Department of

Mathematics


Seminar Calendar
for Operator Algebra Learning Seminar events the year of Saturday, October 19, 2019.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
    September 2019          October 2019          November 2019    
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  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
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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

Adam Dor-On (UIUC)

Monday, February 11, 2019

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

Introduction to differential and Riemannian geometry part II

Adam Dor-On (UIUC)

Monday, February 18, 2019

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

Introduction to differential and Riemannian geometry part III

Adam Dor-On (UIUC)

Monday, February 25, 2019

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

Curvature in Riemannian geometry

Adam Dor-On (UIUC)

Monday, March 4, 2019

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

Curvatures of Riemannian Lie groups

Adam Dor-On (UIUC)

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 Arvesonís 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.