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geolab/contact.md

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Mentors for Fall 2024:
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<h2 class="mb-3">Contact Us</h2>
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### Mentors for Fall 2024:
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- [Bakhyt Aitzhanova](https://math.virginia.edu/people/axh7cj/)
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- [Adam Friedman-Brown](https://math.virginia.edu/people/asm4pr/)
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- [Oliver Wang](https://math.virginia.edu/people/dfh3fs/)
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- [Michael Wills](https://sites.google.com/view/michael-wills/)
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Faculty Advisors:
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### Faculty Advisors:
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- [J.D. Quigley](https://quigleyjd.github.io/)
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- [Sara Maloni](https://sites.google.com/view/sara-maloni)
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Projects Fall 2024:
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### Projects Fall 2024:
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1. **Geometry over finite fields**: Many familiar objects from geometry can be described using polynomial equations. For instance, the unit circle is the set of points in the xy-plane such that x^2+y^2-1=0, while the equation x^2-y^2-1=0 describes a hyperbola. In this project, we will study polynomials in exotic contexts for arithmetic called ``finite fields.” We will try to understand the geometry of solutions to polynomial equations over finite fields, both by hand and with computer algebra software. Prerequisites: MATH 1210/1310
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2. **Zome and polyhedra**: The Zome toolkit makes it easy to build toy models of polyhedra, 3 dimensional solid shapes like cubes and pyramids built out of polygons on the outside. Using the Zome pieces, we can show why there are only 5 polyhedra whose faces are all the same shape, and also why in the fourth dimension there are only 6 shapes with the same kind of property. We will explore the geometry of shapes we can build using Zome, such as angles, counting faces of solid shapes, symmetries, knots, and/or many other possibilities. No prerequisites needed, though in previous semesters some comfort with trigonometry has been helpful.

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