Department of

# Mathematics

Seminar Calendar
for Operator Algebra Learning Seminar events the year of Thursday, October 10, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2019          October 2019          November 2019
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  5  6  7          1  2  3  4  5                   1  2
8  9 10 11 12 13 14    6  7  8  9 10 11 12    3  4  5  6  7  8  9
15 16 17 18 19 20 21   13 14 15 16 17 18 19   10 11 12 13 14 15 16
22 23 24 25 26 27 28   20 21 22 23 24 25 26   17 18 19 20 21 22 23
29 30                  27 28 29 30 31         24 25 26 27 28 29 30



Monday, January 28, 2019

5:00 pm in 241 Altgeld Hall,Monday, January 28, 2019

#### Quantum Null Energy Conjecture

###### Tom Faukner (UIUC physics)

Abstract: We will explain and discuss a recent result on the Quantum Null Energy Conjecture

Monday, February 4, 2019

5:00 pm in 241 Altgeld Hall,Monday, February 4, 2019

#### A brief introduction to differential and Riemannian geometry

Monday, February 11, 2019

5:00 pm in 241 Altgeld Hall,Monday, February 11, 2019

#### Introduction to differential and Riemannian geometry part II

Monday, February 18, 2019

5:00 pm in 241 Altgeld Hall,Monday, February 18, 2019

#### Introduction to differential and Riemannian geometry part III

Monday, February 25, 2019

5:00 pm in 241 Altgeld Hall,Monday, February 25, 2019

#### Curvature in Riemannian geometry

Monday, March 4, 2019

5:00 pm in 241 Altgeld Hall,Monday, March 4, 2019

#### Curvatures of Riemannian Lie groups

Monday, March 11, 2019

5:00 pm in 241 Altgeld Hall,Monday, March 11, 2019

#### Riemannian geometry and Clifford algebras

###### Nijholt, Eeltje Cornelis (UIUC)

Monday, March 25, 2019

5:00 pm in 241 Altgeld Hall,Monday, March 25, 2019

#### Riemannian geometry and Clifford algebras II

###### Nijholt, Eeltje Cornelis (UIUC)

Monday, April 15, 2019

5:00 pm in 241 Altgeld Hall,Monday, April 15, 2019

#### Complete Logarithmic Sobolev Inequalities (CSLI) and Ricci Curvature

###### Haojian Li (UIUC)

Abstract: First we would continue Eddie's talk and start with how the connection on a G-bundle induces a connection on the associated bundle naturally. Then a brief introduction about the quantum information will be included. We would focus on formulating the CLSI problem today and show that the CLSI constants depend on the lower bound of Ricci curvature. If time permits, we would also apply our machinery to Hormander system.

Monday, April 22, 2019

5:00 pm in Altgeld Hall,Monday, April 22, 2019

#### The complete logarithmic Sobolev inequality and Ricci curvature.

###### Haojian Li (UIUC)

Abstract: Today we are going to prove the main theorem and show how the lower bound of Ricci curvature get involved with algebra.

Monday, April 29, 2019

5:00 pm in 241 Altgeld Hall,Monday, April 29, 2019

#### Khalkali's notion of Ricci curvature in rotation algebras

###### Marius Junge (UIUC)

Abstract: As promised, we finish our exploration on Ricci curvature in operator algebras today. We may start 5minutes late.

Monday, September 9, 2019

5:00 pm in 241 Altgeld Hall,Monday, September 9, 2019

#### What can be in an IGL project on C*-algebras?

###### Chris Linden (UIUC)

Abstract: Report on IGL project in C*-algebras by Chris Linden

Monday, September 16, 2019

5:00 pm in 241 Altgeld Hall,Monday, September 16, 2019

#### Stability property of conditional probabilities

###### Chris Linden (UIUC)

Abstract: We will present the second part on different forms of equivalences for conditional probabilities developed in the IGL project last semester.

Monday, September 23, 2019

5:00 pm in 241 Altgeld Hall,Monday, September 23, 2019

#### Boundary Representations

###### Chris Linden (UIUC)

Abstract: We will continue the discussion of boundary of previously considered operator algebras, and launch into Arveson’s general general.

Monday, October 7, 2019

5:00 pm in 241 Altgeld Hall,Monday, October 7, 2019

#### Some properties of alpha fidelities.

###### Xiaojing Yan

Abstract: The alpha fidelities constitute a family of information measures that generalize the well-known fidelity, inheriting many of its properties. In the first half of the talk, we will introduce some natural properties for quantum alpha fidelities, including data-processing inequalities and monotonicity and so on. In the second, we will calculate the quantum α-fidelity between unitary orbits.

Monday, October 14, 2019

5:00 pm in 241 Altgeld Hall,Monday, October 14, 2019

#### The Dixmier Trace

###### Haojian Li (UIUC)

Abstract: We will construct so-called exotic traces on the space of bounded operators on a Hilbert space, the so called Dixmier traces. In the long run we are interested in geometric applications of Connes' Dixmier trace calculus.

Monday, October 21, 2019

5:00 pm in 243 Altgeld Hall,Monday, October 21, 2019

#### Dixmier Trace

###### Haojian Li

Abstract: Diximer traces, heat kernel, and Zeta functions.

Monday, October 28, 2019

5:00 pm in 241 Altgeld Hall ,Monday, October 28, 2019

#### The Dixmier trace

###### Haojian Li (UIUC)

Abstract: The interplay between heat kernel functional, zeta function and the Dixmier trace. If time permits, I would also introduce pseudo differential operator.

Monday, November 4, 2019

5:00 pm in 241 Altgeld Hall,Monday, November 4, 2019

#### The Dixmier trace

###### Haojian Li (University of Illinois at Urbana-Champaign)

Abstract: I would introduce pseudo-differential operators and noncommutative residues. The calculus of pseudo-differential operators is the prototype of Alain Connes' quantum calculus in noncommutative geometry. Mariusz Wodzicki defined the non-commutative residue on the classical compactly supported pseudo differential operators by integrating the principal symbol. Connes gave the first result to identify Wodzicki residue with a singular trace, i.e., so-called Dixmier trace. This result is considered as the foundation of the noncommutative geometry.

Monday, November 11, 2019

5:00 pm in 241 Altgeld Hall,Monday, November 11, 2019

#### CLSI of graphs

###### Nicholas LaRacuente (University of Illinois at Urbana-Champaign)

Abstract: Quantum Markov semigroups (QMSs) model continuous time-evolution of quantum states exposed to environmental noise. A key aspect of a selfadjoint QMS is how quickly an arbitrary state or density decays toward an invariant fixed point algebra. A modified logarithmic Sobolev inequality (MLSI) quantifies exponential decay of relative entropy with respect to the fixed point algebra. A complete logarithmic Sobolev inequality (CLSI) does so in the presence of an arbitrary auxiliary system that is untouched by decay. I will describe our recent proof that error models described by finite graphs have CLSI. This follows joint work with Marius Junge and Haojian Li.

Monday, November 18, 2019

5:00 pm in 241 Altgeld Hall,Monday, November 18, 2019

#### Graph Hormanders

###### Marius Junge (University of Illinois at Urbana-Champaign)

Abstract: I would talk about the link between graph Laplacians and Hormander systems of orthogonal groups.

Monday, December 2, 2019

5:00 pm in 241 Altgeld Hall,Monday, December 2, 2019

#### Dixmier Trace

###### Haojian Li (UIUC)

Abstract: 1. Recap some basic facts of pseudo differential operators. 2. Pseudo differential calculus. (adjoint and multiplication) 3. Regularity. 4. Modulated operator. (if time permitting)

Monday, December 9, 2019

5:00 pm in 241 Altgeld Hall,Monday, December 9, 2019

#### The Dixmier trace

###### Haojian Li (University of Illinois at Urbana-Champaign)

Abstract: 1. Banach algebra of modulated functions. 2. Extension of the non-commutative residue.

Monday, December 16, 2019

5:00 pm in 241 Altgeld Hall,Monday, December 16, 2019

#### No talk this week!

Abstract: See you next semester!