Fall 2021

* Organisers*

Marcel de Jeu (mdejeu@math.leidenuniv.nl)

Bram Mesland (b.mesland@math.leidenuniv.nl)

Jan Harm van der Walt (janharm.vanderwalt@up.ac.za)

*Contact*

If you are interested, please contact Marcel de Jeu, Bram Mesland, or Jan Harm van der Walt.

*Intended for*

Students, PhD students, and faculty.

*Prerequisites*

Proficiency in the functional analytic language at the level corresponding to a solid `pass' for the national functional analysis course in the Mastermath programme. An introductory course in functional analysis is *not* sufficient.

*Literature*

Vern Paulsen: *Completely bounded maps and operator algebras*. Cambridge Studies in Advanced Mathematics, 78. Cambridge University Press, Cambridge, 2002. ISBN: 0-521-81669-6.

*Lecture 1*: 1 October 2021, 16.15-18.00, Snellius room 401: Bram Mesland

Chapter 1: Introduction.

Pictures of the blackboards are herec

*Lecture 2*: 8 October 2021, 15.15-17.00, Gorlaeus Lecture Hall room C7: Chun Ding

Chapter 2: Positive maps.

Notes are here.

*Lecture 3*: 15 October 2021, 15.00-17.00, Gorlaeus Lecture Hall room C7: Jack Ekenstamm

Chapter 3: Completely positive maps.

Pictures of the blackboards are here; notes are here.

* Lecture 4*: 22 October 2021, 15.00-17.00, Gorlaeus Lecture Hall room C7: Yufan Ge

Chapter 4: Dilation theorems.

Pictures of the blackboards are here.

*Lecture 5*: 5 November 2021, 15.00-17.00, Gorlaeus Lecture Hall room C7: Jesse Reimann

Chapter 5: Commuting contractions on Hilbert space.

Pictures of the blackboards are here; notes are here.

* Lecture 6*: 12 November 2021, 15.00-17.00, Gorlaeus Lecture Hall room C7: Mick Gielen

Chapter 6: Completely positive maps into M_n.

Pictures of the blackboards are here; notes are here.

*Lecture 7*: 19 November 2021, 15.00-17.00, Gorlaeus Lecture Hall room C7: Rui Dong

Chapter 7: Arveson's extension theorems.

Pictures of the blackboards are here.

*Lecture 8*: 26 November 2021, 15.00-17.00, Gorlaeus Lecture Hall room C7: Yuezhao Li

Chapter 8: Completely bounded maps.

Pictures of the blackboards are here; the handout is here.

*Lecture 9*: 3 December 2021, 15.00-17.00, Gorlaeus Lecture Hall room C7: Matthijs Vernooij

Chapter 9: Completely bounded homomorphisms.

Pictures of the blackboards are here.

*Lecture 10*:17 December 2021, 15.00-17.00, Gorlaeus Lecture Hall room C7: Onno van Gaans

Chapter 10: Polynomially bounded and power-bounded operators.

Pictures of the blackboards are here.

*Lecture 11*: 21 January 2022, 15.00-17.00, Snellius room 401: Malte Leimbach

Chapter 12: Tensor products and joint spectral sets.

Pictures of the blackboards are here.

*Lecture 12*: 28 January 2022, 15.00-17.00, Snellius room 312: Miek Messerschmidt

Chapter 13: Abstract characterizations of operator systems and operator spaces.

Pictures of the blackboards are here.