Sunday 3 November 2024 |

Events for day: Wednesday 22 February 2023 |

14:00 - 15:00 Combinatorics and Computing Weekly SeminarSaturation Numbers in Random Graphs School MATHEMATICS For some fixed graph $F$, a graph $G$ is said to be $F$-saturated if it is a maximal $F$-free graph, i.e., $G$ does not contain any copies of $F$ as a subgraph, but adding any missing edge to $G$ creates one. The saturation number $sat(n, F)$ is defined to be the minimum number of edges in an $F$-saturated graph on $n$ vertices. The saturation problem of finding $sat(n, F)$ is in some sense the opposite of the well-known Tur{a}n problem. Since the 1960s, the saturation number $sat(n, F)$ has been extensively studied for various different choices of $F$. In this talk, we consider the random analog of this problem: minimizing the number of edge ... 16:00 - 17:00 Mathematics ColloquiumMoving Interfaces and Free Boundary problems School MATHEMATICS The term moving interfaces and free boundary refers to a class of problems in which the domain of the problem itself is also an a priori unknown, as well as the basic unknown solution to governing equations. Hence, finding the domain is part of the problem. In this lecture I shall present some basic models in moving interfaces and free boundary problems. These includes obstacle problem, Stefan problem, Hele-Shaw flow and Muskat problem. I will also review the state of art for regularity results in obstacle problem. Subscribing the Mathematics Colloquium mailing list: https://groups.google.com/g/ipm-math-colloquium ... |