Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, November 30, 2005.

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Questions regarding events or the calendar should be directed to Tori Corkery.
     October 2005          November 2005          December 2005
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1          1  2  3  4  5                1  2  3
2  3  4  5  6  7  8    6  7  8  9 10 11 12    4  5  6  7  8  9 10
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16 17 18 19 20 21 22   20 21 22 23 24 25 26   18 19 20 21 22 23 24
23 24 25 26 27 28 29   27 28 29 30            25 26 27 28 29 30 31
30 31


Wednesday, November 30, 2005

2:00 pm in 347 Altgeld Hall,Wednesday, November 30, 2005

#### Lie Pseudoalgebras

###### Bojko Bakolov (North Carolina State University)

Abstract: One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra. A Lie pseudoalgebra is a generalization of the notion of a Lie conformal algebra for which ${\mathbb{C}}[\partial]$ is replaced by the universal enveloping algebra $U({\mathfrak{d}})$ of a finite-dimensional Lie algebra ${\mathfrak{d}}$. I will review the classification of finite simple Lie pseudoalgebras, and I will discuss their relationship to solutions of the classical Yang--Baxter equation. I will also describe the irreducible representations of the Lie pseudoalgebra $W({\mathfrak{d}})$, which is closely related to the Lie--Cartan algebra $W_N$ of vector fields, where $N=\dim{\mathfrak{d}}$. (Based on joint work with A.~D'Andrea and V.~G.~Kac.)

3:00 pm in 441 Altgeld Hall,Wednesday, November 30, 2005

#### No Seminar this week

###### (UIUC Math)

4:00 pm in 245 Altgeld Hall,Wednesday, November 30, 2005

#### Counting objects in infinite sets

###### Slawomir Solecki (Dept. of Mathematics, UIUC)

Abstract: I will talk about comparing the size of possibly infinite sets by counting objects in them. This will lead us to basic ideas of modern theory of definable equivalence relations. On the way, we may encounter some measure theory, ergodicity, and strange curves called indecomposable continua.