MATH 415(S) Geometric Group Theory (Q)
Groups were first invented to study the patterns in geometric shapes. Most notably were the symmetry groups of the Platonic solids, such as the cube and the dodecahedron. We extend and generalize these ideas to higher dimensional polytopes, leading to the beautiful world of reflection groups. By discovering elegant ways of moving between the worlds of (theoretical) algebra and (visual) geometry, problems in one world can be solved using techniques in another. Concrete geometric examples will continually motivate our ideas, as well as provide connections to topology, combinatorics, and physics.
Format: lecture. Evaluation will be based primarily on problem sets and exams.
Prerequisites: Mathematics 312 or 315 or 317. No enrollment limit (expected: 20).
Hour: DEVADOSS