The course will focus on the Galois representations attached to automorphic forms and their deformation theory. Topics include the Taylor-Wiles method and its generalizations, the structure of automorphic Hecke algebras, and applications.
Prerequisites: Refer to course syllabus.
Continuation of IEOR E6711 covering further topics in stochastic modeling in the context of queueing, reliability, manufacturing, insurance risk, financial engineering and other engineering applications. Topics from among generalized semi-Markov processes; processes with a non-discrete state space; point processes; stochastic comparisons; martingales; introduction to stochastic calculus.
In recent years, the growing inequality within countries that have achieved enormous economic and democratic advancements has sparked fascinating debates on its causes, consequences, and ramifications. This course investigates the nexus between economic growth and social investment policies (e.g., education, housing, social assistance, labor market policies, and healthcare) and how a variety of factors, including political actors, processes, and institutions, influence the nature of the relationship. It equips students with the theoretical tools, empirical data, and historical materials necessary to better understand regional trends as well as distinctive domestic outcomes. The East Asian experience is set as the starting point, followed by a close examination of reform efforts in Latin America and Africa. Case studies are utilized to delve deeper into specific issues, such as racial divisions, adverse systemic shocks, and gender inequality.
This is a Public Health Course. Public Health classes are offered on the Health Services Campus at 168th Street.For more detailed course information, please go to Mailman School of Public Health Courses website at http://www.mailman.hs.columbia.edu/academics/courses
Survey of American architecture from the 17th century to the centennial, with scrutiny of the relationship between social and cultural ideals and architectural style and form. Consideration of the influence of European high style on American building and the connection between high style and vernacular forms. Domestic, religious, civic, commerical, and industrial architecture.
Prerequisites: A Course in at least One of the following: AI, Robotics, Computer Graphics, or Computer Vision
Seminar on Humanoid Robots. Analysis of existing hardware and software platforms. Programming of multi-degree-of-freedom robots. Understanding sensor feedback in perceive-act-sense control paradigms. Task-level planning and reasoning. Final project includes implementing a humanoid robot task on either a simulated or physical robot.
Prerequisites:
COMS W4731
or the instructor's permission.
Computational imaging uses a combination of novel imaging optics and a computational module to produce new forms of visual information. Survey of the state of art in computational imaging. Review of recent papers on: omni directional and panoramic imaging, catadioptric imaging, high dynamic range imaging, mosaicing and superresolution. Classes are seminars with the instructor, guest speakers, and students presenting papers and discussing them.
This course introduces students to international human rights law (IHRL). In what sense are internationally-defined human rights "rights" and in what sense can the instruments which define them be considered "law"? How do we know that a claim is actually a "human right"? What are the relations among international, regional and national institutions in establishing and enforcing (or not) IHRL? Does IHRL represent an encroachment on national sovereignty? Is the future of IHRL regional? What enforcement mechanisms can we use, and who can decide upon their use? Finally, what redress is there for human rights violations, and how effective is it? Attendance is required in the first class.
Prerequisites: Knowledge of programming; ELEN E4703 or related; or CSEE W4119; or instructor's permission.
Internet of Things from the point of view of data. Methods for data analytics to understand tradeoffs and partitioning between cloud-based data-analytics and physical-device data-analytics. Two-way interaction between data and physical devices to support a truly ubiquitous, networked and autonomous cyber-physical ecosystem. System-focused design of architectures, algorithms, networks, protocols, communications, power, security and standards. Focus on a significant design project.
Prerequisites: Recommended preparation: CSEE W4119 or E6761, ability to comprehend and track development of sophisticated models.
Mathematical models, analyses of economic and networking interdependencies in the Internet. Topics include microeconomics of pricing and regulations in communications industry, game theory in revenue allocations, ISP settlements, network externalities, two-sided markets. Economic principles in networking and network design, decentralized vs. centralized resource allocation, “price of anarchy”, congestion control. Case studies of topical Internet issues. Societal and industry implications of Internet evolution.
This course examines persistence and change in the global distribution of income, both within and across countries. We will consider philosophical arguments about inequality and whether or not it is a problem. Then we will review and discuss the measurement and positive economics of inequality. Finally, we will discuss political consequences of and policy responses to increases in inequality.
This course will be devoted to an analytic study of the transformation. The bulk of the course will be devoted to understanding the reforms that are under way or must be undertaken to accelerate growth and poverty reduction. On the macroeconomic front, we will discuss the issues related to fiscal deficit, public debt and the likelihood of a macroeconomic crisis. Special attention will be paid to the external sector reforms including trade liberalization, foreign investment liberalization, capital account convertibility, preferential trade arrangements and multilateral trade negotiations. Among domestic reforms, we will discuss the reform of the tax system, subsidies, agriculture, product and factor markets, infrastructure and social sectors. Cautionary Note: This is a new course whose content will evolve as the semester progresses. Therefore, the description should be viewed as tentative.
The purpose of this course is to provide students with a grounding in the practical side of implementation of economic sanctions as a tool of foreign policy. At the conclusion of the course, students will: 1) Understand the concepts associated with the implementation of economic sanctions; 2) Be conversant in the bureaucractic structures associated with sanctions implementation; and, 3) Understand the complicated and difficult choices required in the imposition of economic sanctions, including the risks of unintended consequences.
This course focuses on the use of special operations as an instrument of national strategy. While militaries have traditionally given precedence to conventional forces, since the end of the Second World War special operations forces have assumed an increasingly prominent role in statecraft. Civilian policymakers have been drawn to special operations, like air power, because it promises a less costly alternative to the use of conventional, ground forces. In practice, the effectiveness of special operations has varied with the problem at hand, the organizations involved, and the integration among civilian policy makers, special forces, and conventional military commands. The course opens with a review of the portfolio of roles and missions assigned to special operations forces. We will then narrow our focus to the use of special operations in the context of insurgency, counterinsurgency, and counterterrorism. In the second half of the course, we will examine a number of historical and contemporary cases to gauge the potential and the limits of special operations in various contexts.
There are two purposes to this course: 1. to develop your ability to negotiate in a purposeful, principled and effective way; and 2. to teach you how to build consensus and broker wise agreements with others. Negotiation is a social skill, and like all social skills you have to practice it if you want to get better at it. To give you the chance to practice, we'll do a number of simulated negotiations in and out of class. We'll also use lectures, case studies, exercises, games, videos, and demonstrations to help you develop your understanding. As we advance in the course, our focus will shift from simple one-on-one negotiations to more complex ones involving many parties, agents, coalitions, and organizations.
Prerequisites:
ECON G6211
and
G6215
.
G6806 is the second of two courses in the Public Economics sequence. The first course focused on issues related to taxation and redistribution. This course focuses on the role of the government in enhancing economic efficiency. In particular, it covers topics related to externalities (e.g., pollution), public good provision, and social insurance and social security. The course will combine applied theory (including behavioral models) and empirical work (including applications from developing countries), with a special emphasis on recent research in the field.