An introduction to string theory, with a focus on non-perturbative physics and dualities. Topics may include: quantization, spectrum and interactions of bosonic strings; strings in background fields; D-branes and T-duality; superstrings and the five ten-dimensional superstring theories; S-duality and M-theory; Calabi-Yau compactification; mirror symmetry; gauge theories; conformal field theories; the AdS/CFT correspondence; black holes.

In this course, we will investigate how quantum field theories emerge in quantum condensed matter systems. The emphasis will be on modern non-perturbative aspects of such field theories in low dimensions. Topics covered will include Ising spins, duality and Majorana field theory; bosonization and Luttinger liquids; aspects of conformal field theory; discrete gauge theories, deconfinement, and topological order; continuous spins, superfluidity and topological defects.

Many-body physics puts together the fundamental microscopic laws and produces new emergent principles that describe the macroscopic behavior of the system. Quantum field theory is a universal language that describes the emergent behavior, typical examples of which are "quasiparticle excitations." This is one of the notions that make quantum condensed matter systems so fascinating. We will cover many topics including Green's functions and Feynman diagrams, Landau's Fermi liquid theory, the quantum Hall effect, topological states of matter, fermionization, and more.

Newspapers, media-outlets, and online platforms inform us, almost every day, of the declaration of a state of emergency, the imposition of exceptional measures or the activation of the martial law to deal with economic, social, environmental and political crises, or to tackle scenarios of political violence. In short, the normalization of this dispositive in contemporary democracies has produced a broad understanding of what it is and how it is implemented. However, this course would argue that the paradigm of the state of exception remains underdeveloped.

The calculus of variations is the study of the minimization of integrals with respect to a function, whose integrand depends on the function and its derivatives. It is a powerful tool for solving PDE with an associated energy functional and arises in the theory of minimal surfaces. This course will consider both the classical methods and the direct methods in the theory of the calculus of variations. Applications will be made to classical mechanics as well as to the development of numerical methods.

The design and analysis of efficient algorithms for important computational problems. Emphasis on the relationships between algorithms and data structures and on measures of algorithmic efficiency. Sorting (heapsort, mergesort, quicksort), searching, graph algorithms. Experimental analysis of algorithms also emphasized. Use of computer required.

The design and analysis of efficient algorithms for important computational problems. Emphasis on the relationships between algorithms and data structures and on measures of algorithmic efficiency. Sorting (heapsort, mergesort, quicksort), searching, graph algorithms. Experimental analysis of algorithms also emphasized. Use of computer required.

The design and analysis of efficient algorithms for important computational problems. Emphasis on the relationships between algorithms and data structures and on measures of algorithmic efficiency. Sorting (heapsort, mergesort, quicksort), searching, graph algorithms. Experimental analysis of algorithms also emphasized. Use of computer required.

Drawing on U.S. Supreme Court jurisprudence, gender and sexuality studies, sociological literature, policy papers, documentary, and international law, we will examine the ways in which gender, sexuality, and race are constructed, contested, and regulated within legal, legislative, and juridical frameworks, across systems, spaces, and temporalities. Throughout this course, we will consider what the law is, what it does, how it operates to uphold systems of power and oppression and how it can be deployed in the service of intervention.

The objective of this course is to develop an understanding of Massachusetts wetlands regulations and techniques for wetlands assessments with an emphasis on wildlife habitat evaluation. Indoor lectures for the first eight weeks of the course are used to familiarize students with various assessment methodologies as well as Massachusetts wetlands protection regulations. Outdoor labs during the last five weeks of the semester will provide opportunities to apply information learned in lectures and gain experience conducting assessments in the field.