Subfactor Seminar
Fall 2012

• Date: 8/31/12
  • Vaughan Jones, Vanderbilt University
  • Title: AF-algebras, Cuntz algebras, free Gaussian functor and several algebra structures associated with a planar algebra
  • Abstract: We will begin by reminding people of AF-algebras, Cuntz algebras and Voiculescu's free Gaussian functor. Then we will introduce planar algebras with three examples and show how the previous algebras can be generalised and what new phenomena, and many open questions, occur with the generalisation.

• Date: 9/7/12
  • Natasha Blitvic, Vanderbilt University
  • Title: Two-parameter non-commutative Gaussian processes
  • Abstract: The setting for this talk is the deformed commutation relations and Fock space representations of deformed quantum harmonic oscillator algebras. Building on the work of Bozejko and Speicher in the single-parameter case, we will begin by constructing the (q,t)-Fock space, a two-parameter deformation of the bosonic and fermionic Fock spaces. We will focus on the probabilistic interpretation of the algebras of bounded linear operators on this space with particular emphasis on the operators playing the role of the Gaussian random variables. We will discuss the combinatorial structure underlying these objects, their role in a generalized non-commutative Central Limit Theorem, and several surprising connections to well-studied mathematical objects.

• Date: 9/13/12, Mathematics Colloquium (4:10-5:00pm in SC 5211)
  • Nigel Higson, Penn State University
  • Title: Contractions of Lie Groups and Representation Theory
  • Abstract: Let K be a closed subgroup of a Lie group G. The contraction of G to K is a Lie group, usually more elementary in structure than G itself, that approximates G to first order near K. The terminology is due to the mathematical physicists, who examined the group of Galilean transformations as a contraction of the group of Lorentz transformations. My focus will be on a related but different class of examples, the prototype of which is the group of isometric motions of Euclidean space, viewed as a contraction of the group of isometric motions of hyperbolic space. It is natural to expect some sort of limiting relation between representations of the contraction and representations of G. But in the 1970s George Mackey carried out a few calculations pointing to an interesting rigidity phenomenon: as the contraction group is deformed back to G, the representation theory remains in some sense unchanged. In particular the irreducible representations of the contraction group parametrize the irreducible representations of G. I shall formulate a reasonably precise conjecture that was inspired by subsequent developments in C*-algebra theory and noncommutative geometry, and describe the evidence in support of it, which is by now substantial. However a conceptual explanation for Mackey's rigidity phenomenon remains elusive.

• Date: 9/14/12
  • Natasha Blitvic, Vanderbilt University
  • Title: Two-parameter non-commutative Gaussian processes, continued
  • Abstract: see talk from 9/7/12.

• Date: 9/21/12
  • Michael Brandenbursky, Vanderbilt University
  • Title: Link and braid invariants via counting surfaces
  • Abstract: A Gauss diagram is a simple, combinatorial way to present a link. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting subdiagrams of certain combinatorial types. In this talk I will present simple formulas for an infinite family of invariants in terms of counting surfaces of certain genus and number of boundary components in a Gauss diagram associated with link/closed braid. I will identify the resulting invariants with partial derivatives of the HOMFLY-PT polynomial.

• Date: 9/28/12
  • No Meeting.

• Date: 10/5/12
  • No Meeting, Fall Break.
• Date: 10/12/12
  • Michael Brandenbursky, Vanderbilt University
  • Title: Link and braid invariants via counting surfaces, continued
  • Abstract: see talk from 9/21/12.

• Date: 10/19/12
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• Date: 10/26/12
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• Date: 11/2/12
  • Feng Xu, UC Riverside (tentative)
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• Date: 11/9/12
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• Date: 11/16/12
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• Date: 11/23/12
  • No Meeting, Thanksgiving Break.

• Date: 11/30/12
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• Date: 12/7/12
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• End of Fall Semester.

Past Subfactor and NCGOA seminars