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Operator Algebra Seminars
Seminar information archive ～03/13｜Next seminar｜Future seminars 03/14～
| Date, time & place | Wednesday 16:30 - 18:00 122Room #122 (Graduate School of Math. Sci. Bldg.) |
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Seminar information archive
2011/11/22
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Spyridon Michalakis ( Institute for Quantum Information and Matter (Caltech))
Stability of topological phases of matter (ENGLISH)
Spyridon Michalakis ( Institute for Quantum Information and Matter (Caltech))
Stability of topological phases of matter (ENGLISH)
[ Abstract ]
The first lecture will be an introduction to quantum mechanics and a proof of Lieb-Robinson bounds for constant range interaction Hamiltonians. The second lecture will build on the first to prove a powerful lemma on the transformation of the interactions of generic gapped Hamiltonians to a new set of rapidly-decaying interactions that commute with the groundstate subspace. I call this "The Energy Filtering Lemma". Then, the third lecture will be on the construction of the Spectral Flow unitary (Quasi-adiabatic evolution) and its properties; in particular, the perfect simulation of the evolution of the groundstate subspace within a gapped path. I will end with a presentation of the recent result on the stability of the spectral gap for frustration-free Hamiltonians, highlighting how the previous three lectures fit into the proof.
The first lecture will be an introduction to quantum mechanics and a proof of Lieb-Robinson bounds for constant range interaction Hamiltonians. The second lecture will build on the first to prove a powerful lemma on the transformation of the interactions of generic gapped Hamiltonians to a new set of rapidly-decaying interactions that commute with the groundstate subspace. I call this "The Energy Filtering Lemma". Then, the third lecture will be on the construction of the Spectral Flow unitary (Quasi-adiabatic evolution) and its properties; in particular, the perfect simulation of the evolution of the groundstate subspace within a gapped path. I will end with a presentation of the recent result on the stability of the spectral gap for frustration-free Hamiltonians, highlighting how the previous three lectures fit into the proof.
2011/11/17
16:30-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Takehiko Yamanouchi (Tokyo Gakugei University)
Hecke pairs in ergodic measured equivalence relations (JAPANESE)
Takehiko Yamanouchi (Tokyo Gakugei University)
Hecke pairs in ergodic measured equivalence relations (JAPANESE)
2011/10/07
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Takeshi Katsura (Keio University)
Towards the classification of non-simple $C^*$-algebras of real rank zero (ENGLISH)
Takeshi Katsura (Keio University)
Towards the classification of non-simple $C^*$-algebras of real rank zero (ENGLISH)
2011/07/21
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Jean Roydor (Univ. Tokyo)
Almost completely isometric maps and applications (ENGLISH)
Jean Roydor (Univ. Tokyo)
Almost completely isometric maps and applications (ENGLISH)
2011/07/14
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Raphael Ponge (IPMU)
New perspectives for the local index formula in noncommutative geometry (ENGLISH)
Raphael Ponge (IPMU)
New perspectives for the local index formula in noncommutative geometry (ENGLISH)
2011/06/16
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Yusuke Isono (Univ. Tokyo)
Introduction to rigidity theory of von Neumann algebras (JAPANESE)
Yusuke Isono (Univ. Tokyo)
Introduction to rigidity theory of von Neumann algebras (JAPANESE)
2011/06/09
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Hiroaki Yoshida (Ochanomizu Univ.)
On the free Fisher information distance and the free logarithmic Sobolev inequality (JAPANESE)
Hiroaki Yoshida (Ochanomizu Univ.)
On the free Fisher information distance and the free logarithmic Sobolev inequality (JAPANESE)
2011/04/14
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Masayoshi Matsumura (Univ. Tokyo)
Amenable actions and crossed products of $C^*$-algebras (JAPANESE)
Masayoshi Matsumura (Univ. Tokyo)
Amenable actions and crossed products of $C^*$-algebras (JAPANESE)
2011/02/18
10:30-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Pedram Hekmati (Univ. Adelaide)
Dirac families and 1-cocycles (ENGLISH)
Pedram Hekmati (Univ. Adelaide)
Dirac families and 1-cocycles (ENGLISH)
[ Abstract ]
Families of Dirac type operators, transforming covariantly under the projective action of the loop group $LG$, determine a class in twisted K-theory on compact Lie groups $G$. The loop group is the gauge group of a principal $G$-bundle over the circle and an interesting problem is to try to generalise the circle to a higher dimensional compact manifold. This is far from obvious and some of the difficulties can be modelled in a slightly simpler setting, by replacing $LG$ and gauge connections by objects which have only small differentiability in the Sobolev sense. In this talk, I will provide some background to this problem and explain how 1-cocycles naturally appear in this construction.
Families of Dirac type operators, transforming covariantly under the projective action of the loop group $LG$, determine a class in twisted K-theory on compact Lie groups $G$. The loop group is the gauge group of a principal $G$-bundle over the circle and an interesting problem is to try to generalise the circle to a higher dimensional compact manifold. This is far from obvious and some of the difficulties can be modelled in a slightly simpler setting, by replacing $LG$ and gauge connections by objects which have only small differentiability in the Sobolev sense. In this talk, I will provide some background to this problem and explain how 1-cocycles naturally appear in this construction.
2011/02/10
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Alan Weinstein (UC Berkeley)
Symplectic and quantum categories (ENGLISH)
Alan Weinstein (UC Berkeley)
Symplectic and quantum categories (ENGLISH)
2011/01/28
14:45-16:15 Room #122 (Graduate School of Math. Sci. Bldg.)
Takeshi Katsura (Keio University)
Semiprojectivity of graph algebras (ENGLISH)
Takeshi Katsura (Keio University)
Semiprojectivity of graph algebras (ENGLISH)
2011/01/27
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Hiroshi Takai (Tokyo Metropolitan University)
Entire Cyclic Cohomology of Noncommutative Riemann Surfaces (JAPANESE)
Hiroshi Takai (Tokyo Metropolitan University)
Entire Cyclic Cohomology of Noncommutative Riemann Surfaces (JAPANESE)
2011/01/20
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Masato Mimura (Univ. Tokyo)
Property (TT)/T and homomorphism rigidity into Out$(F_n)$ (JAPANESE)
Masato Mimura (Univ. Tokyo)
Property (TT)/T and homomorphism rigidity into Out$(F_n)$ (JAPANESE)
2011/01/18
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Claude-Alain Pillet (Univ. de Toulon et du Var)
Scattering induced current in a tight binding band (ENGLISH)
Claude-Alain Pillet (Univ. de Toulon et du Var)
Scattering induced current in a tight binding band (ENGLISH)
2011/01/13
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Robert Coquereaux (CNRS/CPT)
Global dimensions for fusion categories of type $(G,k)$ (ENGLISH)
Robert Coquereaux (CNRS/CPT)
Global dimensions for fusion categories of type $(G,k)$ (ENGLISH)
2011/01/11
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Raphael Ponge (Univ. Tokyo)
Noncommutative geometry and diffeomorphism-invariant geometries (ENGLISH)
Raphael Ponge (Univ. Tokyo)
Noncommutative geometry and diffeomorphism-invariant geometries (ENGLISH)
2010/12/16
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Marco Merkli (Memorial Univ. Newfoundland)
Evolution of Quantum Dynamical Systems (ENGLISH)
Marco Merkli (Memorial Univ. Newfoundland)
Evolution of Quantum Dynamical Systems (ENGLISH)
2010/12/16
15:15-16:15 Room #122 (Graduate School of Math. Sci. Bldg.)
Nicolas Monod (EPFL)
Fixed point theorems and derivations (ENGLISH)
Nicolas Monod (EPFL)
Fixed point theorems and derivations (ENGLISH)
2010/12/09
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Ryszard Nest (Univ. Copenhagen)
Spectral flow associated to KMS states with periodic KMS group action (ENGLISH)
Ryszard Nest (Univ. Copenhagen)
Spectral flow associated to KMS states with periodic KMS group action (ENGLISH)
2010/11/30
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Yi-Jun Yao (Fudan Univ.)
Noncommutative geometry and Rankin-Cohen brackets (ENGLISH)
Yi-Jun Yao (Fudan Univ.)
Noncommutative geometry and Rankin-Cohen brackets (ENGLISH)
2010/11/25
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Reiji Tomatsu (Tokyo Univ. Science)
Classification of actions of Kac algebras (JAPANESE)
Reiji Tomatsu (Tokyo Univ. Science)
Classification of actions of Kac algebras (JAPANESE)
2010/11/18
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Jean Roydor (Univ. Tokyo)
Perturbation of dual operator algebras and similarity (ENGLISH)
Jean Roydor (Univ. Tokyo)
Perturbation of dual operator algebras and similarity (ENGLISH)
2010/11/04
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Yoshiko Ogata (Univ.Tokyo)
Nonequilibrium Statistical Mechanics (JAPANESE)
Yoshiko Ogata (Univ.Tokyo)
Nonequilibrium Statistical Mechanics (JAPANESE)
2010/10/28
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Makoto Yamashita (Univ. Tokyo)
Type III representations of the infinite symmetric group (ENGLISH)
Makoto Yamashita (Univ. Tokyo)
Type III representations of the infinite symmetric group (ENGLISH)
[ Abstract ]
Based on earlier results about the structure of the II$_1$ representations of the infinite symmetric group, we investigate its type III representations and the related inclusion of von Neumann algebras of type III.
Based on earlier results about the structure of the II$_1$ representations of the infinite symmetric group, we investigate its type III representations and the related inclusion of von Neumann algebras of type III.
2010/10/21
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Benoit Collins (Univ. Ottawa)
Free probability and entropy additivity problems for Quantum information theory (ENGLISH)
Benoit Collins (Univ. Ottawa)
Free probability and entropy additivity problems for Quantum information theory (ENGLISH)
