Spring 2007

**Organizer: Dietmar Bisch**

**Mondays, 4:10-5:30pm in SC 1310**

- Date:
**1/22/07**- Speaker:
**Shamindra Ghosh, Vanderbilt University** - Title:
**Planar algebras and their representations** - Abstract: We will construct a planar algebra starting from a 1-cell in a pivotal strict $2$-category. We introduce the concept of an affine representation of a planar algebra and prove some finiteness results for the affine representations of a finite depth planar algebra.

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- Date:
**2/5/07**- Speaker:
**Shamindra Ghosh, Vanderbilt University** - Title:
**Planar algebras and their representations II**

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- Date:
**2/12/07**- Speaker:
**Pinhas Grossman, Vanderbilt University** - Title:
**Quadrilaterals of Factors**

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**2/19/07**- Speaker:
**Pinhas Grossman, Vanderbilt University** - Title:
**Quadrilaterals of Factors, continued**

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**3/5/07****no meeting, spring break**

- Date:
**3/15/07 (Thursday), Mathematics Colloquium, 4:10-5:00pm in SC 5211**- Speaker:
**Ken Dykema, Texas A&M University** - Title:
**Free probability and free entropy dimension** - Abstract: More than 20 years ago, Voiculescu found a noncommutative probabalistic notion called freeness that corresponds to the situation of words in a free group. The theory based on this definition is called free probability theory and in this theory free products play a role analogous to the usual (Cartesian) product of spaces in the classical probabalistic theory of independence. The parallels with classical probability theory are far-reaching and surprising. After introducing freeness, we will describe one of its fundamental examples, which is the asymptotic behavior of random matrices as the matrix size grows without bound. We'll also describe the use of freeness to investigate von Neumann algebras, including applications of the related quantity, free entropy dimension.

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**4/16/07**- Speaker:
**Paramita Das, Vanderbilt University** - Title:
**The planar algebra of group-type subfactors** - Abstract: We describe the planar algebra, or equivalently, the standard invariant, of a family of subfactors introduced by Bisch and Haagerup some 10 years ago. These subfactors play an important role in the theory, since they provide a very simple mechanism to construct irreducible subfactors whose standard invariant has infinite depth. This is joint work with Dietmar Bisch and Shamindra Ghosh.

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**4/23/07****Note: This talk will be in room SC 1308.**- Speaker:
**Andrew Ranicki, University of Edinburgh** - Title:
**Introduction to surgery I** - Abstract: Introduction to surgery II will take place in the NCG Seminar, tomorrow, Tue, 4/24/07.

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