Brendan McKay "Complex Martingales and Regular Graphs"
Brendan McKay from Australian National University will give the talk "Complex Martingales and Regular Graphs" based on the joint work with Mikhail Isaev from Monash University & MIPT on the labs' Big Seminar.
Password: first 6 decimal places of $\pi$
The asymptotic enumeration of regular graphs, and more generally of graphs with specified degree sequences, has occupied combinatorialists for a long time. We will start with a survey of previous results, with a quick summary of the methods used. Then we will focus on the application of complex-analytic methods to degree sequences that are sufficiently dense. Next we will show how a general theorem on complex martingales can be applied to the estimation of the necessary integrals. Then we will apply a theorem of Isaev on cumulant expansions to find an asymptotic expansion for the number of regular graphs of degree at least $n^t$ for some $t>0$.
Everyone is invited to attend. The language of the lecture is English. The event is aimed at master and graduate students, as well as researchers in the field of combinatorics.