This course is an introduction to the foundations of symplectic geometry. We will discuss a motivating example—Hamiltonian mechanics—before defining what it means to be symplectic. Afterwards we will study some consequences of the general definitions. Importantly, we will show that locally, all symplectic spaces look the same: there are no local symplectic invariants! This is a consequence of...
This course is an introduction to the foundations of symplectic geometry. We will discuss a motivating example—Hamiltonian mechanics—before defining what it means to be symplectic. Afterwards we will study some consequences of the general definitions. Importantly, we will show that locally, all symplectic spaces look the same: there are no local symplectic invariants! This is a consequence of...
This course is an introduction to the foundations of symplectic geometry. We will discuss a motivating example—Hamiltonian mechanics—before defining what it means to be symplectic. Afterwards we will study some consequences of the general definitions. Importantly, we will show that locally, all symplectic spaces look the same: there are no local symplectic invariants! This is a consequence of...
After the introductory course in symplectic geometry, we analyze symplectic manifolds which are symmetric under the action of a Lie group, leading in particular to the symplectic quotient construction. The important concept is the notion of the moment map, generalizing the concept of momentum and angular momentum in classical mechanics, and capturing all preserved quantities coming from...
After the introductory course in symplectic geometry, we analyze symplectic manifolds which are symmetric under the action of a Lie group, leading in particular to the symplectic quotient construction. The important concept is the notion of the moment map, generalizing the concept of momentum and angular momentum in classical mechanics, and capturing all preserved quantities coming from...
After the introductory course in symplectic geometry, we analyze symplectic manifolds which are symmetric under the action of a Lie group, leading in particular to the symplectic quotient construction. The important concept is the notion of the moment map, generalizing the concept of momentum and angular momentum in classical mechanics, and capturing all preserved quantities coming from...
Abstract: General relativity is a beautifully geometric and mathematically rigorous theory describing our universe on large scales, where gravity plays a crucial role. After an introduction to differential and Riemannian geometry we will look in more detail at the mathematical underpinnings of this theory and talk about geodesics, normal coordinates, Einstein equations, and other interesting...
Abstract: General relativity is a beautifully geometric and mathematically rigorous theory describing our universe on large scales, where gravity plays a crucial role. After an introduction to differential and Riemannian geometry we will look in more detail at the mathematical underpinnings of this theory and talk about geodesics, normal coordinates, Einstein equations, and other interesting...
Abstract: General relativity is a beautifully geometric and mathematically rigorous theory describing our universe on large scales, where gravity plays a crucial role. After an introduction to differential and Riemannian geometry we will look in more detail at the mathematical underpinnings of this theory and talk about geodesics, normal coordinates, Einstein equations, and other interesting...
After a quick introduction on the physical background of superconductivity and its phenomenological models, I will address the mathematical formalism leading to the derivation of the Bardeen-Cooper-Schrieffer functional, present the state of the art and comment on open problems and possible research directions.
After a quick introduction on the physical background of superconductivity and its phenomenological models, I will address the mathematical formalism leading to the derivation of the Bardeen-Cooper-Schrieffer functional, present the state of the art and comment on open problems and possible research directions.
After a quick introduction on the physical background of superconductivity and its phenomenological models, I will address the mathematical formalism leading to the derivation of the Bardeen-Cooper-Schrieffer functional, present the state of the art and comment on open problems and possible research directions.
