If you are a physicist interested in the geometry of modern theoretical physics, then this course was created for you.
In only five lessons — of two hours each — you will become familiar with the main mathematical concepts that build the foundations of Einstein's general theory of relativity and the standard model of particle physics.
After taking this course you will know exactly what a mathematician or a theoretical physicist means when he talks about differentiable manifolds, fiber bundles, tensor fields, connections and curvatures. In addition, you will know about the most interesting global aspects involved. See below for a more detailed description of the course. As a prerequisite, you only need some multivariable calculus and linear algebra.
Pricing: The normal price for this live course is US$800. However, for a very limited period of time we are offering this course for only $650. That is, you save $150 if you enroll today.
Maximum number of students: In order to provide the best teaching experience, only one student is allowed per class. The teacher will then be able to personalize as much as possible the course to your needs, encourage high quality interactions, be able to constantly check your progress and adapt the lessons accordingly, and, ultimately, guarantee the positive results you desire.
Note: This is not a pre-recorded video course. All classes are live (by Skype or Zoom).
Download Description of A Crash Course on Differential Geometry O Zapata.pdf
Oswaldo Zapata PhD has more than 20 years of experience helping physics students and professionals understand the mathematics of physics.
He received his Bachelor's degree from Universidad Central de Venezuela, then he went to study particles physics in Paris (MSc) and string theory in Rome (PhD). Afterwards, he carried out research at the Albert Einstein Institute for Gravitational Physics in Golm (Germany), the International Center for Theoretical Physics in Trieste (Italy), the Kavli Institute for Theoretical Physics in Beijing (China), and the London School of Economics (UK).
Instead of $800!
1 Manifolds and Fiber Bundles
In the first class we define differentiable manifolds and see why it is natural to consider its tangent bundle. We extend this somehow intuitive object to the more general concept of a fiber bundle. We then see that, in addition to tangent bundles, fiber bundles include the so called vector bundles and principal bundles. These constructs are of fundamental importance to general relativity and gauge theories.
2 Tensor Fields
We begin the second class with a formal mathematical definition of a well-know concept in physics: vector fields. However, we do it taking into account the general objects introduced in the first lesson. Follows the definition of a dual of vector fields, known as covector fields, or more commonly, differential 1- forms. Vector fields and differential forms are the building blocks of tensor fields, in particular, of differential k-forms. We conclude the class with the definition of vector-valued differential forms -- crucial for studying connections and curvature on principal bundles.
3 Connections
Connections are well known objects in Riemannian geometry; that is, differentiable manifolds with a smooth inner product on each tangent space of the manifolds. We extend this concept to arbitrary vector bundles. Connections may as well be defined on principal bundles. We spend the second half of the class discussing several equivalent definitions of a connection on a principal bundle.
4 Curvature
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5 Global Aspects
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After completing this course, you will be able to fully understand the following definitions from the book of Kobayashi and Nomizu — perhaps the most authoritative text in the field. In contrast to Kobayashi and Nomizu's abstract approach though, this course is more visual in nature. In fact, dozens of figures are used along the way to illustrate every concept discussed; even the most abstract ones.
If you are not confident with the following definitions, you may seriously consider taking this course!
Only $650, instead of $800
This is a Limited-Time Offer!
