#
Monday Lecture and Colloquium

**Monday, June 22, 2015**

Freie Universität Berlin

Takustr. 9

14195 Berlin

room 005

** Lecture - 14:15**

### Bernd Sturmfels -
UC Berkeley

### Rational Design of Antibiotic Treatment Plans

*Abstract:*

We present work with Portia Mira, Kristina Crona, Devin Greene, Juan Meza and Miriam
Barlow, aimed at developing antibiotic treatment plans that can reverse the evolution
of antibiotic resistance. The Barlow lab at UC Merced generated adaptive landscapes for
16 genotypes of the TEM beta-lactamase that vary from the wild type genotype TEM-1
through all combinations of four amino acid substitutions, and determined the growth
rate of each genotype when treated with each of 15 beta-lactam antibiotics. Using growth
rates for fitness in two models from population genetics, we computed the probability of
each amino acid substitution in each beta-lactam treatment, and we searched through
the 15 treatments for substitution paths leading from each of the 16 genotypes back
to TEM-1. We identified treatment paths with the highest probabilities of returning
TEM to the wild type state, thus offering promise for reversing the evolution of
resistance to antibiotics. This lecture highlights the mathematics in this project.

**Colloquium - 16:00**

### Jan Hofmann
- FU Berlin

### Convex-normal (pairs of) polytopes

*Abstract:*

A polytope * P * is * k*-convex-normal, if every rational multiple *rP* for *r* ∈ [2, *k*] can be
covered by certain copies of P. This notion was introduced by Gubeladze, who used
it to prove that polytopes with long edges have the integer decomposition property.
In this talk we introduce the notion, show how to improve the aforementioned result
and how convex-normality and the integer decomposition property can be extended
to pairs of polytopes.

This is joint work with Christian Haase.

Letzte Aktualisierung:
19.06.2015