# Mathematical Careers and Ideas:

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*"The Number of Crossings of Curves on Surfaces"
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## Department of Mathematics, Stony Brook University

In *Mathematical
Careers and Ideas,* the Department of Mathematics is offering a series
of talks for undergraduates.
This is the next event in the series.

**Abstract: **
Start with a piece of paper whose boundary forms a polygon, choose
some pairs of edges and glue them together. This yields what
mathematicians call a "surface".

Now, take a closed curve C in that surface. Imagine that you can shrink, stretch and slide C on the surface with the only restriction that the curve cannot leave the surface. All the curves C that you can make this way are "equivalent" to C and the whole set of curves you can obtain this way is called the free homotopy class of C.

The number of times a curve C crosses itself is the self-intersection number of C. The self-intersection of a free homotopy class of curves is the smallest number of crossings of curves in the class.

In this talk I will discuss algorithms to compute the self-intersection number of a class of curves and some statistics related to the self-intersection number.

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TUESDAY, MARCH 22, 2011
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FREE PIZZA AND SOFT DRINKS FROM 5:00 IN HILL 703
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TALK 5:20 TO 6:20 IN HILL 705
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No food in Hill 705, please.
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All students are welcome — and their instructors too.
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