Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, February 15, 2006.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, February 15, 2006

2:00 pm in 341 Altgeld Hall,Wednesday, February 15, 2006

#### To Be Announced

###### F. Boca (UIUC)

2:00 pm in 143 Altgeld Hall,Wednesday, February 15, 2006

#### Organizational Meeting

###### (UIUC Math)

3:00 pm in 343 Altgeld Hall,Wednesday, February 15, 2006

#### The classical and quantum open string

###### Sean Nowling (UIUC Physics)

Abstract: The discussion of the classical open string in lightcone gauge will be completed, then we will turn to the quantum theory.

4:00 pm in 245 Altgeld Hall,Wednesday, February 15, 2006

#### The isoperimetric problem in sub-Riemannian geometry

###### Jeremy Tyson (Department of Mathematics, UIUC)

Abstract: Sub-Riemannian geometry is, roughly speaking, differential geometry relative to a singular, or degenerate, metric. For those of us working in nonsmooth geometric analysis, sub-Riemannian spaces provide a rich source of examples motivating a more general, abstract theory. I will describe the geometric and analytic structure of the simplest non-Euclidean sub-Riemannian space -- the three-dimensional Heisenberg group -- and its connection with the classical isoperimetric problem of Queen Dido (discussed in Virgil's Aeneid). The sub-Riemannian isoperimetric problem in the Heisenberg group (among all sets in the Heisenberg group with fixed volume, classify those which minimize the sub-Riemannian surface area) is a famous and long-standing open question. I'll trace the history of this problem and describe its current status. I'll also discuss some related analytic inequalities (Sobolev-Poincare inequalities) in this setting.