Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, March 30, 2006.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2006            March 2006             April 2006
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4             1  2  3  4                      1
5  6  7  8  9 10 11    5  6  7  8  9 10 11    2  3  4  5  6  7  8
12 13 14 15 16 17 18   12 13 14 15 16 17 18    9 10 11 12 13 14 15
19 20 21 22 23 24 25   19 20 21 22 23 24 25   16 17 18 19 20 21 22
26 27 28               26 27 28 29 30 31      23 24 25 26 27 28 29
30


Thursday, March 30, 2006

1:00 pm in 347 Altgeld Hall,Thursday, March 30, 2006

#### No meeting this week

1:00 pm in 241 Altgeld Hall,Thursday, March 30, 2006

#### A New Identity in Two Complex Variables for the Dedekind eta function/ Five new partition identities

###### Bruce Berndt and/or William Hart (UIUC)

Abstract: Possible Double Header - Two for the Price (Free, however) of One. Feature (Title) No. 1: A New Identity in Two Complex Variables for the Dedekind Eta-Function Abstract: You have never seen an identity of this type before; it is likely the only one of its kind. Feature (Title) No. 2 (To be given by BCB): Five New Partition Identities. Abstract: In a talk earlier this semester, the speaker spoke on one of these identities. There appear to be only five partition identities of this type. If the second feature of this double header runs, you will be informed of the remaining four partition identities.

2:00 pm in 241 Altgeld Hall,Thursday, March 30, 2006

#### The one-variable Main Conjecture.

###### Iwan Duursma   [email] (UIUC Math)

Abstract: (RAP Elliptic Curves and Iwasawa Theory, Part 8) For an elliptic curve E with CM by a quadratic imaginary field K and for a rational prime p that splits in K, p=p1*p2, adjoining the p1-power torsion points to K yields an Iwasawa tower. The one-variable main conjecture describes the p-part of the class group in the Iwasawa tower in terms of elliptic units. We formulate the results and give details of the proof.

2:00 pm in 243 Altgeld Hall,Thursday, March 30, 2006

#### Numerical range, dilation theory, and norm estimations

###### Chi-Kwong Li (College of William & Mary)

Abstract: We discuss how one can use the numerical range of an operator to find dilations of the operator with simple structures. Furthermore, one can use the location of the numerical range to find optimal norm bounds for the sum of operators, and the norm of the derivation operators, etc.

3:00 pm in 345 Altgeld Hall,Thursday, March 30, 2006

#### Parabolic Harnack Inequality for the Mixture of Brownian Motion and Stable Processes

###### Zoran Vondracek (University of Zagreb)

3:00 pm in 241 Altgeld Hall,Thursday, March 30, 2006

#### Symplectic embeddings in R^4

###### Richard Hind (Notre Dame)

Abstract: Symplectic embeddings, and in particular Hamiltonian diffeomorphisms, preserve the volume of subsets of Euclidean space. But Gromov's nonsqueezing theorem shows that volume is not the only obstruction to embedding one domain into another. We will discuss how to improve Gromov's estimate for the radius of balls which can be embedded in certain domains in R^4.

7:30 pm in 245 Altgeld Hall,Thursday, March 30, 2006

#### MathWorld: Collecting and Communicating Mathematics on the Internet

###### Eric Weisstein (Wolfram Research)

Abstract: MathWorld is the internet's most popular mathematical resource. Its entries usually find their way into the top 3 (if not top 1) results meturned by a Google search for any given mathematical term. This talk will provide a survey of MathWorld, its history, future directions, and the processes through which it continues to thrive and grow. In addition, the role of the technical computing environment Mathematica---long instrumental in the creation of the site---will be discussed. Free pizza will be served at 7pm.