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The Square Peg Problem for Two Curves
Student-Run Research Seminar| Speaker: | Alexander Black, UC Davis |
| Location: | 2112 MSB |
| Start time: | Tue, Oct 22 2019, 12:30PM |
Toeplitz conjectured in 1911 that every simple closed curve in the plane inscribes a square. This problem has garnered a great deal of attention due to its simple statement and surprising plausibility. In pursuit of this problem, many generalizations to higher dimensions and other shapes have been asked. We instead generalize this question to the case of having 2 curves and in doing so discover some fairly nice geometric arguments. In this talk, we will discuss exactly what a reasonable formulation for two curves is, how to resolve it and in how much generality, and its relationship to some other natural geometric questions.