Department Seminars & Colloquia
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Vertex colouring of graphs is an active research area in graph theory. It has wide applications to practical problems and also has many theoretically deep results and challenging problems. Circular colouring of graphs is a refinement of the conventional vertex colouring of graphs. It has atttract a lot of attention in the past twenty years, and becomes an important branch of chromatic graph theory, with many exciting results and new techniques. This talk gives a survey on research in this area.
The purpose of this talk is to discover how Koreans worked hard to learn modern western mathematics and science in late 19th century by themselves. We will see many hundred years old Korean mathematics books which were written in Korean. We will talk aboutfrontiers of Korean modern mathematics between 1894 to 1945 such as LEE Sang-Seol, YU Il-Sun, CHOE Gyu-Dong, REE Im-Hak and CHOE Yun-Sik. It will give us a fine view of Korean efforts in Western modernity for mathematics in Korea that was not known before.
We introduce knots and links in dimension three and their deformation in dimension four which was first introduced by Fox and Milnor. We discuss its key role in understanding the topology of 4-dimensional manifolds and the interplay with 3-dimensional topology. We discuss briefly recent developments, including joint work with Kent Orr which presents new L2-theoretic methods for amenable groups.
A page in Ramanujan's lost notebook contains two identities for trigonometric sums in terms of doubly infinite series of Bessel functions. One is related to the famous "circle problem'' and the other to the equally famous "divisor problem." These relations are discussed as well as various attempts to prove the identities. Our methods also yield new identities for certain trigonometric sums, for which analogues of the circle and divisor problems are proposed. The research to be described is joint work with Sun Kim and Alexandru Zaharescu.