Abstract: We will discuss several problems concerning the n-cube and briefly survey some recent developments. We will cover a variety of topics, including Ramsey and Turan problems for hypercubes, isoperimetric properties of hypercubes, routing in hypercubes, and algorithmic aspects. In particular, we will mention a number of unsolved problems and future directions in related areas on hypercubes.
Bio: Fan Chung is a Professor in Mathematics at the University of California, San Diego. She works mainly in the areas of spectral graph theory, extremal graph theory, random graphs and quasi-random graph theory. In particular, she is known for her work in generalizing the Erdős-Rényi model for graphs with general degree distribution (including power-law graphs) and the analysis of ranking/searching algorithms in the study of large information networks. After she received her Ph. D. in mathematics from the University of Pennsylvania, she joined Bell Labs and subsequently Bellcore, directing several groups in the mathematics and computing areas. Then she was the first tenured woman faculty at the University of Pennsylvania. In 1998, she joined the faculty of the University of California, San Diego and has been there since then. She has written about 300 papers and has over 100 coauthors. She was the founding editor-in-chief of Internet Mathematics and the Journal of Combinatorics and has served on the editorial boards of many journals. She was awarded the Allendoerfer Award by Mathematical Association of America. She gave plenary talks at many conferences including the International Congress of Mathematicians (ICM) in 1994. She is a fellow of the American Academy of Arts and Sciences, a fellow of the American Mathematical Society and a SIAM fellow. Since 2016, she is an academician of Academic Sinica.