Below is the abstract initially proposed by Lizaveta Manzhulina. Due to illness, however, Ekin Ergen did kindly and on our very short notice take over the talk.

A plentitude of highly relevant real-world problems can be modeled by means of linear programs (LP): optimization problems with a linear objective and constraints. Luckily, there are efficient algorithms for solving them. However, once we additionally require the variables to be integers --- which unsurprisingly is oftentimes so in applications --- things go downhill. Integer linear programming (ILP) is NP-hard, and thus to deal with it in practice heuristic methods and approximation algorithms are used.

After convincing ourselves that (I)LP arises everywhere around us, we will explore the intricate relationship between LP and ILP. In particular, we are going to discuss how LP can be of help in tackling NP-hard ILP. Along the way, we will be accompanied by classical examples coming from network problems --- and from combinatorial optimization in general.