# Upcoming seminars

 Upcoming Seminars Fri12/06/2013(tomorrow)4:00pm Seminar: CombinatoricsOn Erdos' conjecture on the number of edges in 5-cyclesZoltan Furedi, Renyi Institute of Mathematics, Budapest, HungaryContact: Dwight Duffus, dwight@mathcs.emory.eduVenue: Mathematics and Science Center, Room W306Download printable flyer (PDF, 57.9 kB)Hide abstractErdos, Faudree, and Rousseau (1992) showed that a graph on n vertices and at least $[n^2/4]+1$ edges has at least $2[n/2]+1$ edges on triangles and this result is sharp. They also considered a conjecture of Erdos that such a graph can have at most $n^2/36$ non-pentagonal edges with an extremal graph having two components, a complete graph on $[2n/3]+1$ vertices and a complete bipartite graph on the rest. This was mentioned in other papers of Erdos and also it is No. 27 in Fan Chung's problem book.\\ \\ In this talk we give a graph of $[n^2/4]+1$ edges with much more, namely $n^2/8(2+\sqrt{2})$ + $O(n) = n^2/27.31…$ pentagonal edges, disproving the original conjecture. We show that this coefficient is asymptotically the best possible.\\ \\ Given graphs H and F let $E_0(H,F)$ denote the set of edges of H which do not appear in a subgraph isomorphic to F, and let $h(n,e,F)$ denote the maximum of $|E_0(H,F)|$ among all graphs H of n vertices and e edges. We asymptotically determine $h(n,cn^2, C_3)$ and $h(n,cn^2, C_5)$ for fixed c, $1/4 < c < 1/2$. For $2k+1\ge$ 7 we establish the conjecture of Erdos et al. that $h(n,cn^2, C_{2k+1})$ is obtained from the above two-component example.\\ \\ One of our main tools (beside Szemeredi's regularity) is a new version of Zykov's symmetrization what we can apply for more graphs, simultaneously. Mon12/09/2013(in 4 days)4:00pm Seminar: Computer ScienceScalable and Privacy-Preserving Searchable Cloud Data ServicesMing Li, Utah State UniversityContact: Li Xiong, lxiong@mathcs.emory.eduVenue: Mathematics and Science Center, Room W301Download printable flyer (PDF, 41.5 kB)Hide abstractCloud computing is envisioned as the next generation architecture of IT enterprises, which provides convenient remote access to massively scalable data storage and application services. Despite the cloud’s promise for huge potential economical savings, its benefits may not be fully realized, due to wide public concerns that users’ private data may be involuntarily exposed to or mishandled by the cloud providers. Although end-to-end encryption has been proposed as a promising solution for secure cloud data storage, how to effectively support flexible data utilization such as searches over encrypted cloud data becomes a primary challenge, which is the key toward building full-fledged privacy-assured cloud data storage. In this talk, I will first identify the system requirements and challenges in privacy-preserving searchable outsourced cloud data services, that is to simultaneously achieve privacy assurance (data and query confidentiality), practical efficiency (scalable with large volumes of data), and high usability (flexible query functionalities). Among these goals, privacy and the other two are often in conflict with each other and our research aims at finding a better tradeoff. As an example, I will present our recent work on privacy-preserving multi-keyword ranked search supporting similarity-based ranking. The proposed approach integrates novel cryptographic primitives with information-retrieval principles and efficient data structures. A “best-effort” privacy model is adopted while much faster-than-linear search time is achieved in an empirical sense. Finally, I will outline some future challenges that need to be resolved to make privacy-preserving searchable cloud data service a reality.\\ \\ Bio:\\ Ming Li is an Assistant Professor in the Computer Science Department at Utah State University. He received his Ph.D. in Electrical and Computer Engineering from Worcester Polytechnic Institute in 2011. His current main research interest is cyber security and privacy, with emphases on security and privacy in cloud computing and big data, security in wireless networks and cyber-physical systems. Tue12/10/2013(in 5 days)3:30pm Defense: DissertationComputational Methods for Centrality Measurements in Complex NetworksChristine Klymko, Emory UniversityContact: Christine Klymko, cklymko@emory.eduVenue: Mathematics and Science Center, Room W302Download printable flyer (PDF, 23.6 kB)