Student Profile: Emily Groves

Emily Groves

La Trobe University

Biography

Miss Emily Groves is a third-year bachelor student at La Trobe University, enrolled in the Bachelor of Science (Honours) and Masters of Nanotechnology. Her studies include a variety of disciplines such as physics, chemistry and mathematics and a little bit of biology. This is ideal to Emily as she enjoys these areas of science, in particular physics and mathematics, and finds it interesting to see where they overlap. Throughout her studies Emily has gained a fond liking of mathematics and aspires to learn and develop within this area. University is at times challenging, but Emily finds it quite rewarding to understand new concepts and to overcome struggles. Overall, her favourite part of studying is the ability to learn from others, especially from those who are passionate about what they do.

Drawings of the Complete Graphs K_5 and K_6, and the Complete Bipartite Graph K_{3,3}

This project is in the field of Topological Graph Theory. For graphs which admit no plane drawings with no edge crossing, a natural question is to determine the structure and the cardinality of the set of pairs of crossing edges. This turns out to be a difficult problem even for relatively small graphs. In the project, we aim to resolve this question for the first unknown case, for the complete graph on six vertices. We will use cohomological relations on the deleted product space of the graph and computer assisted methods.

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