Extremal Combinatorics, Probabilistic Combinatorics

我的博士学位是在图形次要、连通性和拟阵的界面上。最近，嵌入在3-空间中的单连通2-复形被刻画--其刻画方式类似于Kuratowski对图平面性的刻画。换句话说，已经发现了嵌入在3-空间中的单连通2-复形的一个被禁止的次刻划。在我的博士学位上，我想进一步研究这一点。这包括应用这些技术，并进一步发展它们。这项工作与ESPRC的一项拨款有关，该基金名为“在3D和连通性中绘制次要图形”。

My PhD is at the interface of Graph Minors, Connectivity and Matroids. Recently, the simply connected 2-complexes embeddable in 3-space have been characterised - in a way similar to Kuratowski's characterisation of graph planarity. In other words, there has been found a forbidden minor characterisation of simply connected 2-complexes embeddable in 3-space. In my PhD, I want to investigate this further. This includes applying these techniques, and developing them even further. This work is connected to an ESPRC grant called 'Graph Minors in 3D and connectivity'.