========================================================== Computational Prospects of Infinity (20 Jun - 15 Aug 2005) ========================================================== NUS: National University of Singapore IMS: Institute for Mathematical Sciences http://www.ims.nus.edu.sg/Programs/infinity/ Organizing Committee Chi Tat Chong (National University of Singapore), Qi Feng (Chinese Academy of Sciences, China and National University of Singapore), Theodore A. Slaman (University of California at Berkeley), W. Hugh Woodin (University of California at Berkeley), Yue Yang (National University of Singapore) Invited Participants: J Steel, W H Woodin, Q Feng, G Fuchs, S Friedman, M Gitik, J Hamkins, G Hjorth, R Jensen, A Kechris, W Mitchell, T Miyamoto, I Neeman, R Schindler, P Welch, M Zeman, R Downey, T Slaman, K Ambos-Spies, P Cholak, C Chong, S B Cooper, D Ding, S Goncharov, D Hirschfeldt, C Jockusch, A Kucera, M Kumabe, S Lempp, M Lerman, A Li, H Lu, A Nies, G Sacks, S Simpson, R Shore, R I Soare, R Solomon, A Sorbi, F Stephan, K Tanaka, G Wu, Y Yang, L Yu Overview This two-month program on Computational Prospects of Infinity will focus on recent developments in Set Theory and Recursion Theory, which are two main branches of mathematical logic. Topics for Set Theory will include topics related to Cantor's Continuum Hypothesis (CH), with special attention paid to the importance of the Omega Conjecture. Topics for Recursion Theory will include recursive enumerability and randomness. Specifically, the program will focus on the following topics: 1. Omega-conjecture 2. Fine Structures 3. Recursive Enumerability 4. Effective Randomness Tutorials * Two tutorials each consisting of 5 lectures. The primary purpose is to provide background material to the participants, especially the student participants, on the main topics of the program. * For the first month, the tutorials will be in Omega-logic (Woodin) and Fine Structure (to be determined). * During the second month, the tutorials will be in Recursive Enumerability (Slaman) and Effective Randomness (to be determined). Seminars and Talks * Seminars and talks will be given by participants on recent results latest developments related to the core themes of the programs. IMS Membership is not required for participation in above activities. For attendance at these activities, a registration form will be made available when the dates are confirmed. If you are an IMS member or are applying for IMS membership, you do not need to register for these activities.