Preparing for the seminar is one of the most important ways for me to learn something new. It forces me to organize what I have already learned in a clear logic and present it to others clearly.
Records are uploaded on YouTube. See: Yutai's Videos - YouTube
Topics are as follows. Most of them are recorded. * means not recorded, unfortunately:(
SUSY Algebra and its representation*
SU(2) Spinor representation and upper lower indices*
Component field and Superfield formalism*
N=1 Chiral and Vector Superfield *
N=1 Abelian/Non-Abelian gauge theory*
Affine Lie Algebra and Center extension of Virasoro algebra.
OPE, operator formalism and free boson.
Verma Module and Kac determinant
Review of how to extract CFT data from Lagrangian Theory, free fermion.
Physics
Seiberg Witten Theory I
An introduction to cohomological field theory. (Ref: A short course on topological string theory)
Superfield as a function on the Supermanifold. Susy theory as a result of Haar measure on the supergroup.
Higgs Bundle and Class S Theory
Kaehler/ Hyperkaehler Indentity from 2d sigma model.
Fujikawa Analysis for chiral anomaly.*
Chiral anomaly, gauge anomaly, and its calculation from Feynman diagrams.
DAHA and brane quantization
Mathematics
Quantum Mechanics; Hibert space of SUSY sigma model and Kaehler/Hyperkaehler identity. (For math student)*
Clifford algebra and its representation. Spin group and spin structure.(For math student)*
Topological aspect of equivariant cohomology.
GTM133 I: Some algebra. Noetherian space.
GTM133 II: Affine coordinate ring and affine variety.
Heegaard Diagram and Heegaard splitting.
Symplectic Geometry I: Hamiltonian action and Moment Map.
Symplectic Geometry II: Moment Map Continued and System with Constraints.