Department of

# Mathematics

Seminar Calendar
for Operator Algebra Learning Seminar events the year of Friday, September 14, 2018.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2018           September 2018          October 2018
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4                      1       1  2  3  4  5  6
5  6  7  8  9 10 11    2  3  4  5  6  7  8    7  8  9 10 11 12 13
12 13 14 15 16 17 18    9 10 11 12 13 14 15   14 15 16 17 18 19 20
19 20 21 22 23 24 25   16 17 18 19 20 21 22   21 22 23 24 25 26 27
26 27 28 29 30 31      23 24 25 26 27 28 29   28 29 30 31
30


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

#### Organizational meeting

Monday, September 10, 2018

5:00 pm in 241 Altgeld Hall,Monday, September 10, 2018

#### Slow continued fractions and permutative representations of Cuntz algebras

###### Chris Linden

Abstract: We will also discuss organization and start with Chris Talk Following the work of Bratteli and Jorgensen, I will show how permutative representations of the Cuntz algebras $\mathcal{O}_n$ arise from iterated function systems. I will then discuss a special case of this construction studied by Hayashi, Kawamura and Lascu where the function system is the Gauss map, which allows all (unitary equivalence classes of) irreducible permutative representations of $\mathcal{O}_{\infty}$ to be labeled by the orbits of a $PGL_2(\mathbb{Z})$ action. Finally, I will discuss my own work which extends this construction to $2 \leq n < \infty$ with the help of slow continued fraction algorithms.

Monday, September 17, 2018

5:00 pm in 241 Altgeld Hall,Monday, September 17, 2018

#### Slow continued fractions and permutative representations of Cuntz algebras

###### (UIUC)

Abstract: Following the work of Bratteli and Jorgensen, I will show how permutative representations of the Cuntz algebras $\mathcal{O}_n$ arise from iterated function systems. I will then discuss a special case of this construction studied by Hayashi, Kawamura and Lascu where the function system is the Gauss map, which allows all (unitary equivalence classes of) irreducible permutative representations of $\mathcal{O}_{\infty}$ to be labeled by the orbits of a $PGL_2(\mathbb{Z})$ action. Finally, I will discuss my own work which extends this construction to $2 \leq n < \infty$ with the help of slow continued fraction algorithms.