This course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear is mathematics in many different ways: as a result of analytic continuation, as quotients of complex domains under discontinuous group actions, as algebraic ...
The course studies the fundamental concepts of complex analysis and Laplace analysis with a view to their use to solve multidisciplinary scientific engineering problems. ...
This course serves as an introduction to the theory of complex analysis, Fourier series and Fourier transforms, the Laplace transform, with applications to the theory of ordinary and partial differential equations. These tools play an integral role in most ...
This course is an introduction to intersection theory on algebraic varieties.An important aim of the course is to develop geometric intuition while using the language of schemes developed in the basic algebraic geometry course, thus building a solid foun ...
The goal of this course is to treat selected topics in complex analysis. We will mostly focus on holomorphic functions in one variable. At the end we will also discuss holomorphic functions in several variables ...
Smooth manifolds constitute a certain class of topological spaces which locally look like some Euclidean space R^n and on which one can do calculus. We introduce the key concepts of this subject, such as vector fields, differential forms, etc. ...
The course will deepen the fundamentals of heat transfer. Particular focus will be put on radiative and convective heat transfer, and computational approaches to solve complex, coupled heat transfer problems. ...
We will study classical and modern deformation theory of schemes and coherent sheaves. Participants should have a solid background in scheme-theory, for example being familiar with the first 3 chapters of Hartshorne's 'Algebraic Geometry'. ...
The monstrous moonshine is an unexpected connection between the Monster group and modular functions. In the course we will explain the statement of the conjecture and study the main ideas and concepts leading to its proof. Our final goal is to study Borc ...
Quantum mechanics is one of the most successful physical theories. This course presents the mathematical formalism (functional analysis and spectral theory) that underlies quantum mechanics. It is simultaneously an introduction to mathematical physics and ...