# Search result: Catalogue data in Autumn Semester 2019

Mathematics Master | ||||||

Electives For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields. | ||||||

Electives: Applied Mathematics and Further Application-Oriented Fields ¬ | ||||||

Selection: Numerical Analysis | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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401-4657-00L | Numerical Analysis of Stochastic Ordinary Differential Equations Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods" | W | 6 credits | 3V + 1U | K. Kirchner | |

Abstract | Course on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables. | |||||

Objective | The aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues. | |||||

Content | Generation of random numbers Monte Carlo methods for the numerical integration of random variables Stochastic processes and Brownian motion Stochastic ordinary differential equations (SODEs) Numerical approximations of SODEs Applications to computational finance: Option valuation | |||||

Lecture notes | There will be English, typed lecture notes for registered participants in the course. | |||||

Literature | P. Glassermann: Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York, 2004. P. E. Kloeden and E. Platen: Numerical Solution of Stochastic Differential Equations. Springer-Verlag, Berlin, 1992. | |||||

Prerequisites / Notice | Prerequisites: Mandatory: Probability and measure theory, basic numerical analysis and basics of MATLAB programming. a) mandatory courses: Elementary Probability, Probability Theory I. b) recommended courses: Stochastic Processes. Start of lectures: Wednesday, September 18, 2019. | |||||

401-4785-00L | Mathematical and Computational Methods in Photonics | W | 8 credits | 4G | H. Ammari | |

Abstract | The aim of this course is to review new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods used to address challenging problems in nanophotonics. The emphasis will be on analyzing plasmon resonant nanoparticles, super-focusing & super-resolution of electromagnetic waves, photonic crystals, electromagnetic cloaking, metamaterials, and metasurfaces | |||||

Objective | The field of photonics encompasses the fundamental science of light propagation and interactions in complex structures, and its technological applications. The recent advances in nanoscience present great challenges for the applied and computational mathematics community. In nanophotonics, the aim is to control, manipulate, reshape, guide, and focus electromagnetic waves at nanometer length scales, beyond the resolution limit. In particular, one wants to break the resolution limit by reducing the focal spot and confine light to length scales that are significantly smaller than half the wavelength. Interactions between the field of photonics and mathematics has led to the emergence of a multitude of new and unique solutions in which today's conventional technologies are approaching their limits in terms of speed, capacity and accuracy. Light can be used for detection and measurement in a fast, sensitive and accurate manner, and thus photonics possesses a unique potential to revolutionize healthcare. Light-based technologies can be used effectively for the very early detection of diseases, with non-invasive imaging techniques or point-of-care applications. They are also instrumental in the analysis of processes at the molecular level, giving a greater understanding of the origin of diseases, and hence allowing prevention along with new treatments. Photonic technologies also play a major role in addressing the needs of our ageing society: from pace-makers to synthetic bones, and from endoscopes to the micro-cameras used in in-vivo processes. Furthermore, photonics are also used in advanced lighting technology, and in improving energy efficiency and quality. By using photonic media to control waves across a wide band of wavelengths, we have an unprecedented ability to fabricate new materials with specific microstructures. The main objective in this course is to report on the use of sophisticated mathematics in diffractive optics, plasmonics, super-resolution, photonic crystals, and metamaterials for electromagnetic invisibility and cloaking. The book merges highly nontrivial multi-mathematics in order to make a breakthrough in the field of mathematical modelling, imaging, and optimal design of optical nanodevices and nanostructures capable of light enhancement, and of the focusing and guiding of light at a subwavelength scale. We demonstrate the power of layer potential techniques in solving challenging problems in photonics, when they are combined with asymptotic analysis and the elegant theory of Gohberg and Sigal on meromorphic operator-valued functions. In this course we shall consider both analytical and computational matters in photonics. The issues we consider lead to the investigation of fundamental problems in various branches of mathematics. These include asymptotic analysis, spectral analysis, mathematical imaging, optimal design, stochastic modelling, and analysis of wave propagation phenomena. On the other hand, deriving mathematical foundations, and new and efficient computational frameworks and tools in photonics, requires a deep understanding of the different scales in the wave propagation problem, an accurate mathematical modelling of the nanodevices, and fine analysis of complex wave propagation phenomena. An emphasis is put on mathematically analyzing plasmon resonant nanoparticles, diffractive optics, photonic crystals, super-resolution, and metamaterials. | |||||

Selection: Probability Theory, Statistics | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-4597-67L | Random Walks on Transitive Graphs | W | 4 credits | 2V | V. Tassion | |

Abstract | In this course, we will present modern topics at the interface between probability and geometric group theory. We will be mainly focused on the random walk, and discuss its behavior depending on the geometric properties of the underlying graph. | |||||

Objective | ||||||

Prerequisites / Notice | - Probability Theory. - Basic properties of Markov Chains. - No prerequisite on group theory, all the background will be introduced in class. | |||||

401-4619-67L | Advanced Topics in Computational StatisticsDoes not take place this semester. | W | 4 credits | 2V | not available | |

Abstract | This lecture covers selected advanced topics in computational statistics. This year the focus will be on graphical modelling. | |||||

Objective | Students learn the theoretical foundations of the selected methods, as well as practical skills to apply these methods and to interpret their outcomes. | |||||

Content | The main focus will be on graphical models in various forms: Markov properties of undirected graphs; Belief propagation; Hidden Markov Models; Structure estimation and parameter estimation; inference for high-dimensional data; causal graphical models | |||||

Prerequisites / Notice | We assume a solid background in mathematics, an introductory lecture in probability and statistics, and at least one more advanced course in statistics. | |||||

401-3628-14L | Bayesian Statistics | W | 4 credits | 2V | F. Sigrist | |

Abstract | Introduction to the Bayesian approach to statistics: decision theory, prior distributions, hierarchical Bayes models, empirical Bayes, Bayesian tests and model selection, empirical Bayes, Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods. | |||||

Objective | Students understand the conceptual ideas behind Bayesian statistics and are familiar with common techniques used in Bayesian data analysis. | |||||

Content | Topics that we will discuss are: Difference between the frequentist and Bayesian approach (decision theory, principles), priors (conjugate priors, noninformative priors, Jeffreys prior), tests and model selection (Bayes factors, hyper-g priors for regression),hierarchical models and empirical Bayes methods, computational methods (Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods) | |||||

Lecture notes | A script will be available in English. | |||||

Literature | Christian Robert, The Bayesian Choice, 2nd edition, Springer 2007. A. Gelman et al., Bayesian Data Analysis, 3rd edition, Chapman & Hall (2013). Additional references will be given in the course. | |||||

Prerequisites / Notice | Familiarity with basic concepts of frequentist statistics and with basic concepts of probability theory (random variables, joint and conditional distributions, laws of large numbers and central limit theorem) will be assumed. | |||||

401-3619-69L | Mathematics Tools in Machine Learning | W | 4 credits | 2G | F. Balabdaoui | |

Abstract | The course reviews many essential mathematical tools used in statistical learning. The lectures will cover the notions of hypotheses classes, sample complexity, PAC learnability, model validation and selection as well as results on several well-known algorithms and their convergence. | |||||

Objective | In the exploding world of artifical intelligence and automated learning, there is an urgent need to go back to the basis of what is driving many of the well-establsihed methods in statistical learning. The students attending the lectures will get acquainted with the main theoretical results needed to establish the theory of statistical learning. We start with defining what is meant by learning a task, a training sample, the trade-off between choosing a big class of functions (hypotheses) to learn the task and the difficulty of estimating the unknown function (generating the observed sample). The course will also cover the notion of learnability and the conditions under which it is possible to learn a task. In a second part, the lectures will cover algoritmic apsects where some well-known algorithms will be described and their convergence proved. Through the exerices classes, the students will deepen their understanding using their knowledge of the learned theory on some new situations, examples or some counterexamples. | |||||

Content | The course will cover the following subjects: (*) Definition of Learning and Formal Learning Models (*) Uniform Convergence (*) Linear Predictors (*) The Bias-Complexity Trade-off (*) VC-classes and the VC dimension (*) Model Selection and Validation (*) Convex Learning Problems (*) Regularization and Stability (*) Stochastic Gradient Descent (*) Support Vector Machines (*) Kernels | |||||

Literature | The course will be based on the book "Understanding Machine Learning: From Theory to Algorithms" by S. Shalev-Shwartz and S. Ben-David, which is available online through the ETH electronic library. Other good sources can be also read. This includes (*) the book "Neural Network Learning: Theoretical Foundations" de Martin Anthony and Peter L. Bartlett. This book can be borrowed from the ETH library. (*) the lectures notes on "Mathematics of Machine Learning" taught by Philippe Rigollet available through the OpenCourseWare website of MIT | |||||

Prerequisites / Notice | Being able to follow the lectures requires a solid background in Probability Theory and Mathematical Statistical. Notions in computations, convergence of algorithms can be helpful but are not required. | |||||

401-0625-01L | Applied Analysis of Variance and Experimental Design | W | 5 credits | 2V + 1U | L. Meier | |

Abstract | Principles of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power. | |||||

Objective | Participants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R. | |||||

Content | Principles of experimental design, one-way analysis of variance, contrasts and multiple comparisons, multi-factor designs and analysis of variance, complete block designs, Latin square designs, random effects and mixed effects models, split-plot designs, incomplete block designs, two-series factorials and fractional designs, power. | |||||

Literature | G. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000. | |||||

Prerequisites / Notice | The exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held. | |||||

401-0649-00L | Applied Statistical Regression | W | 5 credits | 2V + 1U | M. Dettling | |

Abstract | This course offers a practically oriented introduction into regression modeling methods. The basic concepts and some mathematical background are included, with the emphasis lying in learning "good practice" that can be applied in every student's own projects and daily work life. A special focus will be laid in the use of the statistical software package R for regression analysis. | |||||

Objective | The students acquire advanced practical skills in linear regression analysis and are also familiar with its extensions to generalized linear modeling. | |||||

Content | The course starts with the basics of linear modeling, and then proceeds to parameter estimation, tests, confidence intervals, residual analysis, model choice, and prediction. More rarely touched but practically relevant topics that will be covered include variable transformations, multicollinearity problems and model interpretation, as well as general modeling strategies. The last third of the course is dedicated to an introduction to generalized linear models: this includes the generalized additive model, logistic regression for binary response variables, binomial regression for grouped data and poisson regression for count data. | |||||

Lecture notes | A script will be available. | |||||

Literature | Faraway (2005): Linear Models with R Faraway (2006): Extending the Linear Model with R Draper & Smith (1998): Applied Regression Analysis Fox (2008): Applied Regression Analysis and GLMs Montgomery et al. (2006): Introduction to Linear Regression Analysis | |||||

Prerequisites / Notice | The exercises, but also the classes will be based on procedures from the freely available, open-source statistical software package R, for which an introduction will be held. In the Mathematics Bachelor and Master programmes, the two course units 401-0649-00L "Applied Statistical Regression" and 401-3622-00L "Statistical Modelling" are mutually exclusive. Registration for the examination of one of these two course units is only allowed if you have not registered for the examination of the other course unit. | |||||

401-3627-00L | High-Dimensional Statistics | W | 4 credits | 2V | P. L. Bühlmann | |

Abstract | "High-Dimensional Statistics" deals with modern methods and theory for statistical inference when the number of unknown parameters is of much larger order than sample size. Statistical estimation and algorithms for complex models and aspects of multiple testing will be discussed. | |||||

Objective | Knowledge of methods and basic theory for high-dimensional statistical inference | |||||

Content | Lasso and Group Lasso for high-dimensional linear and generalized linear models; Additive models and many smooth univariate functions; Non-convex loss functions and l1-regularization; Stability selection, multiple testing and construction of p-values; Undirected graphical modeling | |||||

Literature | Peter Bühlmann and Sara van de Geer (2011). Statistics for High-Dimensional Data: Methods, Theory and Applications. Springer Verlag. ISBN 978-3-642-20191-2. | |||||

Prerequisites / Notice | Knowledge of basic concepts in probability theory, and intermediate knowledge of statistics (e.g. a course in linear models or computational statistics). | |||||

401-4623-00L | Time Series AnalysisDoes not take place this semester. | W | 6 credits | 3G | N. Meinshausen | |

Abstract | Statistical analysis and modeling of observations in temporal order, which exhibit dependence. Stationarity, trend estimation, seasonal decomposition, autocorrelations, spectral and wavelet analysis, ARIMA-, GARCH- and state space models. Implementations in the software R. | |||||

Objective | Understanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R. | |||||

Content | This course deals with modeling and analysis of variables which change randomly in time. Their essential feature is the dependence between successive observations. Applications occur in geophysics, engineering, economics and finance. Topics covered: Stationarity, trend estimation, seasonal decomposition, autocorrelations, spectral and wavelet analysis, ARIMA-, GARCH- and state space models. The models and techniques are illustrated using the statistical software R. | |||||

Lecture notes | Not available | |||||

Literature | A list of references will be distributed during the course. | |||||

Prerequisites / Notice | Basic knowledge in probability and statistics | |||||

401-3612-00L | Stochastic SimulationDoes not take place this semester. | W | 5 credits | 3G | ||

Abstract | This course provides an introduction to statistical Monte Carlo methods. This includes applications of simulations in various fields (Bayesian statistics, statistical mechanics, operations research, financial mathematics), algorithms for the generation of random variables (accept-reject, importance sampling), estimating the precision, variance reduction, introduction to Markov chain Monte Carlo. | |||||

Objective | Stochastic simulation (also called Monte Carlo method) is the experimental analysis of a stochastic model by implementing it on a computer. Probabilities and expected values can be approximated by averaging simulated values, and the central limit theorem gives an estimate of the error of this approximation. The course shows examples of the many applications of stochastic simulation and explains different algorithms used for simulation. These algorithms are illustrated with the statistical software R. | |||||

Content | Examples of simulations in different fields (computer science, statistics, statistical mechanics, operations research, financial mathematics). Generation of uniform random variables. Generation of random variables with arbitrary distributions (quantile transform, accept-reject, importance sampling), simulation of Gaussian processes and diffusions. The precision of simulations, methods for variance reduction. Introduction to Markov chains and Markov chain Monte Carlo (Metropolis-Hastings, Gibbs sampler, Hamiltonian Monte Carlo, reversible jump MCMC). | |||||

Lecture notes | A script will be available in English. | |||||

Literature | P. Glasserman, Monte Carlo Methods in Financial Engineering. Springer 2004. B. D. Ripley. Stochastic Simulation. Wiley, 1987. Ch. Robert, G. Casella. Monte Carlo Statistical Methods. Springer 2004 (2nd edition). | |||||

Prerequisites / Notice | Familiarity with basic concepts of probability theory (random variables, joint and conditional distributions, laws of large numbers and central limit theorem) will be assumed. | |||||

Selection: Financial and Insurance Mathematics In the Master's programmes in Mathematics resp. Applied Mathematics 401-3913-01L Mathematical Foundations for Finance is eligible as an elective course, but only if 401-3888-00L Introduction to Mathematical Finance isn't recognised for credits (neither in the Bachelor's nor in the Master's programme). For the category assignment take contact with the Study Administration Office (www.math.ethz.ch/studiensekretariat) after having received the credits. | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

401-3925-00L | Non-Life Insurance: Mathematics and Statistics | W | 8 credits | 4V + 1U | M. V. Wüthrich | |

Abstract | The lecture aims at providing a basis in non-life insurance mathematics which forms a core subject of actuarial sciences. It discusses collective risk modeling, individual claim size modeling, approximations for compound distributions, ruin theory, premium calculation principles, tariffication with generalized linear models and neural networks, credibility theory, claims reserving and solvency. | |||||

Objective | The student is familiar with the basics in non-life insurance mathematics and statistics. This includes the basic mathematical models for insurance liability modeling, pricing concepts, stochastic claims reserving models and ruin and solvency considerations. | |||||

Content | The following topics are treated: Collective Risk Modeling Individual Claim Size Modeling Approximations for Compound Distributions Ruin Theory in Discrete Time Premium Calculation Principles Tariffication Generalized Linear Models and Neural Networks Bayesian Models and Credibility Theory Claims Reserving Solvency Considerations | |||||

Lecture notes | M. V. Wüthrich, Non-Life Insurance: Mathematics & Statistics http://ssrn.com/abstract=2319328 | |||||

Prerequisites / Notice | The exams ONLY take place during the official ETH examination period. This course will be held in English and counts towards the diploma of "Aktuar SAV". For the latter, see details under www.actuaries.ch. Prerequisites: knowledge of probability theory, statistics and applied stochastic processes. | |||||

401-3922-00L | Life Insurance Mathematics | W | 4 credits | 2V | M. Koller | |

Abstract | The classical life insurance model is presented together with the important insurance types (insurance on one and two lives, term and endowment insurance and disability). Besides that the most important terms such as mathematical reserves are introduced and calculated. The profit and loss account and the balance sheet of a life insurance company is explained and illustrated. | |||||

Objective | ||||||

401-3928-00L | Reinsurance Analytics | W | 4 credits | 2V | P. Antal, P. Arbenz | |

Abstract | This course provides an introduction to reinsurance from an actuarial perspective. The objective is to understand the fundamentals of risk transfer through reinsurance and models for extreme events such as natural or man-made catastrophes. The lecture covers reinsurance contracts, Experience and Exposure pricing, natural catastrophe modelling, solvency regulation, and insurance linked securities | |||||

Objective | This course provides an introduction to reinsurance from an actuarial perspective. The objective is to understand the fundamentals of risk transfer through reinsurance and the mathematical approaches associated with low frequency high severity events such as natural or man-made catastrophes. Topics covered include: - Reinsurance Contracts and Markets: Different forms of reinsurance, their mathematical representation, history of reinsurance, and lines of business. - Experience Pricing: Modelling of low frequency high severity losses based on historical data, and analytical tools to describe and understand these models - Exposure Pricing: Loss modelling based on exposure or risk profile information, for both property and casualty risks - Natural Catastrophe Modelling: History, relevance, structure, and analytical tools used to model natural catastrophes in an insurance context - Solvency Regulation: Regulatory capital requirements in relation to risks, effects of reinsurance thereon, and differences between the Swiss Solvency Test and Solvency 2 - Insurance linked securities: Alternative risk transfer techniques such as catastrophe bonds | |||||

Content | This course provides an introduction to reinsurance from an actuarial perspective. The objective is to understand the fundamentals of risk transfer through reinsurance and the mathematical approaches associated with low frequency high severity events such as natural or man-made catastrophes. Topics covered include: - Reinsurance Contracts and Markets: Different forms of reinsurance, their mathematical representation, history of reinsurance, and lines of business. - Experience Pricing: Modelling of low frequency high severity losses based on historical data, and analytical tools to describe and understand these models - Exposure Pricing: Loss modelling based on exposure or risk profile information, for both property and casualty risks - Natural Catastrophe Modelling: History, relevance, structure, and analytical tools used to model natural catastrophes in an insurance context - Solvency Regulation: Regulatory capital requirements in relation to risks, effects of reinsurance thereon, and differences between the Swiss Solvency Test and Solvency 2 - Insurance linked securities: Alternative risk transfer techniques such as catastrophe bonds | |||||

Lecture notes | Slides and lecture notes will be made available. | |||||

Prerequisites / Notice | Basic knowledge in statistics, probability theory, and actuarial techniques | |||||

401-3927-00L | Mathematical Modelling in Life Insurance | W | 4 credits | 2V | T. J. Peter | |

Abstract | In life insurance, it is essential to have adequate mortality tables, be it for reserving or pricing purposes. The course provides the tools necessary to create mortality tables from scratch. Additionally, we study various guarantees embedded in life insurance products and learn to price them with the help of stochastic models. | |||||

Objective | The course's objective is to provide the students with the understanding and the tools to create mortality tables on their own. Additionally, students should learn to price embedded options in life insurance. Aside of the mere application of specific models, they should develop an intuition for the various drivers of the value of these options. | |||||

Content | Following main topics are covered: 1. Guarantees and options embedded in life insurance products. - Stochastic valuation of participating contracts - Stochastic valuation of Unit Linked contracts 2. Mortality Tables: - Determining raw mortality rates - Smoothing techniques: Whittaker-Henderson, smoothing splines,... - Trends in mortality rates - Stochastic mortality model due to Lee and Carter - Neural Network extension of the Lee-Carter model - Integration of safety margins | |||||

Lecture notes | Lectures notes and slides will be provided | |||||

Prerequisites / Notice | The exams ONLY take place during the official ETH examination period. The course counts towards the diploma of "Aktuar SAV". Good knowledge in probability theory and stochastic processes is assumed. Some knowledge in financial mathematics is useful. | |||||

Selection: Mathematical Physics, Theoretical Physics | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |

402-0843-00L | Quantum Field Theory ISpecial Students UZH must book the module PHY551 directly at UZH. | W | 10 credits | 4V + 2U | N. Beisert | |

Abstract | This course discusses the quantisation of fields in order to introduce a coherent formalism for the combination of quantum mechanics and special relativity. Topics include: - Relativistic quantum mechanics - Quantisation of bosonic and fermionic fields - Interactions in perturbation theory - Scattering processes and decays - Elementary processes in QED - Radiative corrections | |||||

Objective | The goal of this course is to provide a solid introduction to the formalism, the techniques, and important physical applications of quantum field theory. Furthermore it prepares students for the advanced course in quantum field theory (Quantum Field Theory II), and for work on research projects in theoretical physics, particle physics, and condensed-matter physics. | |||||

402-0861-00L | Statistical Physics | W | 10 credits | 4V + 2U | G. M. Graf | |

Abstract | The lecture focuses on classical and quantum statistical physics. Various techniques, cumulant expansion, path integrals, and specific systems are discussed: Fermions, photons/phonons, Bosons, magnetism, van der Waals gas. Phase transitions are studied in mean field theory (Weiss, Landau). Including fluctuations leads to critical phenomena, scaling, and the renormalization group. | |||||

Objective | This lecture gives an introduction into the the basic concepts and applications of statistical physics for the general use in physics and, in particular, as a preparation for the theoretical solid state physics education. | |||||

Content | Thermodynamics, three laws of thermodynamics, thermodynamic potentials, phenomenology of phase transitions. Classical statistical physics: micro-canonical-, canonical-, and grandcanonical ensembles, applications to simple systems. Quantum statistical physics: single particle, ideal quantum gases, fermions and bosons, statistical interaction. Techniques: variational approach, cumulant expansion, path integral formulation. Degenerate fermions: Fermi gas, electrons in magnetic field. Bosons: photons and phonons, Bose-Einstein condensation. Magnetism: Ising-, XY-, Heisenberg models, Weiss mean-field theory. Van der Waals gas-liquid transition. Landau theory of phase transitions, first- and second order, tricritical. Fluctuations: field theory approach, Gauss theory, self-consistent field, Ginzburg criterion. Critical phenomena: scaling theory, universality. Renormalization group: general theory and applications to spin models (real space RG), phi^4 theory (k-space RG), Kosterlitz-Thouless theory. | |||||

Lecture notes | Lecture notes available in English. | |||||

Literature | No specific book is used for the course. Relevant literature will be given in the course. | |||||

402-0830-00L | General Relativity Special Students UZH must book the module PHY511 directly at UZH. | W | 10 credits | 4V + 2U | P. Jetzer | |

Abstract | Manifold, Riemannian metric, connection, curvature; Special Relativity; Lorentzian metric; Equivalence principle; Tidal force and spacetime curvature; Energy-momentum tensor, field equations, Newtonian limit; Post-Newtonian approximation; Schwarzschild solution; Mercury's perihelion precession, light deflection. | |||||

Objective | Basic understanding of general relativity, its mathematical foundations, and some of the interesting phenomena it predicts. | |||||

Literature | Suggested textbooks: C. Misner, K, Thorne and J. Wheeler: Gravitation S. Carroll - Spacetime and Geometry: An Introduction to General Relativity R. Wald - General Relativity S. Weinberg - Gravitation and Cosmology N. Straumann - General Relativity with applications to Astrophysics | |||||

402-0897-00L | Introduction to String Theory | W | 6 credits | 2V + 1U | B. Hoare | |

Abstract | This course is an introduction to string theory. The first half of the course covers the bosonic string and its quantization in flat space, concluding with the introduction of D-branes and T-duality. The second half will cover some advanced topics, which will be selected from those listed below. | |||||

Objective | The objective of this course is to motivate the subject of string theory, exploring the important role it has played in the development of modern theoretical and mathematical physics. The goal of the first half of the course is to give a pedagogical introduction to the bosonic string in flat space. Building on this foundation, an overview of various more advanced topics will form the second half of the course. | |||||

Content | I. Introduction II. The relativistic point particle III. The classical closed string IV. Quantizing the closed string V. The open string and D-branes VI. T-duality in flat space Possible advanced topics include: VII. Conformal field theory VIII. The Polyakov path integral IX. String interactions X. Low energy effective actions XI. Superstring theory | |||||

Literature | Lecture notes: String Theory - D. Tong http://www.damtp.cam.ac.uk/user/tong/string.html Lectures on String Theory - G. Arutyunov http://stringworld.ru/files/Arutyunov_G._Lectures_on_string_theory.pdf Books: Superstring Theory - M. Green, J. Schwarz and E. Witten (two volumes, CUP, 1988) Volume 1: Introduction Volume 2: Loop Amplitudes, Anomalies and Phenomenology String Theory - J. Polchinski (two volumes, CUP, 1998) Volume 1: An Introduction to the Bosonic String Volume 2: Superstring Theory and Beyond Errata: http://www.kitp.ucsb.edu/~joep/errata.html Basic Concepts of String Theory - R. Blumenhagen, D. Lüst and S. Theisen (Springer-Verlag, 2013) | |||||

402-0878-00L | Field Theory with Symmetries and the Batalin-Vilkovisky Formalism | W | 4 credits | 2G | M. Schiavina | |

Abstract | The course is an introduction to the Batalin-Vilkovisky formalism, which provides a rigorous toolkit to treat classical and quantum field theories with symmetries, generalising the BRST approach. The course will feature applications to gauge theories and general relativity, and possibly to theories with defects (boundaries and corners). | |||||

Objective | The objective of this course is to expose master and graduate physics students to modern techniques in theoretical and mathematical physics to handle gauge symmetries in classical and quantum field theory. We aim to provide a solid mathematical background for third-semester master and graduate students to adventure further in this research direction. | |||||

Content | The course will start with a review of the BRST formalism expanding on its introduction in Quantum Field Theory II. It will provide a mathematical background on (Lie algebra) cohomology and the necessary requirements to describe the BV formalism, including an introduction to symplectic geometry on graded vector spaces. Applications of the BV formalism to different examples like gauge theories, general relativity and sigma models will be presented, and a discussion on quantisation of classical field theories in this setting, together with possible inclusion of defects, will be considered as concluding topics for the course. |

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