2016 Research in the Capitol

Title

Bridge Numbers: A Knotty Journey

Presentation Type

Poster Presentation

Keywords

Knot theory;

Abstract

Take a long string, tie it in a complicated knot, and fuse the ends together. This gives you a mathematical knot. In your knot, you will have sections which go over other sections, and only over. These are called bridges. The least number of bridges in any drawing of a knot is called the bridge number of that knot. We can use the bridge number to tell knots apart. We are studying ways to draw the knot so that we have the fewest number of bridges. There are a large number of knots with unknown bridge numbers, including the knots with 12 crossings. Because these bridge numbers are unknown, there is a gap in the knowledge in knot theory. We are trying to fill that gap.

Start Date

29-3-2016 11:30 AM

End Date

29-3-2016 1:30 PM

Event Host

University Honors Programs, Iowa Regent Universities

Faculty Advisor

TJ Hitchman

Department

Department of Mathematics

Comments

Location: Iowa State House, Rotunda, Des Moines, Iowa

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Mar 29th, 11:30 AM Mar 29th, 1:30 PM

Bridge Numbers: A Knotty Journey

Take a long string, tie it in a complicated knot, and fuse the ends together. This gives you a mathematical knot. In your knot, you will have sections which go over other sections, and only over. These are called bridges. The least number of bridges in any drawing of a knot is called the bridge number of that knot. We can use the bridge number to tell knots apart. We are studying ways to draw the knot so that we have the fewest number of bridges. There are a large number of knots with unknown bridge numbers, including the knots with 12 crossings. Because these bridge numbers are unknown, there is a gap in the knowledge in knot theory. We are trying to fill that gap.