Combinatorics is a field of study concerned with discrete objects, and it has broad applications in mathematics and science. For instance, combinatorial reasoning plays a crucial role in solving biological challenges such as deciphering genomes and constructing phylogenetic trees. Researchers in quantum gravity also rely on combinatorial techniques to evaluate integrals, while many problems in statistical mechanics are formulated as combinatorial problems. In recognition of the significance of combinatorics, three of the four Fields Medals awarded in 2006 were related to combinatorial work. Specifically, Okounkov's research on random matrices and Kontsevich's conjecture, Tao's work on primes in arithmetic progression, and Werner's work on percolation were all awarded Fields Medals.
Graph theory is a branch of mathematics that deals with the study of graphs, which are abstract representations of objects and their relationships. Combinatorics is closely related to graph theory, as it provides the mathematical framework for analyzing the structures of graphs. In fact, many problems in graph theory are formulated as combinatorial problems, and combinatorial methods are often used to solve these problems.”
Department Members in This Field
Faculty
Dr Kenneth Dadedzi Spectral Graph Theory
Graduate Students
- TBA