Basic course on strings and mathematics 1
Student No.:50
Time:Wed. 15:00-16:30 (Math part)/ Wed. 16:40-18:10 (String part), 2014-10-15~2014-12-24
Instructor:Hiroyuki Fuji,Francois-Xavier Machu  
Place:Conference Room 4, Floor 2, Jin Chun Yuan West Building
Starting Date:2014-10-15
Ending Date:2014-12-24

(Math part)


Title: Riemann surfaces & Curves



Complex analysis of a single variable when combined with algebraic functions, leads to the construction of Riemann surfaces. These real two-dimensional manifolds are locally covered by complex analytic charts. When one think of compact Riemann surfaces as global objects, they most naturally interpreted as nonsingular complex projective algebraic curves.


Covered topics:

Riemann Surfaces and Algebraic Curves, Hurwitz theorem, monodromy, sheaves, cohomology, divisors (and line bundles if the time enables it).



A basic knowledge of differential geometry and complex analysis.



P. Griffits : Introduction to Algebraic Curves. Translations of Mathematical Monograph, vol 76, AMS(1989).

P. Griffiths and J. Harris : Principles of Algebraic Geometry. Willey Interscience (1978).

V.V.Shokurov : Riemann Surfaces and Algebraic Curves. AG1, edited by I.R. Shafarevich, Encyclopedia of Math Sciences, Vol 23, S-V (1994).


(String part)

Title: Some basic aspects of string theory



This course deals with physical aspects of the string theory. In this semester, we will discuss about some basics topics of string theory. The following contents will be discussed:

0. Short survey on quantum mechanics and quantum field theory


1. Classical strings


2. Quantization of closed strings


3. String spectrum and its modular property


4. Compactification and T-duality


5. Quantization of open strings


6. D-branes


In addition, if time permits, some basic topics of the superstring theory or topological string theory may be discussed depending on requests of participants.



Undergraduate physics, Some basics of quantum field theory



J. Polchinski, String Theory Vol.I/II, Cambridge University Press.

M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory Vol.1/2, Cambridge University Press.

B.Zwieback, A First Course in String Theory, Cambridge University Press.