Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

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GGT seminar: Practical 3-manifold algorithms using ideal loops

Event Type
Seminar/Symposium
Sponsor
Groups, Geometry, and Topology Seminar
Location
347 Altgeld Hall
Date
Feb 6, 2025   11:00 am - 12:00 pm  
Speaker
Alex He (Oklahoma State University)
Views
27
Originating Calendar
Groups, Geometry, and Topology Calendar

Crushing normal surfaces is a key tool for modern 3-manifold software: it lies at the heart of algorithms for problems like unknot recognition, 3-sphere recognition and connected-sum decomposition. Crushing works well for spheres and discs, but things become more difficult when we wish to cut up our 3-manifold along more complicated surfaces. For example, it is natural to work with annuli if we want to detect composite knots, Seifert fibre spaces with nonempty boundary, or product I-bundles over surfaces. In this talk, I will present a workaround for annuli. Roughly, the idea is to fill in boundary components of a 3-manifold with solid tori, so that the annuli of interest become spheres and discs that we know how to crush. We track the fillings using an object called an ideal loop. In joint work with Eric Sedgwick and Jonathan Spreer, this idea has led to a practical algorithm for deciding whether a knot is prime or composite, and we hope to extend the idea to design algorithms for other problems

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