Understanding the distribution of subgraph counts has long been a central question in the study of random graphs. In this talk, we consider the distribution of Sn, the number of K4 subgraphs, in the Erdös Rényi random graph G(n, p). When the edge probability p \in (0, 1) is constant, a classical central limit theorem for Sn states that (Sn−µn)/σn converges in distribution. We establish a stronger form of convergence, namely the corresponding local limit theorem, which is joint work with O. Riordan.
 

I was speak on the way Newton carries out his calculus in the Principia in the framework of classical geometry rather than with fluxions, his deficiencies, and the relation of this work to inverse-square laws.

The Czech lands were the most industrial part of the Austrian-Hungarian monarchy, broken up at the end of the WW1. As such, Czechoslovakia inherited developed industry supported by developed system of tertiary education, and Czech and German universities and technical universities, where the first chairs for applied mathematics were set up. The close cooperation with the Skoda company led to the establishment of joint research institutes in applied mathematics and spectroscopy in 1929 (1934 resp.).

The development of industry was followed by a gradual introduction of social insurance, which should have helped to settle social contracts, fight with pauperism and prevent strikes. Social insurance institutions set up mathematical departments responsible for mathematical and statistical modelling of the financial system in order to ensure its sustainability. During the 1920s and 1930s Czechoslovakia brought its system of social insurance up to date. This is connected with Emil Schoenbaum, internationally renowned expert on insurance (actuarial) mathematics, Professor of the Charles University and one of the directors of the General Institute of Pensions in Prague.

After the Nazi occupation in 1939, Czech industry was transformed to serve armament of the Wehrmacht and the social system helped the Nazis to introduce the carrot and stick policy to keep weapons production running up to early 1945. There was also strong personal discontinuity, as the Jews and political opponents either fled to exile or were brutally persecuted.

In 1897 J.J. Thomson 'discovered' the electron. The previous year, he and his research student Ernest Rutherford (later to 'discover' theatomic nucleus), collaborated in experiments to work out why gases exposed to x-rays became conducting. 

This talk will discuss the very different mathematical educations of the two men, and the impact these differences had on their experimental investigation and the theory they arrived at. This theory formed the backdrop to Thomson's electron work the following year. 

James Clerk Maxwell (1831–1879) was, by any measure, a natural philosopher of the first rank who made wide-ranging contributions to science. He also, however, wrote poetry.

In this talk examples of Maxwell’s poetry will be discussed in the context of a biographical sketch. It will be  argued that not only was Maxwell a good poet, but that his poetry enriches our view of his life and its intellectual context.