The main objective of the Lecture Notes Series is to make available to a wider audience the notes of the tutorial lectures given at the Institute's programs in its original or revised form. The Series will occasionally include special lectures and workshop proceedings organized wholly or jointly by the Institute.

**Vol. 35 Combinatorial and Toric Homotopy: Introductory Lectures (Forthcoming) **

edited by Alastair Darby (*Fudan University, China*), Jelena Grbić (*University of Southampton, UK*), Zhi Lü (*Fudan University, China*), Jie Wu (*National University of Singapore*)

**Vol. 34 White Noise Analysis and Quantum Information (Forthcoming) **

edited by Masanori Ohya (*Tokyo University of Science, Japan*), Louis H Y Chen (*National University of Singapore*), Si Si (*Aichi Prefectural University, Japan & Yangon University, Myanmar*), Noboru Watanabe (*Tokyo University of Science, Japan*), Luigi Accardi (*University of Roma II, Tor Vergata, Italy*), Takeyuki Hida (*Nagoya University, Japan & Meijo University, Japan*)

**Vol. 33 Sets and Computations **

edited by Dilip Raghavan (*National University of Singapore*), Sy-David Friedman (*Universität Wien, Austria*), Yue Yang (*National University of Singapore*)

**Vol. 32 Mathemusical Conversations Mathematics and Computation in Music Performance and Composition **

edited by Jordan B L Smith (*National Institute for Advanced Industrial Research and Technology (AIST), Japan*), Elaine Chew (*Queen Mary University of London, UK*), Gérard Assayag (*Sciences and Technologies of Music and Sound Lab (STMS), France & Institut de Recherche et de Coordination Acoustique/Musique (IRCAM), France & French National Centre for Scientific Research (CNRS), France & Pierre and Marie Curie University (UMPC), France*)

**Vol. 31 Geometric Analysis Around Scalar Curvatures **

edited by Fei Han (*National University of Singapore*), Xingwang Xu (*National University of Singapore*), Weiping Zhang (*Nankai University, China*)

**Vol. 30 Modular Representation Theory of Finite and p-Adic Groups **

edited by Wee Teck Gan (

**Vol. 29 Forcing, Iterated Ultrapowers, and Turing Degrees **

edited by Chitat Chong (*National University of Singapore*), Qi Feng (*Chinese Academy of Sciences, China*), Theodore A Slaman (*University of California at Berkeley, USA*), W Hugh Woodin (*Harvard University, USA*), Yue Yang (*National University of Singapore*)

**Vol. 28 Slicing the Truth: On the Computable and Reverse Mathematics of Combinatorial Principles **

edited by Denis R Hirschfeldt (*The University of Chicago, USA*), Chitat Chong (*National University of Singapore*), Qi Feng (*Chinese Academy of Sciences, China*), Theodore A Slaman (*University of California at Berkeley, USA*), W Hugh Woodin (*Harvard University, USA*), Yue Yang (*National University of Singapore*)

**Vol. 27 E-Recursion, Forcing and C*-Algebras **

edited by Chitat Chong (

**Vol. 26 Notes on Forcing Axioms **

edited by Stevo Todorcevic (*University of Toronto, Canada*), Chitat Chong (*National University of Singapore*), Qi Feng (*National University of Singapore*), Theodore A Slaman (*University of California at Berkeley, USA*), W Hugh Woodin (*University of California at Berkeley, USA*), Yue Yang (*National University of Singapore*)

**Vol. 25 Infinity and Truth **

edited by Chitat Chong (*National University of Singapore*), Qi Feng (*National University of Singapore*), Theodore A Slaman (*University of California at Berkeley, USA*), W Hugh Woodin (*University of California at Berkeley, USA*)

**Vol. 24 Complex Quantum Systems: Analysis of Large Coulomb Systems **

edited by Heinz Siedentop (*Ludwig-Maximilians-Universität München, Germany*)

**Vol. 23 Geometry, Topology and Dynamics of Character Varieties **

edited by William Goldman (*University of Maryland, USA*), Caroline Series (*University of Warwick, UK*), Ser Peow Tan (*National University of Singapore*)

**Vol. 22 Multiscale Modeling and Analysis for Materials Simulation **

edited by Weizhu Bao (*National University of Singapore*), Qiang Du (*Pennsylvania State University, USA*)

**Vol. 21 Environmental Hazards: The Fluid Dynamics and Geophysics of Extreme Events **

edited by H K Moffatt (*University of Cambridge, UK*), Emily Shuckburgh (*British Antarctic Survey, UK*)

**Vol. 20 Mathematical Horizons for Quantum Physics **

edited by Huzihiro Araki (*Kyoto University, Japan*), Berthold-Georg Englert (*Centre for Quantum Technologies, National University of Singapore*), Leong-Chuan Kwek (*Centre for Quantum Technologies, National University of Singapore & Nanyang Technological University, Singapore*), Jun Suzuki (*National Institute of Informatics, Japan*)

**Vol. 19 Braids: Introductory Lectures on Braids, Configurations and Their Applications **

edited by A Jon Berrick (*National University of Singapore*) , Frederick R Cohen (*University of Rochester, USA*) , Elizabeth Hanbury (*National University of Singapore & Durham University, UK*) , Yan-Loi Wong (*National University of Singapore*) , Jie Wu (*National University of Singapore*)

**Vol. 18 Random Matrix and its Applications: Multivariate Statistics and Wireless Communications **

edited by Zhidong Bai (*National University of Singapore & Northeast Normal University, China*) , Yang Chen (*Imperial College London, UK*) , Ying-Chang Liang (*Institute for Infocomm Research, Singapore*)

**Vol. 17 Interface Problems and Methods in Biological and Physical Flows **

edited by Boo Cheong Khoo (*National University of Singapore*), Zhilin Li (*North Carolina State University, USA*), Ping Lin (*National University of Singapore*)

**Vol. 16 Mathematical Understanding of Infectious Disease Dynamics **

edited by Stefan Ma (*Ministry of Health Singapore, Singapore*), Yingcun Xia (*National University of Singapore*)

**Vol. 15 Computational Prospects of Infinity, Part II: Presented Talks **

edited by Chitat Chong (*National University of Singapore*), Qi Feng (*Chinese Academy of Sciences, China & National University of Singapore*), Theodore A Slaman (*University of California at Berkeley, USA*), W Hugh Woodin (*University of California at Berkeley, USA*), Yue Yang (*National University of Singapore*)

**Vol. 14 Computational Prospects of Infinity, Part I: Tutorials **

edited by Chitat Chong (*National University of Singapore*), Qi Feng (*Chinese Academy of Sciences, China & National University of Singapore*), Theodore A Slaman (*University of California at Berkeley, USA*), W Hugh Woodin (*University of California at Berkeley, USA*), Yue Yang (*National University of Singapore*)

**Vol. 13 Econometric Forecasting and High-Frequency Data Analysis **

edited by Roberto S Mariano (*Singapore Management University, Singapore & University of Pennsylvania, USA*), Yiu-Kuen Tse (*Singapore Management University, Singapore*)

**Vol. 12 Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory **

edited by Jian-Shu Li (Hong Kong University of Science & Technology, Hong Kong), Eng-Chye Tan (National University of Singapore), Nolan Wallach (University of California, San Diego, USA), Chen-Bo Zhu (National University of Singapore)

**Vol. 11 Mathematics and Computation in Imaging Science and Information Processing **

edited by Say Song Goh (*National University of Singapore*), Amos Ron (*University of Wisconsin-Madison, USA*), Zuowei Shen (*National University of Singapore*)

**Vol. 10 Gabor and Wavelet Frames **

edited by Say Song Goh (*National University of Singapore*), Amos Ron (*University of Wisconsin-Madison,USA*), Zuowei Shen (*National University of Singapore*)

**Vol. 9 Dynamics in Models of Coarsening, Coagulation, Condensation and Quantization **

edited by Weizhu Bao (*National University of Singapore*), Jian-Guo Liu (*University of Maryland, USA*)

**Vol. 8 Transition and Turbulence Control **

edited by Mohamed Gad-el-Hak (*Virginia Commonwealth University, USA*), Her Mann Tsai (*National University of Singapore*)

**Vol. 7 Markov Chain Monte Carlo: Innovations and Applications **

edited by W S Kendall (*University of Warwick, UK*), F Liang (*Texas A&M University, USA*), J-S Wang (*National University of Singapore*)

**Vol. 6 Computational Methods in Large Scale Simulation **

edited by Khin-Yong Lam (*Institute of High Performance Computing, Singapore*), Heow-Pueh Lee (*Institute of High Performance Computing, Singapore*)

**Vol. 5 Stein's Method and Applications **

edited by A D Barbour (*University of Zürich*), Louis H Y Chen (*National University of Singapore*)

**Vol. 4 An Introduction to Stein's Method **

edited by A D Barbour (*University of Zürich*), Louis H Y Chen (*National University of Singapore*)

**Vol. 3 Selected Topics in Post-Genome Knowledge Discovery **

edited by Limsoon Wong (*National University of Singapore*), Louxin Zhang (*National University of Singapore*)

**Vol. 2 Representations of Real and P-Adic Groups **

edited by Eng-Chye Tan (

**Vol. 1 Coding Theory and Cryptology **

edited by Harald Niederreiter (*National University of Singapore*)