Department of

Mathematics


Seminar Calendar
for Operator Algebra Learning Seminar events the year of Friday, November 9, 2018.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
     October 2018          November 2018          December 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

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.

Monday, September 24, 2018

5:00 pm in 241 Altgeld Hall,Monday, September 24, 2018

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

Chris Linden (UIUC)

Abstract: Continuation from last week

Monday, October 1, 2018

5:00 pm in 241 Altgeld Hall,Monday, October 1, 2018

Introduction to quantum relative entropy

Marius Junge

Abstract: We will review basic properties of von Neumann entropy and quantum relative entropy.

Monday, October 8, 2018

5:00 pm in 241 Altgeld Hall,Monday, October 8, 2018

On Talagrand's deviation inequality for product measures

Pavlos Motakis (UIUC)

Abstract: We follow Ledoux's approach to deviation inequalities.

Monday, October 15, 2018

5:00 pm in 241 Altgeld Hall,Monday, October 15, 2018

On Talagrand's deviation inequality for product measures

Pavlos Motakis (UIUC)

Abstract: We follow Ledoux's approach to deviation inequalities.

Monday, October 22, 2018

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

On Talagrand's deviation inequality for product measures, II

Abstract: We follow Ledoux's approach to deviation inequalities.

Monday, November 5, 2018

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

Noncommutative Talagrand inequality

Marius Junge (UIUC)

Abstract: We wll show how formulate and proof mareix valued versions of Talagrand type concentration inequalities.