Almost surely connected: random graphs and logic

for each pair of vertices flip the coin to decide whether
the pair should be joined by an edge. What will the graph we
construct in this manner look like? Depending on what you want
to know about the graph, this question might be answered by a
0-1 law from finite model theory.

In this talk I will give an overview of the 0-1 laws in finite
model theory: explain what they say, discuss their strenghts
and their weaknesses, and explain an ongoing research project
of my own, which is aimed at overcoming one of these weaknesses.