报告题目： The minimal equal length of a pair of simple closed curves in a once punctured torus as the torus runs over its relative Teichmuller space
摘要：We consider the problem of minimizing the equal length of a pair of simple closed geodesics of given topological type in a once punctured hyperbolic torus with fixed geometric boundary data as the torus runs over its relative Teichmuller space. For specific pairs with symmetry, we are able to determine the minimizing torus and hence the minimal length. It is natural to compare the minimal lengths for inequivalent pair of the same intersection number. As computer experiments show, there is a conjecture that the specific pair of slopes (1/0, 1/n) has its minimal length smaller than any other pair of slopes (1/0, m/n), regardless of the geometric boundary data. In joint work with Da Lei, we are able to establish a stronger result as the geometric boundary of the torus is a conic point and the cone angle is approaching 2π.