Operator Algebra Seminar

Abstract: Haag duality is a simple property of algebras attached to regions in QFT that expresses a form of completeness of the theory. Violations of Haag duality are due to "non-local operators".  These may be charged with respect to global symmetries. When this happens for a continuous symmetry there is an obstruction for the validity of Noether's theorem. This is behind all known examples when the Noether current is absent, including the ones covered by Weinberg-Witten theorem. An abstract classification of the simplest possibilities is divided into two classes. In the first one there are non compact sectors, which leads to free models. The other possibility, allowing interacting models, corresponds to the ABJ anomaly. This interpretation unifies the features of the anomaly --- anomaly matching, anomaly quantization, non-existence of the Noether current, and validity of Goldstone theorem --- from a symmetry based perspective.

Abstract: we discuss the emergence of logarithmic Sobolev inequalities from energy/entropy inequalities and then derive from them the existence and uniqueness of the ground state of Hamiltonians as well the spectral gap. The method is an infinitesimal extension of the one introduced by Len Gross in case the ground state is a probability or a trace and is based on the monotonicity of the relative entropy.

Abstract:  The duality between algebraic structures and geometric spaces is of paramount importance in mathematics and physics, because provides a dictionary to describe manifolds and variaties in a purely algebraic fashion. In his seminal paper, Gelfand showed that a topological space can be functorially reconstructed from its Banach algebra of continuous functions. Conversely, the Gelfand spectrum of the algebra of continuous functions is homeomorphic to the underlying topological space.

The goal of this talk is to constrcut a sufficiently robust notion of spectrum for general rings that allows one to implement a noncommutative analog of Gelfand duality. Our notion of spectrum, although formally reminiscent of the Grothendieck spectrum, is new. Remarkably, an appropriately refined relative version of our spectrum agrees with the Grothendieck spectrum for finitely generated commutative algebras over the complex numbers, among others. 

This is a joint project with Federico Bambozzi and Matteo Capoferri.

• Pierre Bieliavsky (UCLovain)

 Geometric methods for locally compact quantum groups

Dec 20, 2023, h 16:00
Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Christopher J Fewster (University of York)

Exact measurement schemes for local observables and the preparation of physical local product states

Dec 12, 2023, h 16:00
Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Rainer Verch (Uni. Leipzig)

Relative entropy for states on the CAR algebra

Nov 29, 2023, h 16:00
Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Yuto Moriwaki (Riken, Wako, Japan)
  Operator product expansion in two-dimension conformal field theory
  
  Nov 22, 2023, h 16:00
  Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Valerio Proietti (University of Oslo)
  Nonlocal games and Grothendieck's inequalities
  
  Oct 18, 2023, h 16:00
  Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Timothy Rainone (Occidental College)
  The Matricial Field property in cross-sectional C*-algebras
  
  Jul 14, 2023, h 15:00
  Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Maria Stella Adamo (The University of Tokyo)
  Wightman fields and their construction for 2D CFTs with pointed representation categories
  
  Jun 28, 2023, h 16:00
  Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Claudio Dappiaggi (University of Pavia)
  Stochastic partial differential equations and renormalization à la Epstein-Glaser
  
  Jun 7, 2023, h 16:00
  Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Karl-Hermann Neeb (FAU Erlangen-Nürnberg)
  Causal symmetric spaces and nets of operator algebras
  
  Mar 29, 2023, h 16:00
  Aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata

• Yasuyuki Kawahigashi (The University of Tokyo)
  α-induction for bi-unitary connections
  
  Mar 15, 2023, h 17:00
  Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Mizuki Oikawa (The University of Tokyo)
  New center construction and α-induction for equivariantly braided tensor categories
  
  Mar 15, 2023, h 16:00
  Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Roberto Conti (Università Sapienza di Roma)
  Heat properties for groups
  
  Jan 21, 2023, h 16:00
  Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Luca Giorgetti (Università di Roma Tor Vergata)
  A planar algebraic description of conditional expectations
  
  Dec 3, 2021, h 16:00
  Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Erik Tonni (SISSA)
  Modular Hamiltonians for the massless Dirac field in the presence of a boundary or of a defect
  
  Oct 27, 2021, h 16:00
  Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Jean-Luc Sauvageot, (Institut de Mathématiques de Jussieu)
  Misurabilità, densità spettrali e tracce residuali in geometria non commutativa
  
  Oct 20, 2021, h 16:00
  Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Edoardo D'Angelo (University of Genova)
  Role of the relative entropy in the entropy of dynamical black holes
  
  Oct 6, 2021, h 16:00
  Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Christian Gass (University of Göttingen)
  Renormalization in string-localized field theories: a microlocal analysis
  
  Sep 24, 2021, h 16:00
  Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata

• Maria Stella Adamo (Sapienza University of Rome)
  Reflection positive representations and Hankel operators in the multiplicity free case
  
  Jul 14, 2021, h 16:00
  online seminar

• Aleksei Bykov (Tor Vergata University of Rome)
  Hamiltonian approach to QFT on quantum spacetime and its adiabatic limits
  
  Jul 7, 2021, h 16:00
  online seminar

• Daniele Guido (Tor Vergata University of Rome)
  Noncommutative self-similar fractals as self-similar C*-algebras
  
  Jun 30, 2021, h 16:00
  online seminar

• Nicola Pinamonti (University of Genova)
  Sine-Gordon fields with non vanishing mass on Minkowski spacetime and equilibrium states
  
  Jun 16, 2021, h 16:00
  online seminar

• Laszlo Zsido (Tor Vergata University of Rome)
  On the equality and inequality of weights and operator valued weights
  
  Jun 9, 2021, h 16:00
  online seminar

• Detlev Buchholz (Universität Göttingen)
  Resolvent algebras and Bose-Einstein-condensation
  
  Jun 3, 2021, h 16:00
  online seminar

• Fabio Cipriani (Politecnico di Milano)
  Densities and their measurability in NCG
  
  May 26, 2021, h 16:00
  online seminar

• Jacopo Bassi (Tor Vergata University of Rome)
  Amenability properties for SL(3,Z)
  
  May 12, 2021, h 16:00
  online seminar

• Gerardo Morsella (Tor Vergata University of Rome)
  UV and IR finiteness on quantum spacetime through perturbative algebraic QFT
  
  Mar 31, 2021, h 16:00
  online seminar

• Lorenzo Panebianco (Tor Vergata University of Rome)
  Quantum Null Energy Condition on conformal nets
  
  Mar 24, 2021, h 16:00
  online seminar

• Alexander Stottmeister (Univ. of Hannover)
  Operator-algebraic renormalization, fermions and conformal field theory
  
  Mar 3, 2021, h 16:00
  online seminar

• Benedikt Wegener (Tor Vergata University of Rome)
  Modular operator for null plane algebras in free fields
  
  Feb 24, 2021, h 16:00
  online seminar

• Yoh Tanimoto (Tor Vergata University of Rome)
  Towards integral perturbation of two-dimensional CFT
  
  Feb 10, 2021, h 16:00
  online seminar

• Vincenzo Morinelli (Tor Vergata University of Rome)
  Covariant Homogeneous nets of standard subspaces
  
  Feb 3, 2021, h 16:00
  online seminar