Seminar Calendar
for Analytic Aspects of Quantum Groups events the next 12 months of Friday, August 1, 2008.

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Questions regarding events or the calendar should be directed to Tori Corkery. 
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                        31

Tuesday, September 16, 2008

Analytic Aspects of Quantum Groups
3:00 pm   in 130 Lincoln Hall,  Tuesday, September 16, 2008
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Pierre Fima   [email] (Department of Mathematics, University of Illinois)
Introduction to compact quantum groups
Abstract: This talk is a basic introduction to compact quantum groups. I will give the definition and the examples coming from classical compact and discrete groups. Next I will show that every commutative compact quantum group is a compact group. Finally I will introduce the notion of compact quantum group of matrices and give some examples.

Tuesday, September 23, 2008

Analytic Aspects of Quantum Groups
3:00 pm   in 130 Lincoln Hall,  Tuesday, September 23, 2008
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Pierre Fima (UIUC Math)
Introduction to compact quantum groups, II
Abstract: In the last talk I gave the definition of a compact quantum group. In this talk I will explain explicit examples.

Tuesday, September 30, 2008

Analytic Aspects of Quantum Groups
3:00 pm   in 130 Lincoln Hall,  Tuesday, September 30, 2008
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Tom Cooney (Department of Mathematics, University of Illinois)
The Haar Measure on a Compact Quantum Group
Abstract: We will prove the existence of the Haar measure on a compact quantum group.

Tuesday, October 7, 2008

Analytic Aspects of Quantum Groups
3:00 pm   in 130 Lincoln Hall,  Tuesday, October 7, 2008
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Florin Boca (Department of Mathematics, University of Illinois)
Unitary representations of compact quantum groups
Abstract: In preparation for the Peter-Weyl theorem I plan to discuss the (right) regular representation of a compact quantum group and some elements of representation theory.

Tuesday, October 14, 2008

Analytic Aspects of Quantum Groups
3:00 pm   in 130 Lincoln Hall,  Tuesday, October 14, 2008
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Florin Boca (Department of Mathematics, University of Illinois)
Unitary representations of compact quantum groups II
Abstract: We will speak about the Peter-Weyl theory for unitary representations of a compact quantum group.

Tuesday, October 21, 2008

Analytic Aspects of Quantum Groups
3:00 pm   in 130 Lincoln Hall,  Tuesday, October 21, 2008
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Florin Boca (Department of Mathematics, University of Illinois)
Unitary representations of compact quantum groups III
Abstract: We will prove the Peter-Weyl Theorem for unitary representations of a compact quantum group

Tuesday, October 28, 2008

Analytic Aspects of Quantum Groups
3:00 pm   in 130 Lincoln Hall,  Tuesday, October 28, 2008
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Florin Boca (UIUC Math)
Unitary representations of compact quantum groups IV

Tuesday, November 4, 2008

Analytic Aspects of Quantum Groups
3:00 pm   in 130 Lincoln Hall,  Tuesday, November 4, 2008
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Florin Boca (Department of Mathematics, University of Illinois)
Unitary representations of compact quantum groups V

Tuesday, November 11, 2008

Analytic Aspects of Quantum Groups
3:00 pm   in 130 Lincoln Hall,  Tuesday, November 11, 2008
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Florin Boca (UIUC Math)
Unitary representations of compact quantum groups VI

Tuesday, November 18, 2008

Analytic Aspects of Quantum Groups
3:00 pm   in 130 Lincoln Hall,  Tuesday, November 18, 2008
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Steve Avsec (Department of Mathematics, University of Illinois)
Fusion Rules and Haar Measure for SUq(2)
Abstract: We will define the quantum group SUq(2), give the representation theory and the fusion rules and compute the Haar measure.

Tuesday, December 2, 2008

Analytic Aspects of Quantum Groups
3:00 pm   in 130 Lincoln Hall,  Tuesday, December 2, 2008
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Steve Avsec (Department of Mathematics, University of Illinois)
Fusion Rules and Haar Measure for SUq(2), II

Tuesday, December 9, 2008

Analytic Aspects of Quantum Groups
3:00 pm   in 130 Lincoln Hall,  Tuesday, December 9, 2008
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I. C. Baianu (FSHN, UIUC)
Beyond Quantum Groups And Hopf Algebras
Abstract: An Algebraic Topology approach to Supersymmetry (SUSY) and Symmetry Breaking in Quantum Field and Quantum Gravity theories is presented with a view to developing a wide range of physical applications, such as: controlled nuclear fusion and other nuclear reaction studies in quantum chromodynamics, nonlinear physics at high energy densities, dynamic Jahn-Teller effects, superuidity, high temperature superconductors, multiple scattering by molecular systems, molecular or atomic paracrystal structures, nanomaterials, ferromagnetism in glassy materials, spin glasses, quantum phase transitions and supergravity. This approach requires a uni ed conceptual framework that utilizes extended symmetries and quantum groupoid, algebroid and functorial representations of non-Abelian higher dimensional structures pertinent to quantized spacetime topology and state space geometry of quantum operator algebras. Fourier transforms, generalized Fourier-Stieltjes transforms, and duality relations link, respectively, the quantum groups and quantum groupoids with their dual algebraic structures; quantum double constructions are also discussed in this context in relation to quasitriangular, quasiHopf algebras, bialgebroids, Grassmann-Hopf algebras and Higher Dimensional Algebra. On the one hand, this quantum algebraic approach is known to provide solutions to the quantum Yang-Baxter equation. On the other hand, our novel approach to extended quantum symmetries and their associated representations is shown to be relevant to locally covariant General Relativity theories that are consistent with nonlocal quantum field theories.

Tuesday, February 3, 2009

Analytic Aspects of Quantum Groups
4:00 pm   in 241 Altgeld Hall,  Tuesday, February 3, 2009
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Pierre Fima (Department of Mathematics, University of Illinois)
Discrete Quantum Groups
Abstract: I will define discrete quantum groups: The C*-algebra and the von Neumann algebra, the comultiplication and the Haar weights.

Tuesday, February 10, 2009

Analytic Aspects of Quantum Groups
4:00 pm   in 241 Altgeld Hall,  Tuesday, February 10, 2009
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Pierre Fima (Department of Mathematics, University of Illinois)
Discrete Quantum Group II
Abstract: I will give explicit formulas for GNS representation and modular theory of the Haar State and then explain the defintion of a discrete quantum group.

Tuesday, February 17, 2009

Analytic Aspects of Quantum Groups
4:00 pm   in 241 Altgeld Hall,  Tuesday, February 17, 2009
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Pierre Fima (Department of Mathematics, University of Illinois)
Discrete Quantum Groups, III

Tuesday, February 24, 2009

Analytic Aspects of Quantum Groups
4:00 pm   in 241 Altgeld Hall,  Tuesday, February 24, 2009
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Pierre Fima (UIUC Math)
Discrete Quantum Groups, IV

Tuesday, March 3, 2009

Analytic Aspects of Quantum Groups
4:00 pm   in 241 Altgeld Hall,  Tuesday, March 3, 2009
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Pierre Fima (UIUC Math)
Discrete Quantum Groups, V
Abstract: I will prove invariance of the Haar weights

Tuesday, March 17, 2009

Analytic Aspects of Quantum Groups
4:00 pm   in 241 Altgeld Hall,  Tuesday, March 17, 2009
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Pierre Fima (UIUC Math)
Some examples of discrete quantum groups

Tuesday, March 31, 2009

Analytic Aspects of Quantum Groups
4:00 pm   in 241 Altgeld Hall,  Tuesday, March 31, 2009
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Pierre Fima (UIUC Math)
Twisting

Tuesday, April 7, 2009

Analytic Aspects of Quantum Groups
4:00 pm   in 241 Altgeld Hall,  Tuesday, April 7, 2009
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Marius Junge (UIUC Math)
Random Walks on Discrete Quantum Groups

Tuesday, April 28, 2009

Analytic Aspects of Quantum Groups
4:00 pm   in 241 Altgeld Hall,  Tuesday, April 28, 2009
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Pierre Fima (UIUC Math)
Topological boundary for universal orthogonal quantum group
Abstract: We construct the topological boundary for the dual of universal orthogonal quantum group and explain how it is related to the Poisson boundary.

Tuesday, May 5, 2009

Analytic Aspects of Quantum Groups
4:00 pm   in 241 Altgeld Hall,  Tuesday, May 5, 2009
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Pierre Fima (Department of Mathematics, University of Illinois)
Poisson boundary of dual of universal orthogonal quantum group
Abstract: I will explain how to obtain the Poisson boundary from the topological boundary for the dual of universal orthogonal quantum group.