KWMS Winter Workshop

Date: February 14, 2023

Venue: Seoul National Univeristy, Department of Mathematical Sciences, building 27, room 220, Seoul, Korea

List of Speakers

Soojin Cho (Ajou University)

Hyung Ju Hwang (POSTECH)

Youngju Kim (Konkuk University)

Kyungwha Lee (Seoul National University)

Program

  1. Lecture 1. Deforming hyperbolic structures in dimension 4, by Youngju Kim (10:00-10:50)

    Abstract: A thrice-punctured sphere group is a non-elementary group generated by two parabolic isometries whose product is a parabolic isometry. We will consider a thrice-punctured sphere group acting on hyperbolic 4-space and discuss its deformations space. This gives us a quasiconformal instability in dimension 4 which is contrast to lower dimensions where all geometrically finite discrete groups are quasiconformally stable.

  2. Lecture 2. Chromatic quasisymmetric functions, by Soojin Cho (11:00-11:50)

    Astract: Chromatic symmetric functions were introduced by Stanley as a generalization of the chromatic polynomials, and the Stanley-Stembridge conjecture asserts that the chromatic symmetric functions of certain graphs positively expand into elementary symmetric functions. Chromatic quasi-symmetric functions were defined as refinements of the chromatic symmetric functions by Shareshian and Wachs, and the Stanley-Stembridge conjecture was also refined in a natural way. A surprising fact is that chromatic quasisymmetric functions are corresponding to the Frobenius series of the Hessenberg varieties under the involution of the symmetric functions. In this lecture, I will explain the e-positivity conjecture and the correspondence between the chromatic quasisymmetric functions and the cohomology of the Hessenberg varieties, then present some recent works on the e-positivity conjecture.

  3. Lunch: @ Rakgujeong in Seoul National University (12:00-13:30)

  4. Lecture 3. Neural Solvers of PDEs and Applications to Real-World Problems (13:30-14:20)

    Abstract: Mathematics is closely related to the theory and algorithms of AI and machine learning. In this talk, we look into real-world applications of Neural PDE Solvers. Next, we investigate how deep neural networks (DNNs) can be used in the forward-inverse problems of PDEs. We introduce a loss function that guides neural networks to find solutions of PDEs more efficiently.

  5. Lecture 4. Essential Features in the 2022 Revised School Mathematics Curriculum by Kyungwha Lee (14:30-15:20)

  6. Teatime and Discussions (15:30-16:20)

Zoom link

  ID: 963 1108 4479, PW: KWMS

Organized by KWMS and Homogeneous Dynamics Lab of Seoul National University