Title: C^2-Morse functions on the compactified moduli space M_{g,n} bar
Abstract: I will talk about my finding of C^2-Morse functions, namely what I call by sys_T functions, on the Deligne-Mumford compactification M_{g,n} bar of the moduli space, constructed using Teichm\"uller theory. This improves the result of the topological Morse property of the systole function on M_{g,n}, proved by Hugo Akrout in 2003. I will also talk about some results on critical points for sys_T, and time permitting a potential algorithm to find all critical points.