Seung Jin Lee: D-modules and the Riemann-Hilbert correspondence
Jaeseong Oh: The Kazhdan-Lusztig conjecture (part I)
Abstract: In this series of lectures, I will explain the Kazhdan-Lusztig conjecture and its relation with intersection homology discovered by Bernstein, Beilinson, Brylinski, and Kashiwara. We first review the representation theory of Lie algebra and the problem of decomposing certain Verma modules. Then we relate this problem with intersection cohomology on Schubert varieties via the theory of D-modules. Based on Section 12.1 and 12.2 in the book "An Introduction to Intersection Homology Theory".
Donghyun Kim: The Kazhdan-Lusztig conjecture (part II)
Abstract: We review section 12.3 and 12.4 in the book "An Introduction to Intersection Homology Theory". Out goal is to give a sketch of the proof for the Kazhdan-Lusztig conjecture.
Jeong Hyun Sung: Chromatic quasisymmetric functions and linked rook placements
Hyeonjae Choi: Lusztig's q-weight multiplicity and combinatorial model
Abstract: Lusztig's q-weight multiplicity is q-analogue of Kostant partition function. In particular, Lusztig's q-weight multiplicity is Kostka-Foulkes polynomial in type A. These polynomials can be written with all non-negative coefficients. A statistic called charge on semistandard young tableaux describes the q-weight multiplicity for type A. In this talk, we dicuss type B, C version of this theory . In type B, we consider the Sundaram tableau for integral weight and spin tableau for spin weight. In type C, we consider the King tableau. In both type, we discuss an energy function, which appears in affine crystal theory, on semistandard oscillating tableaux.