Department of

# Mathematics

Seminar Calendar
for Operator Algebra Learning Seminar events the year of Monday, April 16, 2018.

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events for the
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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
      March 2018             April 2018              May 2018
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Monday, January 22, 2018

5:00 pm in Altgeld Hall 241,Monday, January 22, 2018

#### organization meeting

###### Marius Junge (UIUC)

Abstract: We are collecting talks on L_2-Betti numbers and special topics on type III von Neumann algebras

Monday, January 29, 2018

5:00 pm in 241 Altgeld Hall,Monday, January 29, 2018

#### Von Neumann Dimension and W*-Modules

###### Marius Junge (UIUC)

Abstract: We start our investigation on L2 Betti numbers by analyzing Hilbert modules over von Neumann algebras and their dimension function.

Monday, February 5, 2018

5:00 pm in 241 Altgeld Hall,Monday, February 5, 2018

#### The reduced C*algebra of the free product is simple

###### Li Gao (UIUC)

Abstract: We follow Connes' approach via cocycles proving this classical result.

Monday, February 12, 2018

5:00 pm in 241 Altgeld Hall,Monday, February 12, 2018

#### More on W*-modules

###### Marius Junge (UIUC)

Abstract: We study the von Neumann version of Hilbert C*-modules and their dimension.

Monday, February 19, 2018

5:00 pm in 241 Altgeld Hall,Monday, February 19, 2018

#### Modules and Cost

###### Marius Junge and Anush Tserunyan

Abstract: We will present some examples of Hilbert W*-modules and start with the cost of an equivalence relation.

Monday, February 26, 2018

5:00 pm in 241 Altgeld Hall,Monday, February 26, 2018

#### Type III Algebras and Noncommutative Integration

###### Thomas Scheckter (UNSW )

Abstract: We introduce some aspects of the theory of type III von Neumann algebras. We will begin by reviewing the basics of the classification of von Neumann algebras, and introduce some concrete constructions for type III algebras motivated by probability theory. We will then introduce the basics of modular theory, and outline the construction of Haagerup's noncommutative $L^p$ spaces.

Monday, March 5, 2018

5:00 pm in 241 Altgeld Hall,Monday, March 5, 2018

#### Cost and treeability of pmp equivalence relations

###### Anush Tserunyan (Illinois Math)

Abstract: We will continue the introduction to the theory of cost and discuss its relation to treeable probability measure preserving equivalence relations.

Monday, March 12, 2018

5:00 pm in 241 Altgeld Hall,Monday, March 12, 2018

#### More on equivalence relations

###### Anush Tserunyan (UIUC)

Abstract: We will finish the previous results and start with L_2-Betti numbers.

Monday, March 26, 2018

5:00 pm in 241 Altgeld Hall,Monday, March 26, 2018

#### $\ell_2$-(co)homology and $\ell_2$-Betti numbers

###### Anton Bernshteyn (Illinois Math)

Abstract: In this instalment of the Operator Algebra Learning Seminar, we will move on to talking about topological invariants that can by defined using Hilbert $\Gamma$-modules.

Monday, April 9, 2018

5:00 pm in 241 Altgeld Hall,Monday, April 9, 2018

#### An $\ell_2$-proof of Gaboriau's theorem

###### Anton Bernshteyn (Illinois Math)

Abstract: In this episode of the Operator Algebras Learning Seminar, we will finally put everything together and prove Gaboriau's "treeings realize cost" theorem using Hilbert modules and von Neumann dimension.

Monday, April 16, 2018

5:00 pm in 241 Altgeld Hall,Monday, April 16, 2018

#### An $\ell_2$-proof of Gaboriau's theorem II

###### Anton Bernshteyn (Illinois Math)

Abstract: Last time, we defined Hilbert $E$-modules and their von Neumann dimension. In this talk, we will apply this theory to prove that treeings realize cost.

Monday, April 23, 2018

5:00 pm in 241 Altgeld Hall,Monday, April 23, 2018

#### Summary of results using $\ell^2$-cohomology

###### Anush Tserunyan (Illinois Math)

Abstract: I will try to state and give references to various results in measured group theory that are based of $\ell^2$-cohomology à la D. Gaboriau.