A Celebration of the Best Maths Projects in the North West 2023, featuring talks by Jean Al Ani (University of Liverpool) and Rachel Campbell (University of Manchester).
The North West Branch held its third annual celebration of student mathematics projects in July. Universities in the North West of England were invited to submit one entry from the student who had been awarded the highest mark for their final-year projects. Presentations were delivered in a 10-minute virtual setting followed by a five-minute Q&A session, and they could cover any branch of mathematics, statistics, or operational research.
Jean Al Ani and Rachel Campbell were awarded first and second place respectively, and will deliver talks based on their respective projects.
Abstracts
Classifying Higher Spin Bundles on Hyperelliptic Riemann Surfaces, a talk by Jean Al Ani (University of Liverpool)
First I introduce the concepts of a Riemann surface and complex line bundles on it. Second I define divisors on the surface and explain their relationship with complex line bundles. Then state a few of the classification results from my Masters project.
The Geometry of Hyperbolic Knots and Links, a talk by Rachel Campbell (University of Manchester)
What makes two knots different from one another? How do we determine whether two knots are different? This project discusses the mathematics behind these two questions, which turns out to be closely linked to hyperbolic geometry. Considering a knot to be a 1-dimensional loop embedded in the 3-dimensional space S3, we take the knot complement (the space in S3 not occupied by the knot) and apply a hyperbolic geometry to it. By examining the geometric properties of the knot complement, such as volume, we can learn more about the knot itself. The project finishes by exploring knots embedded in a different space, namely the thickened torus (T x I). Here, we see how SnapPy, a computer program, can be used to find thousands of knots satisfying certain criteria. For example, we use SnapPy to find 18,467 different knots embedded in T x I.
Registration
This talk will be given remotely, via Zoom. If you wish to register for attendance at this North West branch talk, please register here. A joining link will be sent 24 hours before the event.
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No charge is made to attend meetings. Non-IMA members are welcome.
Image credits:
[1] Image of Jean Al Ani provided by speaker.
[2] Generated by SnapPy – M. Culler, N. M. Dunfield, M. Goerner, and J. R. Weeks, SnapPy, a computer program for studying the geometry and topology of 3-manifolds, http://snappy.computop.org
