# Math Subfields use in String Theory

• hola
In summary, the person has been accepted into prestigious universities and is planning to major in physics with a focus on string theory. They are currently struggling to choose their math courses for their fourth year and are seeking advice on which ones would be most useful for string theory. They provide a list of areas and ask for a rating on their usefulness in string theory. They also mention a resource that may be helpful, specifically mentioning Riemann surfaces as a potentially useful topic.
hola
I've been accepted into University of Michigan, Princeton, and MIT, and I am intent on majoring in physics with a strong emphasis on string theory, as I already have some math background. Anyways... I have a tough choice to make... but first I am making my schedule. I'm stuck on 4th year though,in what math courses I should take, so could someone provide insight on which would be the best for string theory?
Could some rate how useful these following areas of areas are in string theory in a following scale: not useful at all, somewhat useful, very useful, essential

-Group Theory, Lie Algebras, Algebra

- Topology (Algebraic, Differential and General, Combanitorics)

- Analysis: (Complex, Real, Calculus of Variations)

-Functional Analysis

-Differential Geometry

-Algebraic Geometry

- Probability Theory

- Set Theory/ Logic

- Number Theory

This might help:

http://superstringtheory.com/math/index.html

i don't know much about string theory but I was an invited speaker at the institute for theoretical physics in trieste at a conference on string theory and my topic was riemann surfaces, so presumably riemann surfaces is a useful topic.

## 1. What are the main subfields of math used in string theory?

The main subfields of math used in string theory include differential geometry, complex analysis, topology, algebraic geometry, and group theory.

## 2. How does differential geometry play a role in string theory?

Differential geometry is used in string theory to describe the geometric properties of spacetime in which the strings exist. This includes concepts such as curvature, metrics, and connections.

## 3. What is the importance of complex analysis in string theory?

Complex analysis is used in string theory to study the behavior of strings in complex spacetime dimensions. It also helps to formulate and solve equations in string theory.

## 4. How is topology relevant to string theory?

Topology is used in string theory to study the topological properties of strings and their interactions. This includes the study of knots, manifolds, and other topological structures.

## 5. How does algebraic geometry apply to string theory?

Algebraic geometry is used in string theory to describe and study the algebraic properties of strings and their interactions. This includes the study of symmetries, equations, and transformations.

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