations of simply connected compact semi-simple Lie groups (so for example SU_q(2)) do not admit infinite Sidon sets.
2015-04-30 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Tatiana Shulman (IMPAN)On some lifting problems in C*-algebras and Operator Theory
We will discuss various lifting properties of C*-algebras. The first part of my talk will be about lifting problems that arise as noncommutative analogues of some topological notions. Namely in topology absolute retracts and absolute neighborhood retracts are, roughly speaking, spaces with good extension properties. Their noncommutative analogues are projective and semiprojective C*-algebras, which are C*-algebras with good lifting properties. Some statements about absolute retracts and neighborhood retracts might be false in the noncommutative setting or hard to prove. We are going to discuss some problems of this sort and their connection with problems in Operator Theory. This part of my talk is almost identical to the talk I gave on January at NCG seminar. This is a joint work with Terry Loring. After that we will discuss some other lifting properties of C*-algebras, for example stability of C*-algeraic relations under small perturbations and property of being RFD (residually finite-dimensional). This will include some other joint work with Loring and a work in progress with Don Hadwin.
2015-04-23 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Biswarup Das (IMPAN)From non-commutative separate continuity to non-commutative joint continuity: A non-commutative Ellis joint continuity theorem
In 1954, R. Ellis proved the following remarkable result: Let S be a locally compact (Hausdorff) semi-topological semigroup, which is algebraically (i.e. as a set) a group. Then S is a topological group. A striking aspect of the theorem is that though the assumption "S is algebraically a group" is a purely "abstract algebraic" assumption, it somehow intervenes with the topology and as a result we get joint continuity of the product and continuity of the inverse. Recently, Matthew Daws introduced compact semi-topological quantum semigroup, as a tool to study weak almost periodicity of Hopf von Neumann algebras. We will first find a quantum analogue of the statement "algebraically a group" for these objects and then we will prove an Ellis theorem-type result for these objects. In particular, we will give a new proof of the classical Ellis theorem as well. Joint work with Colin Mrozinski.
2015-03-26 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Mateusz Wasilewski (IMPAN)Non-maximal subspaces of maximal operator spaces
In the theory of operator spaces we consider Banach spaces endowed with a particular embedding into B(H) -- the algebra of bounded operators on a Hilbert space. This gives us a sequence of norms on spaces of matrices with entries in a given Banach space. There exist the largest and the smallest sequences of such norms corresponding to some embedding into B(H). If the sequence of norms obtained for a Banach space X is the largest one then we call it a maximal operator space. We will show many examples of subspaces of maximal operator spaces which are not maximal themselves, using mostly tools from classical theory of Banach spaces. As a by-product we will answer the question of Vern Paulsen concerning amalgamated direct sums.
2015-03-19 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Stuart White (University of Glasgow)Classification of maps by traces
It's well known that *-homomorphisms from a finite injective von Neumann algebra into the ultrapower of the hyperfinite II_1 factor are classified up to unitary equivalence by their behaviour on traces. At the level of C*-algebras there are annoying K-theoretic obstructions to analogous classification results. In this talk, I'll discuss how we can circumvent these obstructions by working with coloured equivalence, and discuss some applications of this result.
2015-03-05 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Mehrdad Kalantar (IMPAN)Boundaries of groups and quantum groups
I will first present a few results that demonstrate the importance ofapplications of boundary theory in analytical (quantum) group theory.After recalling the construction of various boundaries associated toclassical groups, I will introduce boundaries of quantum groups in bothmeasure-theoretical (e.g. the Poisson boundary) and topological (e.g.Furstenberg boundary) settings.
2015-02-26 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Robin Deeley (Université Blaise Pascal, Clermont-Ferrand II)Pullbacks and correspondences for Smale spaces
We discuss some results of a joint project with Brady Killough and Michael Whittaker. The goal of the project is to better understand the functorial properties of the homology theory for Smale spaces introduced by Ian Putnam. This homology theory is conjecturally linked to the K-theory of the C*-algebras associated to a Smale space.Inspired by Connes and Skandalis' notion of correspondences in KK-theory, we define correspondences in the setting of Smale spaces. The basic idea is to encode both types of functorial properties of Smale spaces (with respect to Putnam's homology theory) into a single object. The talk will be very much an introduction and will contain many examples (for the most part coming from the theory of shifts of finite type). No knowledge of Smale spaces or Putnam's homology theory are required for the talk.
2015-01-22 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Karen Strung (IMPAN)C*-algebras, Cantor minimal systems, and minimal diffeomorphisms of odd dimensional spheres
C*-algebras and minimal dynamical systems have a long shared history. Giordano, Putnam and Skau showed that C*-algebraic K-theory, via the crossed product construction, could distinguish minimal Cantor systems up to strong topological orbit equivalence. Putnam subsequently showed that the crossed products were AT algebras, and hence also classified by K-theory. At the other end of the scale, the crossed products associated to minimal diffeomorphisms never have nontrivial projections and always have identical K-theory. This makes classification of the C*-algebras in question more difficult. However, in recent work, I show that by looking at a related system on a product of the sphere and a Cantor set, one may deduce these C*-algebras are distinguished by their tracial state spaces (or equivalent, the space of invariant Borel measures of the dynamical system). In this case, we see that *-isomorphisms of C*-algebras do not necessarily tell us much about equivalence of the underlying dynamical systems.
2015-01-08 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Paweł Kasprzak (KMMF UW)On the center of locally compact quantum group
Let G be a locally compact quantum group. In this talk we will describe the quantum counterpart of the center Z(G) of G. It will be shown that Z(G) is a strongly normal coideal of G and the explicit description of the quotient quantum group G/Z(G) will be given. In the second part of the talk we shall consider an action alpha of G on a von Neumann algebra. Although in general it is impossible to define ker alpha, we shall present the construction of the quantum counterpart of G/(ker alpha) together with the faithful quotient action of G/(ker alpha) on M. We shall show that for alpha being the inner action of G on the von Neumann algebra of the dual hatG, G/(ker alfa) equals G/Z(G). This is joint work with P. Sołtan.
2014-12-11 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Jerzy Lewandowski (IFT UW)Operators of Loop Quantum Gravity
Loop Quantum Gravity is a quantum theory of SU(2) - connections. The kinematic degrees of freedom are the same as those of the Yang-Mills theory. However, the manifest diffeomorphism covariance endows LQG with peculiar structures not known from any otherphysical theory. The advantage of the theory is infinity free derivations of quantum operators. Some of them are diagonalized, some are reduced to finite dimensional subspaces, some are not even shown to be essentially self-adjoint. This framework provides an interesting field for mathematics.
2014-11-27 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Alan Czuroń (IMPAN)Property (T) for groups acting on lp(N) spaces
Bader, Furman, Gelander and Monod defined Property F_lp as a generalisation of Kazhdan's Property (T) onto lp(N) spaces. It is known that groups with Property F_lp share some properties with Kazhdan's groups, e.g. compact generation and compact abelianisation. During my talk I will prove that Property F_lp implies Property F_lq, provided that q
2014-11-20 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Piotr Nowak (IMPAN i MIMUW)Kazhdan's property (T) in Banach spaces
Kazhdan's property (T) is a classical notion with many spectacular applications in group theory, harmonic analysis and index theory. In this talk we will discuss the recent generalisations of property (T) to other Banach space and their applications.
2014-11-13 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Paweł Kasprzak (KMMF)Quantum groups with projection and extensions of locally compact quantum groups (II)
2014-11-06 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Paweł Kasprzak (KMMF)Quantum groups with projection and extensions of locally compact quantum groups
A locally compact quantum group with projection is a quantum counterpart of a semidirect product of groups. Such a group is a (trivial) extension of the image of the projection by the kernel of the projection. For a quantum group with a projection to be extension of the image of the projection a certain additional condition must be satisfied. We shall describe the following examples: U_q(2), quantum az+b groups and the dual of a classical group with projection . It will be shown that U_q(2) is an extension of one dimensional torus if and only if q is real and then U_q(2) is extension of one dimensional torus by SUq(2). Quantum 'az+b' is an extension of the image of the projection if and only if it is classical group. Finally the dual of a classical group is an extension of the dual of the image of the projection if and only if the group is a Cartesian product. This is joint work with P. Sołtan.The seminars take place in room 2.23 at the Physics Department, Pasteura 5 (II p.)P. Kasprzak, P.M. Sołtan, W Pusz.
A locally compact quantum group with projection is a quantum counterpart of a semidirect product of groups. Such a group is a (trivial) extension of the image of the projection by the kernel of the projection. For a quantum group with a projection to be extension of the image of the projection a certain additional condition must be satisfied. We shall describe the following examples: U_q(2), quantum az+b groups and the dual of a classical group with projection . It will be shown that U_q(2) is an extension of one dimensional torus if and only if q is real and then U_q(2) is extension of one dimensional torus by SUq(2). Quantum 'az+b' is an extension of the image of the projection if and only if it is classical group. Finally the dual of a classical group is an extension of the dual of the image of the projection if and only if the group is a Cartesian product. This is joint work with P. Sołtan.
2014-10-30 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Piotr M. Sołtan (KMMF)Quantum groups with projection on von Neumann algebra level, II
The seminars take place in room 2.23 at the Physics Department, Pasteura 5 (II p.)
2014-10-16 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Piotr M. Sołtan (KMMF)Quantum groups with projection on von Neumann algebra level
I will report on the recent work of Paweł Kasprzak and myself on locally compact quantum groups with projection which are non-commutative generalizations of semidirect products of locally compact groups.
2014-10-09 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Stanisław L. Woronowicz (KMMF)Różne oblicza regularności w teorii lokalnie zwartych grup kwantowych
On the various faces of regularity in the locally compact quantum groups theory
2014-10-02 (Czwartek)
Zapraszamy do sali 2.23, ul. Pasteura 5 o godzinie 13:15
Stanisław L. Woronowicz (KMMF)