Course Synopses

Prerequisite: 750:417 Introductory Quantum Mechanics, or equivalent. Historical introduction; waves and wave packets; one-dimensional problems; representation theory; angular momentum and spin; time-dependent and time independent perturbation theory, the WKB approximation; atomic and molecular systems; theory of scattering; semi-classical theory of radiation; Dirac equation.

Prerequisite: 750:417 Introductory Quantum Mechanics, or equivalent. Historical introduction; waves and wave packets; one-dimensional problems; representation theory; angular momentum and spin; time-dependent and time independent perturbation theory, the WKB approximation; atomic and molecular systems; theory of scattering; semi-classical theory of radiation; Dirac equation.

Prerequisites: 750:386 or equivalent. Advanced Electromagnetic theory and related mathematical techniques. Boundary value problems in electrostatics and magnetostatics. Complex variables. Green's function, multipole expansions. Maxwell's equations and plane electromagnetic waves; waveguides. Radiation. Detailed discussion of special relativity, including, for example, space-time diagrams, covariance and invariance, twin paradox, uniform acceleration, motion of a charged particle, stress-energy tensors. Radiation by moving charges, bremsstrahlung, multipole fields, radiation damping.

Prerequisites: 750:386 or equivalent. Advanced Electromagnetic theory and related mathematical techniques. Boundary value problems in electrostatics and magnetostatics. Complex variables. Green's function, multipole expansions. Maxwell's equations and plane electromagnetic waves; waveguides. Radiation. Detailed discussion of special relativity, including, for example, space-time diagrams, covariance and invariance, twin paradox, uniform acceleration, motion of a charged particle, stress-energy tensors. Radiation by moving charges, bremsstrahlung, multipole fields, radiation damping.

Modern optics; atomic and solid-state phenomena; masers, lasers, theory of amplification, oscillation, coherence; photon correlations; nonlinear optics. Electron and nuclear magnetic resonance. Tunneling phenomena.

Prerequisites: 750:326 Experimental Physics and 388 Modern Physics Lab, or equivalent. Modern instruments and techniques in experimental physics. Topics include passive network theory and transient and steady state response analysis; transmission lines; operational amplifiers; digital circuits; a detailed study of noise; phase sensitive detection, including lock-in amplifiers and signal averagers; low-level measurement techniques, including quantum interference devices; particle detection techniques.

The purpose of this course is to acquire hands-on experience with experimental aspects of modern physics and to deepen your understanding of the relations between experiment and theory. You will carry out experiments which, when first performed, led to seminal discoveries in physics. In the process you will acquire a set of basic skills essential to becoming an experimental scientist. You will learn to use advanced laboratory equipment and will acquire computational skills necesasry for data analysis and error estimation. In adition you will acquire the skills to produce credible records of scientific data and you will learn how to disseminate scientific findings through written reports and oral presentations.

Prerequisites: 750:382 Mechanics and 386 Electromagnetism, or equivalent. Advanced classical mechanics, calculus of variations, Hamilton's equations, canonical transformations, Hamilton-Jacobi theory, small oscillations, rigid body motion.

Prerequisite: Programming experience. Survey of applications. Survey of hardware and software of a computer installation, interactive computing. Advanced Fortran, program structures, style, documentation, debugging. Machine language basics, data acquisition, equipment control. Use of data tapes, data processing. Monte Carlo techniques. Statistics and data fitting. Basic numerical methods. Laboratory: programming on several computers. The course is designed for the student who has some experience and wishes to broaden his/her knowledge of applications and develop techniques.

This course introduces logarithmic concepts and familiarizes students with the basic conputational tools which are essential for graduate students in computational physics and related areas. In this course, students work toward mastering computational skills, needed to work in classical and quantum physics using the computer. Examples will be drawn from various areas of physics. As the programing language, we will use mostly Python and its scientific library scipy & numpy. To speed up parts of the code, we will also use C++ and fortran90 for short examples, which will be used through the Python interface. This course has no prerequsites except for familiarity with some programming language. It is designed for the student who wishes to broaden his/her knowledge of applications and develop techniques. To follow the course more efficiently, and perform the hands on training, it is desired that students bring their own laptops to the class.

Prerequisites: 640:403 Complex Variables and 640:423 Partial Differential Equations, or equivalent. Functions of a complex variable, contour integration, calculus of residues, conformal mapping with applications to electrostatics, magnetostatics and fluid dynamics in two dimensions. Solution of boundary-value problems of physics by integral equation methods, construction of Green's functions. Fourier and Laplace transform theory with applications to harmonic motion, electrostatics, heat conduction, circuits and transients.

Prerequisite: 750:503 Elcetricity and Magnetism. Electromagnetic phenomena in astrophysical systems. Radiative transfer. Radiation from moving charges. Emission mechanisms: Bremsstrahlung, synchrotron, Compton scattering. Plasma effects. Atomic and molecular structure and spectroscopy.

Prerequisite: Elementary physics laboratory. Not intended for students in the Ph.D. program. Electronics as it is used in experimental physics. Transistors and their equivalent circuits, amplifiers, networks, digital logic, light and particle detectors, low-level measurements, including quantum interference devices.

Not intended for students in the Ph.D. program. Self-paced course in which the student studies independently and the faculty act as tutors, providing help as needed and administering examinations. Subject matter divided into units, covering a wide range of subjects drawn from classical and modern physics. Units chosen in consultation with an adviser, taking into account the background and interests of each student.

Observed properties of stars. The internal structure of stars, energy generation and transport, neutrinos, solar oscillations. The evolution of isolated and double stars, red giants, white dwarfs, variable stars, supernovae. Challenges presented by the formation of stars, the importance of magnetic fields. Pre-main sequence stellar evolution.

We will study the observed properties and physics of stars, including their internal structure, energy generation and transport, and their atmospheres. We will examine star formation, stellar evolution, and stellar remnants, including white dwarfs, neutron stars, and black holes.

Properties of galaxies; photometry, kinematics, and masses. Disk galaxies, spiral patterns, bars and warps, gas content, star formation rates, chemical evolution. Elliptical galaxies: shapes. Structure of the Milky Way. The nature of dark matter.

Galaxies are an important nexus in the cosmic hierarchy: they serve as lighthouses marking out the vast cosmic structures that can span many millions of parsecs, but are fascinating in themselves as laboratories for the "small scale" processes of stellar birth and evolution. We now have images of billions of galaxies, and can observe them from a time less than a billion years after the Big Bang until the present day. We can study not only the appearance or "morphology" of galaxies, but also in some cases measure properties of their stellar populations, their quota of heavy elements, their gas content, and the internal motions (or kinematics) of their stars and gas. Although galaxies exhibit amazing diversity, they also conform to certain surprisingly tight correlations. From kinematic measurements, we can infer that galaxies contain a major unseen component that influences the motions of their stars and gas: the mysterious "dark matter". Moreover, the stars and gas that we can measure within galaxies falls far short of what we would expect for the cosmic "baryon budget". The study of modern galaxy formation focuses on trying to understand the observed demographics and correlations of galaxy properties and how these evolve over cosmic time, in the context of the "hierarchical structure formation" picture provided by the Cold Dark Matter theory.

In this course, we will warm up with a brief review of stars and radiative processes and basic cosmology. We will start our study of galaxies with our home Galaxy, the Milky Way, our sister galaxy M31 (Andromeda), and our smaller companions the Local Group dwarfs. Even this relatively small population of galaxies in our own "backyard" poses a number of unsolved puzzles. We will then cover the properties of spiral, lenticular, and elliptical galaxies in the 'nearby' Universe, and discuss the larger structures that form galaxy habitats: groups and clusters. One fascinating open question is whether galaxy properties are mainly shaped by "internal" processes or by their environment. We will discuss the evidence that many or even most galaxies harbor supermassive black holes in their nuclei. We will wind up the course with a discussion of how we can find and observe extremely distant (high redshift) galaxies, and of how galaxies were different in the past.

Prerequisite: Permission of instructor. The epistemology of physics; the construction of knowledge; how physicists know what they know.

Prerequisite: Permission of instructor. Pedagogical content knowledge and skills; techniques for planning and assessment.

Prerequisite: Permission of instructor. Multiple representation method used in constructing concepts and problem solving.

Prerequisite: Advanced undergraduate courses in physical chemistry or physics. Focuses on molecular modeling and simulations of biological macromolecules including proteins and nucleic acids, molecular dynamics and Monte Carlo methods, and solvation. Computer simulations and exercises are an integral part of the course. Also offered as 16:118:513.

Prerequisite: Linear algebra, differential equations, thermodynamics, and classical physics (at the junior level). Review of physical phenomena that determine the properties of biological molecules, molecular assemblies, and fundamental biological processes. Also offered as 16:118:507.

This course is designed to introduce biophysics to upper-level physics undergraduate and graduate students. The course will start with a review of big ideas in modern molecular/cellular biology to familiarize physics students with the language used in life science. Thereafter, basic physical principles underling structure and dynamics of macromolecules, such as diffusion, random walks, low Reynolds-number hydrodynamics, entropic force, and osmotic pressure, will be discussed in the light of soft matter physics. Life cannot persist without constant mechanical work of numerous molecular machines inside cells. The working principles of these molecular machines will be studied in more detail through enzyme kinetics and mechano-chemical coupling. Recent developments in biophysical methods that have enabled testing of many physical models in biology will be covered as well.

Prerequisite: 750:501 Quantum Mechanics and 750:507 Classical Mechanics, or permission of the instructor. Statistical analysis techniques including probability distributions, maximum likelihood, significance tests, Bayesian statistics, statistical/machine learning, kernel methods and neural networks, with example applications to current large-scale analysis problems in physics and astronomy.

Prerequisites: 750:502 and 750:351 or equivalent. Introduction to: crystal lattices, scattering of radiation, lattice dynamics, electron bands, interaction among elementary excitations, disordered systems, transport properties, superconductivity and super-fluidity, magnetism, crystal-field effects, phase transitions, optical properties.

Prerequisites: 750:502 and 750:351 or equivalent. Introduction to: crystal lattices, scattering of radiation, lattice dynamics, electron bands, interaction among elementary excitations, disordered systems, transport properties, superconductivity and super-fluidity, magnetism, crystal-field effects, phase transitions, optical properties.

In this course I hope to introduce experimental and theoretical students to a number of contemporary research topics in condensed matter physics including frustrated magnetism, quantum phase transitions and topological insulators. More specifically we will discuss

• "moment-free" magnetism
• topological transitions in spin systems
• quantum vs. classical phase transitions
• topological insulators

This course will be concept-based but technical details will be supplied when needed. We will connect our topics of study with current research through readings of both classic and current papers. More specifically I plan to link the topics to be explored with research areas of ongoing interest: Kitaev spin liquids, emergent topological order in magnetic systems, quantum critical systems and the emergence of new states of matter.

Premi Chandra

Advanced treatment of topics surveyed in 750:601 and their extension to topics of current interest in solid-state physics.

Prerequisite: 750:502, Quantum Mechanics, or equivalent. Survey of essential topics: properties of ground states, shell model, collective model, electromagnetic properties, simple excitations, compound-nucleus and direct reactions, beta decay. Additional topics may include alpha decay, fission, applications of nuclear physics, topics of current interest.

Prerequisites: 750:514 Radiative Processes or 750:504 Electricity and Magnetism II. Stellar properties, internal structure, energy generation and transport, neutrinos, atmospheres, solar oscillations. Stellar evolution, red giants, white dwarfs, variable stars, supernovae, neutron stars, black holes. Brown dwarfs, planets, extrasolar planets.

Prerequisites: 750:507, Classical Mechanics. Galaxy properties: photometry, structure, kinematics, gas content, chemical evolution; Milky Way. Stellar system equilibrium, stability, evolution. Disk and elliptical galaxy dynamics and evolution (spiral patterns, bars, warps). Astrophysical chaos.

Properties of galaxies: photometry, structure, kinematics, gas content, chemical evolution. Structure of the Milky Way. Equilibrium, stability, and evolution of stellar systems. Dynamics and evolution of disk galaxies (spiral patterns, bars, warps) and elliptical galaxies. Examples of chaotic astrophysical systems.

In addition to learning about the observed properties of galaxies, and how they evolve over cosmic time, we will also study the modern theory for how galaxies form in the context of the "hierarchical structure formation" picture provided by the Cold Dark Matter theory. Topics that will be covered include:

• structure formation in the Cold Dark Matter model
• galaxy clustering and bias
• the Milky Way and the Local Group
• demographics of nearby galaxies
• galaxies and their environment
• interactions and mergers
• galaxy evolution over cosmic time
• dynamics and stability of galactic disks
• dynamics and evolution of elliptical galaxies
• black holes and Active Galactic Nuclei

Prerequisites: 750:341-342 Principles of Astrophysics or equivalent. Models of the universe, their fundamental parameters and their estimation from observations. Evolution of the universe from soon after its formation to the present. Growth of structure and the formation of galaxies.

This is a graduate-level course on the origin and evolution of the Universe. Cosmology is a rich field of physics, drawing from astrophysics, gravitation, particle physics, nuclear physics and thermodynamics. The two decades have seen the development of a standard model of cosmology called Lambda Cold Dark Matter (LCDM) which explains a wide array of observed phenomena and has successfully predicted the power spectra of cosmic microwave background and large-scale structure. This class will attempt to highlight the quality of the current match between data and theory.

Prerequisites: 750:507 or equivalent. Fundamental physical properties of liquids, gases, and ionized systems. Includes selected topics from compressible and incompressible flow, electromagnetic interactions, instabilities, turbulence, nonequilibrium phenomena, kinetics, superfluid mechanics, related experimental techniques, and other topics of current interest in fluid and plasma research.

The course will present some aspects of fluid mechanics and the physics of plasmas. While the course has a strong emphasis on applications to astronomy, it should be of value to students in all walks of physics and applications in other areas will creep in from time to time. All students with PhD research projects in astronomy should take this course. No graduate level astronomy courses are required as background, but the course will assume standard graduate level preparation in physics.

Prerequisite: 750:541 or equivalent. Structure of the inter-stellar medium: its molecular, neutral atomic and plasma phases. Radiative transfer, dust, particle acceleration, magnetic fields and cosmic rays. Effects of supernovae, shock fronts and star formation.

Here's the official course catalog listing:
"Structure of the interstellar medium: its molecular, neutral atomic, and plasma phases. Radiative transfer, dust, particle acceleration, magnetic Fields, and cosmic rays. Effects of supernovae, shock fronts, and star formation."

I plan to broaden this list of topics to include the intergalactic medium; in general, I will try to highlight subjects that are important to areas of current research in extragalactic astrophysics and cosmology (e.g., galaxy formation, the enrichment of the intergalactic medium, and the reionization of the universe).

Prerequisites: 750:501, 502, Quantum Mechanics, 507 Classical Mechanics. Statistical methods and probability; the statistical basis for irreversibility and equilibrium; ensemble theory; statistical thermodynamics; classical and quantum statistics; the density matrix; applications of statistical mechanics to non-ideal gases, condensed matter, nuclei and astrophysics; fluctuations, non-equilibrium statistical mechanics; kinetic theory.

Prerequisite: 750:341-342 or equivalent. The origin and detection of high energy photons and particles in the universe. Radiation processes in low density media. Sites of high energy phenomena in astrophysics, such as supernovae, pulsars, active galactic nuclei and quasars and processes such as accretion and shocks.

The Universe is filled with diverse objects and phenomena ranging from those with very low characteristic temperatures, such as the 2.7 K Cosmic Microwave Background Radiation, to the ultrahigh energy cosmic rays in which a single particle can carry 10 J or more of energy. Accordingly in order to attempt a complete understanding of cosmic objects and events, astrophysicists have been driven to conduct studies over the entire electromagnetic spectrum. In this course, the focus will be on the study of high energy astrophysics, that is to say, the field of astronomy that concerns itself with objects and phenomena having a characteristic temperature greater than about 10^6 K or equivalently 0.1 keV. This includes the X-ray and gamma-ray bands of the electromagnetic spectrum, cosmic rays, and neutrinos from the Sun and supernovae. The field is relatively new: cosmic rays were discovered in 1912 (although not explained as high energy particles until 1929) and, although, X-rays were discovered by Rongten in 1895, X-ray astronomy wasn't born until 1949 when the Sun was discovered as the first extraterrestrial X-ray source. In general the history of X-ray and gamma-ray astronomy has paralleled the history of space exploration. Neutrino astronomy is even younger, commencing with the Homestake gold mine experiment in the 1970's which gave rise to the famous "solar neutrino" problem.

This course is intended to provide the student with sufficient background material and knowledge in order to appreciate current research literature in high energy astrophysics. It will draw on graduate level physics and astronomy as prerequisites. Although the text listed above is required, some course material will be taken from other sources, such as "Radiative Precesses in Astrophysics" by Rybicki and Lightman (Wiley), particularly for lectures on radiative processes. Students might consider looking at the readable book on X-ray astronomy "Exploring the X-ray Universe" by Charles and Seward (Cambridge).

Prerequisite: 750:502 Quantum Mechanics, or equivalent. Introduction to the concepts and techniques underlying current research in elementary particles. Assumes knowledge of quantum mechanics, scattering theory, and nuclear spectroscopy. Properties of particles and their interactions based on the standard model of strong and electroweak interactions. Conservation laws. Discussion of specific experiments illustrating the standard model.

Prerequisite: 750:502 Quantum Mechanics, or equivalent. Lorentz group; relativistic wave-equations; second quantization; global and local symmetries; QED and gauge invariance; spontaneous symmetry breaking; nonabelian gauge theories; Standard Model; Feynman diagrams; cross sections, decay rates; renormalization group.

Prerequisite: 750:615 Advanced Quantum Mechanics. Path integral quantization; perturbation theory: dimensional regularization, renormalization; the renormalization group; spontaneous symmetry breaking and effective potential; critical behavior of ferromagnets; d field theory; Yang- Mills perturbation theory.

Prerequisites: 750:507, Classical Mechanics, or equivalent, 504 Electricity and Magnetism. Equivalence principle, tensor analysis with differential forms; review of special relativity and electromagnetism; affine connection and geodesic equation; curvature and geodesic deviation; Einstein field equations; Schwarzschild and Kerr solutions, homogeneous isotropic cosmologies; experimental and observational tests.

This is a graduate course in general relativity. We will cover the mathematical framework behind Einstein's theory, the formulation of Einstein's equations, the Schwarzschild and Kerr metrics, gravitational radiation, and cosmology. The textbook for the course is Spacetime and Geometry by Sean Carroll (2003, Pearson ISBN 978-0805387322).

Additional texts that may be of use to students are General Relativity by Robert Wald and Gravitation by Misner, Thorne, and Wheeler (i.e. the giant black book about gravity). Neither are required for the course.

Prerequisite: 750:502 Quantum Mechanics, or equivalent. Abstract groups and their representations, finite groups and Lie algebras; symmetries and currents; symmetric group, inhomogeneous Lorentz group, SU(n); classification of Lie algebras, Dynkin diagrams. Spontaneous symmetry breaking mechanisms. Gauge theories.

This is a course on group theory primarily intended for physics graduate students intending to specialize in condensed matter or particle theory. It will also have material of interest to mathematics students with some interest in mathematical physics. A more detailed course description of a past incarnation can be found here. 

Prerequisite: 16:750:616 Fields I. Renormalization group applied to Yang- Mills: asymptotic freedom; spontaneous symmetry breaking applied to Yang- Mills: Weinberg-Salam theory; lattice gauge theory; grand unified theories; supersymmetry; strings.

Prerequisite: 750:502 Quantum Mechanics, or equivalent. Hartree-Fock and Thomas-Fermi methods, elementary excitations, theory of the Fermi liquid, properties of liquid helium; many-body perturbation theory at zero and finite temperature, statistical mechanics of many-particle systems, Green's function techniques, systems of interacting bosons and fermions, collective modes, theory of superconductivity and superfluidity, properties of nuclear matter. (A second semester of Many-Body Problems is available, temporarily listed as 682 Advanced Topics in Condensed Matter.)

Many body physics provides the framework for understanding the collective behavior of vast assemblies of interacting particles. This course provides an introduction to this field, introducing you to the main techniques and concepts, aiming to give you first-hand experience in calculations and problem solving using these methods. 

Prerequisite: 16:750:620 or equivalent. Systems of interacting bosons and fermions. Theory of superconductivity and superfluidity. Application of the renormalization group to many-body problems. One-dimensional electron gas. Kondo problem and heavy fermions.

Prerequisite: Consent of Graduate Director. Individual studies supervised by a member of the staff.

Prerequisite: Consent of Graduate Director. Individual studies supervised by a member of the staff.

Introduction to structure and dynamics of clean surfaces, atoms and molecules on surfaces, and interfaces. Topics include: atomistic description of geometrical structure, surface morphology, electronic structure, surface composition, and theoretical and experimental bases of modern experimental methods.

The purpose of the course is to acquaint students in physics, chemistry, materials science and electrical engineering with the static and dynamic behavior of clean and adsorbate-covered solid surfaces and interfaces, from both theoretical and experimental points of view. Topics will include geometrical structure, surface morphology, electronic structure, surface composition, kinetics and dynamics (adsorption, scattering, vibrations, diffusion, desorption), structure and reactivity of surface molecules, non-thermal excitations of surfaces, catalysis and surface reactions. We will discuss surfaces of metals, oxides and semiconductors, as well as solid-solid and solid-liquid interfaces. Modern ultrahigh vacuum experimental methods will be discussed: theoretical basis, experimental aspects, and data interpretation. Topical lectures by guest lecturers addressing thin films, nanostructures and low-dimensional systems will also be offered.

Kinetics and dynamics of processes at surfaces; structure and reactivity of molecules at surfaces; thermal and non-thermal excitations; magnetic properties. Surfaces of metals, oxides and semiconductors, as well as solid-solid and solid-liquid interfaces.

Prerequisite: 750:541 Introductory Astrophysics or equivalent. Introduction to tools and techniques of modern observational astronomy. Survey of instruments and capabilities at current telescope sites around the world and in space. Data reduction methods. Practical experience with Serin Observatory.

Here's the official course catalog listing:
"Introduction to tools and techniques of modern observational astronomy. Survey of instruments and capabilities at current telescope sites around the world and in space. Data reduction methods. Practical experience with Serin Observatory."

I plan to teach this course so that by the end of it you will be able to (1) understand how modern telescopes and instruments acquire data at all wavelengths, (2) understand how modern software packages are used to acquire, reduce, and catalog data, and (3) estimate signal/noise ratios before you obtain a given dataset, and statistically appropriate uncertainties for the quantities you measure from it. I will also spend a little time discussing the sociology of astronomical observing, i.e., how one successfully competes for time on large telescopes.

Prerequisite: Permission of graduate director. Seminars in fields of investigation of current interest.

This Seminar presents faculty of the Physics and Astronomy program discussing their current research. All first-year graduate students are expected to attend -- attendance is taken -- and everyone else is welcome.

Prerequisite: Permission of graduate director. Seminars in fields of investigation of current interest.

This Seminar presents faculty of the Physics and Astronomy program discussing their current research. All first-year graduate students are expected to attend -- attendance is taken -- and everyone else is welcome.

Prerequisite: Permission of instructor. Concurrent teaching assignment in physics or astronomy recommended. Intended for graduate students interested in improving their skills for teaching physics. Topics include teaching goals, results of recent research, lecturing, demonstrations, teaching problem solving, testing, active learning, course development, and teaching difficult concepts in selected areas of physics. Instructor observes the student teaching.

The courses may be taken in any order. Offered in alternate years.

Prerequisite: Permission of instructor. Concurrent teaching assignment in physics or astronomy recommended. Intended for graduate students interested in improving their skills for teaching physics. Topics include teaching goals, results of recent research, lecturing, demonstrations, teaching problem solving, testing, active learning, course development, and teaching difficult concepts in selected areas of physics. Instructor observes the student teaching.

The courses may be taken in any order. Offered in alternate years.

This course will provide an introduction to strongly correlated electron systems.   There will be a lot of discussion and interaction. Starting with a path-integral approach to many body physics, we will discuss broken symmetry in magnetism and superconductivity, going on to discussanisotropic superconductivity,  local moment formation, the Kondo Lattice and the physics of heavy fermion materials and quantum criticality.  We will end with a discussion of topological matter, including the quantum Hall effect and the strong topological insulator.   The course will be based in part on the last seven chapters of my book, "Introduction to Many-Body Physics". 

This course will provide an introduction to strongly correlated electron systems.   There will be a lot of discussion and interaction. Starting with a path-integral approach to many body physics, we will discuss broken symmetry in magnetism and superconductivity, going on to discussanisotropic superconductivity,  local moment formation, the Kondo Lattice and the physics of heavy fermion materials and quantum criticality.  We will end with a discussion of topological matter, including the quantum Hall effect and the strong topological insulator.   The course will be based in part on the last seven chapters of my book, "Introduction to Many-Body Physics". 

Gravitational lensing has matured into a thriving area of astrophysics, with applications across a wide range of scales and redshifts. The goals for this course are as follows:

• Understand the theory and phenomenology of gravitational lensing.
• Gain experience with quantitative aspects of lensing.
• Examine a variety of astrophysical applications of lensing.

We will develop the analytic theory as much as possible and consider computational approaches as appropriate. Some of the applications we will discuss include: properties of stars, planets, and stellar remnants; physical properties of galaxies; dark matter in galaxies and clusters of galaxies; structure of high-redshift galaxies and quasars; cosmological parameters.

This is an advanced graduate course designed for students pursuing research in physics and astronomy. Undergraduate physics and mathematics should provide adequate preparation. Familiarity with intermediate classical mechanics, electrodynamics, and quantum mechanics are helpful, as much of the mathematics encountered in those subjects applies to lensing.

The last decade has witnessed a revolution in our cosmological understanding: multiple lines of evidence show that we live in a Universe dominated by the effects of dark energy and dark matter. Characterizing the properties of these components is the frontier of current research. In this seminar, we will trace the development of these dark components in the standard cosmological model. We will also discuss current and proposed experiments to constrain the nature of dark matter and dark energy, and explore potential alternatives to the standard paradigm.

With quantum fluctuations in the early universe seeding superclusters and voids today, particle dark matter halos shaping and supporting galaxies, and vacuum energy driving the accelerating expansion, modern cosmology directly connects physics at the largest and smallest scales. As such, this course is broadly aimed to engage graduate students across physics, enabling a synthesis of observational, experimental, and theoretical results.

The course will have a reading/seminar format. We will meet weekly to discuss a few (~4) important papers on a specific topic, and two students will be assigned to lead the presentation for that week.

This is a special topics seminar aimed at 1st and 2nd year graduate students who intend to pursue a Ph.D. in experimental particle physics. The course is intended to bridge the gap in knowledge between formal theoretical physics (i.e. QFT) and experimental practice. Particle interactions in matter and detector techniques will be emphasized in relation to the historic development of our understanding of fundamental physics. Students will be expected to do the reading and associated problems prior to class, where the readings will be discussed in a seminar-style format.

The past 20 years have been an exciting time for the interaction of mathematics and physics. Remarkable new mathematical discoveries have been made using the methods of quantum field theory. Conversely, powerful new mathematical techniques have been successfully applied to gain nontrivial insights in sophisticated theories like supersymmetric gauge theories and string theory.

The purpose of this course is to provide some of the mathematical background which one needs in order to learn about these modern developments. The course surveys some aspects of topology and differential geometry of manifolds, with an emphasis on relations to modern mathematical physics. The course will also cover some aspects of supersymmetry.

This course is primarily intended for physics graduate students specializing in theoretical physics.

Some knowledge of manifolds, differential forms, and cohomology will be assumed, but we will try to keep the course material self-contained.