Introductory School - IES Cargèse

Introductory School - IES Cargèse

Introductory School - IES Cargèse

Introductory School - IES Cargèse

Introductory School - IES Cargèse

Lecture series: A class of II$_1$ factors with no non-trivial crossed product decompositions

• Adrian Ioana (UCSD)

Room: Amphitheater Darboux/Hermite In this minicourse, I will present the first examples of separable II$_1$ factors $M$ that admit no non-trivial crossed product decompositions: $M\not\cong B\rtimes\sigma G$, for any trace-preserving action of an infinite countable group $G$ on a tracial von Neumann algebra $(B,\tau)$. Our approach relies on constructing separable II$_1$ factors $M$ with the strong rigidity property that every embedding of $M$ into $M\overline{\otimes}M$ arises from the canonical embeddings $x\mapsto x\otimes 1$ and $x\mapsto 1\otimes x$. I will also discuss the main deformation/rigidity and coarseness techniques used in the proof. This is joint work with Adriana Fernández Quero and Hui Tan.

Lecture series: A class of II$_1$ factors with no non-trivial crossed product decompositions

• Adrian Ioana (UCSD)

Room: Amphitheater Darboux/Hermite In this minicourse, I will present the first examples of separable II$_1$ factors $M$ that admit no non-trivial crossed product decompositions: $M\not\cong B\rtimes\sigma G$, for any trace-preserving action of an infinite countable group $G$ on a tracial von Neumann algebra $(B,\tau)$. Our approach relies on constructing separable II$_1$ factors $M$ with the strong rigidity property that every embedding of $M$ into $M\overline{\otimes}M$ arises from the canonical embeddings $x\mapsto x\otimes 1$ and $x\mapsto 1\otimes x$. I will also discuss the main deformation/rigidity and coarseness techniques used in the proof. This is joint work with Adriana Fernández Quero and Hui Tan.

Lecture series: A class of II$_1$ factors with no non-trivial crossed product decompositions

• Adrian Ioana (UCSD)

Room: Amphitheater Darboux/Hermite In this minicourse, I will present the first examples of separable II$_1$ factors $M$ that admit no non-trivial crossed product decompositions: $M\not\cong B\rtimes\sigma G$, for any trace-preserving action of an infinite countable group $G$ on a tracial von Neumann algebra $(B,\tau)$. Our approach relies on constructing separable II$_1$ factors $M$ with the strong rigidity property that every embedding of $M$ into $M\overline{\otimes}M$ arises from the canonical embeddings $x\mapsto x\otimes 1$ and $x\mapsto 1\otimes x$. I will also discuss the main deformation/rigidity and coarseness techniques used in the proof. This is joint work with Adriana Fernández Quero and Hui Tan.

Workshop 1: OA Groups and Dynamics Room: Amphitheater Darboux/Hermite

Workshop 1: OA Groups and Dynamics Room: Amphitheater Darboux/Hermite

Workshop 1: OA Groups and Dynamics Room: Amphitheater Darboux/Hermite

Workshop 1: OA Groups and Dynamics Room: Amphitheater Darboux/Hermite

Workshop 1: OA Groups and Dynamics Room: Amphitheater Darboux/Hermite

Lecture series: An introduction to higher (T)

• Uri Bader (University of Maryland)

Room: Amphitheater Darboux/Hermite We will study unitary cohomology, that is group cohomology with unitary representations coefficients, with special emphasis on criteria for their vanishing. This topic brings together group theory, homological algebra and operator theory. We will emphasize operator algebraic techniques.

Lecture series: An introduction to higher (T)

• Uri Bader (University of Maryland)

Room: Amphitheater Darboux/Hermite We will study unitary cohomology, that is group cohomology with unitary representations coefficients, with special emphasis on criteria for their vanishing. This topic brings together group theory, homological algebra and operator theory. We will emphasize operator algebraic techniques.

Lecture series: An introduction to higher (T)

• Uri Bader (University of Maryland)

Room: Amphitheater Darboux/Hermite We will study unitary cohomology, that is group cohomology with unitary representations coefficients, with special emphasis on criteria for their vanishing. This topic brings together group theory, homological algebra and operator theory. We will emphasize operator algebraic techniques.

Seminar - Operator Algebras Room: Amphitheatre Darboux

Seminar - Operator Algebras Room: Amphitheatre Darboux

Seminar - Operator Algebras Room: Amphitheatre Darboux

Workshop 2: OA Matricial Approximations Room: Amphitheater Darboux/Hermite

Workshop 2: OA Matricial Approximations Room: Amphitheater Darboux/Hermite

Workshop 2: OA Matricial Approximations Room: Amphitheater Darboux/Hermite

Workshop 2: OA Matricial Approximations Room: Amphitheater Darboux/Hermite

Workshop 2: OA Matricial Approximations Room: Amphitheater Darboux/Hermite

Seminar - Operator Algebras Room: Amphitheatre Darboux

Seminar - Operator Algebras Room: Amphitheatre Darboux

Seminar - Operator Algebras Room: Amphitheatre Darboux

Seminar - Operator Algebras Room: Amphitheatre Darboux

Workshop 3: OA Rigidity and Classification Room: Amphitheater Darboux/Hermite

Workshop 3: OA Rigidity and Classification Room: Amphitheater Darboux/Hermite

Workshop 3: OA Rigidity and Classification Room: Amphitheater Darboux/Hermite

Workshop 3: OA Rigidity and Classification Room: Amphitheater Darboux/Hermite

Workshop 3: OA Rigidity and Classification Room: Amphitheater Darboux/Hermite