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Courses Representation theory or algebraic topology

  1. Mar 29, 2016 #1
    Hello everyone, I'm a undergraduate at UC Berkeley. I'm doing theoretical physics but technically I'm a math major. I really want to study quantum gravity in the future. Now I have a problem of choosing courses. For next semester, I have only one spot available for either representation theory or algebraic topology. Both are graduate courses and I have substantial previous experiences on both subjects. I'm wondering which class is more essential to my academic goal. It's very sad that I cannot choose both at the same time due to scheduling problem. Any help will be appreciated. Thanks!
  2. jcsd
  3. Mar 29, 2016 #2
    First, we will need to know the contents of the courses. In particular, does representation theory deal with finite groups, or with Lie groups/algebras or other? If it's representation theory of Lie groups/algebras then you will want this class for sure.
  4. Mar 29, 2016 #3
    Typically, the official description of the course on representation theory is "structure of finite dimensional algebras, applications to representations of finite groups, the classical linear groups"; and the official description of the course on algebraic topology is "Fundamental group and covering spaces, simplicial and singular homology theory with applications, cohomology theory, duality theorem. Homotopy theory, fibrations, relations between homotopy and homology, obstruction theory, and topics from spectral sequences, cohomology operations, and characteristic classes".

    So are you saying that the more essential knowledge for quantum gravity research is representation theory on lie groups? If so, will a course in lie group/lie algebra be helpful?

    Our school's description of the course on lie algebra is "Lie groups and Lie algebras, fundamental theorems of Lie, general structure theory; compact, nilpotent, solvable, semi-simple Lie groups; classification theory and representation theory of semi-simple Lie algebras and Lie groups, further topics such as symmetric spaces, Lie transformation groups, etc., if time permits. In view of its simplicity and its wide range of applications, it is preferable to cover compact Lie groups and their representations in 261A"

    Thank you very much!!!
  5. Mar 29, 2016 #4
    Yes, I know representation theory of Lie groups and Lie algebras is quite important in this type of theoretical research. So the course you mentioned at the end might be very useful to you. Do consider 261A too.
  6. Mar 29, 2016 #5
    Thanks a lot
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