September 24 
Cesar Ceballos 
Bumping and Sliding : Operations on Young Tableaux. Schenstedbumping operation. Schutzerbergsliding algorithm.
[F, Int, Ch1] 
October 1 
Alexander Caviedes 
Words and Elementary transformations: Words. Knuth Transformations. Schur Polynomials.
[F, Sect 2.1, 2.2] Alex' Notes 
October 8 
Alexander Caviedes 
Schur Polynomials: Schur Polynomials. Pieri's Formula. Kostka Numbers. [F, Sect 2.2] Alex' Notes 
October 15 
Iva Halacheva 
RobinsonSchenstedKnuth Correspondence I: RSK correspondence. [F, Sect 4.1] 
October 22 
Iva Halacheva 
RobinsonSchenstedKnuth Correspondence II: Applications of the RSK correspondence. Symmetry Theorem. Matrix Ball construction. [F, Sect 4.2, 4.3] 
October 29 
Cesar Ceballos 
The LittlewoodRichardson Rule: Yamanouchi word. LittlewoodRichardson Tableaux. LittlewoodRichardson Rule. [F, Ch 5] 
November 5 
Alexander Caviedes 
Symmetric Polynomials: Complete, Elementary, Monomial, Newton and Schur symmetric Polynomials. JacobiTrudi Formula. The ring of symmetric functions. [F, Ch 6] Alex' Notes 
November 12 
Peter Crooks 
The action of the symmetric group on tableaux. Specht Modules I. [F, Sect 7.1, 7.2] 
November 19 
Peter Crooks 
Representations of the symmetric group. Specht Modules II. Irreducible representations of the symmetric group. [F, Sect 7.1, 7.2] Peter's Notes 
November 26 
Iva Halacheva 
The ring of representations and symmetric functions I. [F, Sect 7.3] 
December 10 
Iva Halacheva 
The ring of representations and symmetric functions II. [F, Sect 7.3] 
December 17 
Cesar Ceballos 
A straightening algorithm. [F, Sect 7.4] Cesar's Notes 
January 13* 
Alexander Caviedes 
Schur Modules. [F, Sect 8.1 ] 
January 22 
Alexander Caviedes, Peter Crooks, Iva Halacheva 
Exercise Section I: Hook length formula [F, Sect 4.3, 7.3]. Character of Mlambda [F, Sect 7.2].
Consequences of LitlewoodRichardson's rule [F, Chapter 5] 
January 29 
Alexander Caviedes 
Schur Modules II, Irreducible representations of GLm(C) 
February 5 
Cesar Ceballos, Peter Crooks, Iva Halacheva 
Exercise Section II 
February 12 
Peter Crooks 
Gl(E) representations from Sn representations I. Weyl functor [F, Sect 8.1, 8.2] 
February 26 
Peter Crooks 
Gl(E) representations from Sn representations II. Character of Elambda [F, Sect 8.3, 8.4] 
March 7* 
Iva Halacheva 
Plucker embeddings I. Projective embeddings of flag varieties [F, Sect 9.1] 
March 12 
Iva Halacheva 
Plucker embeddings II. Projective embedding of flag varieties [F, Sect 9.1] 
March 19 
Iva Halacheva 
Plucker embeddings III. Homogeneous coordinate ring of the flag variety. Geometric Invariant theory [F, Sect 9.1, 9.2] 
March 26 
Peter Crooks 
Representations of Gl(E) and line bundles I. [F, Sect 9.3] 
April 2 
Peter Crooks 
Representations of Gl(E) and line bundles II [F, Sect 9.3] 
April 9 
Peter Crooks 
Representations of Gl(E) and line bundles III [F, Sect 9.3] 
April 16 
Cesar Ceballos 
Schubert Calculus on Grassmannians. Schubert cells and varieties. Duality Theorem [F, Sect 9.4] 
April 30 
Cesar Ceballos 
Schubert Calculus on Grassmannians. Schubert cells and varieties. Pieri's Formula [F, Sect 9.4]
Cesar's Notes 
May 7 
Alexander Caviedes 
Fixed points of torus actions. Schubert cells in flag manifolds [F, Sect 10.1, 10.2]

May 14 
Alexander Caviedes 
Schubert varieties. Dual Schubert cells and dual Schubert varieties in flag manifolds. Duality Theorem [F, Sect 10.2]

July 11 
Alexander Caviedes 
Chern Classes of line bundles. Leray Hirsch Theorem [F, Sect 10.2, Appendix B1]

July 18 
Alexander Caviedes 
Cohomology ring of flag manifolds [F, Sect 10.2, Appendix B1]

July 25 
Peter Crooks 
Relations among Schubert varieties I [F, Sect 10.3]

August 1* 
Peter Crooks 
Relations among Schubert varieties II [F, Sect 10.3]

August 8 
Peter Crooks 
Relations among Schubert varieties III [F, Sect 10.3]

August 8 
Cesar Ceballos 
Schubert Polynomials [F, Sect 10.4]

August 15 
Cesar Ceballos 
Bruhat Order [F, Sect 10.5]

August 15 
Iva Halacheva 
Applications to the Grassmannian [F, Sect 10.6]
