# Mathematics Colloquia and Seminars

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### Nonnegative $$C^2$$ interpolation

Student-Run Applied & Math Seminar

 Speaker: Fushuai "Black" Jiang, UC Davis Location: 3106 MSB Start time: Thu, Jan 17 2019, 12:30PM

In this talk, we consider the following extension problem of Whitney-type:

Supposed we are given a finite planar set with prescribed nonnegative values on this set. How do we decide the minimal $$C^2$$ norm of all the globally nonnegative twice continuously differentiable functions (within an order of magnitude) that interpolate these values?

We hope to provide a two-fold answer. First, we want to come up with an algorithm to calculate the minimal norm. Second, we want a find a procedure to recover an interpolant that witnesses the minimal norm.

This is a joint work with Professor Kevin Luli.