# Fall 2023 Colliquia

### November 3, 2023

#### Vladimir Podolskii, Tufts Computer Science Department

**Max-plus polynomials and their roots **

**Time:** 4:00 pm **Location:** Anderson 112, Nelson Auditorium **Reception:** JCC 535 5:00 pm **Abstract:** Max-plus (or tropical) semiring is the set of real numbers with two operations: tropical addition, which is just the usual maximum operation, and tropical multiplication, which is the usual addition. This algebraic structure emerges in several areas of mathematics such as algebraic geometry, mathematical physics and combinatorial optimization. In part, its importance is related to the fact that it makes various parameters of mathematical objects computationally accessible. Max-plus polynomials play a crucial role in this. In this talk we will discuss some results on max-plus polynomials and their roots. In particular, we will discuss max-plus analogs of classical Nullstellensatz, Combinatorial Nullstellensatz, Schwartz-Zippel Lemma and Universal Testing Set.

### December 1, 2023

#### Luis Dorfmann, Department of Civil and Environmental Engineering, Tufts University

**The elastic secrets of the chameleon tongue**

**Time:** 4:00 pm **Location:** JCC 270 **Reception:** JCC 535 5:00 pm **Abstract:** The ballistic projection of the chameleon tongue is an extreme example of quick energy release in the animal kingdom. It is estimated that the total duration of the tongue projection, depending on species, is between 10 and 55 ms. A biophysical model based on a system of nonlinear PDEs is obtained and is used to confirm the hypothesis that the ballistic mechanism requires energy storage in the collagenous intralingual sheaths coupled with muscular activity.