In this talk, I introduce a sharp gradient estimate for linear heat equation on complete non-compact Riemannian manifolds which can be considered as an extension of Hamilton’s gradient estimate. Moreover, I also give Liouville results for some nonlinear equations involving p-Laplacian.

Correlators of a rational conformal field theory (RCFT) can be described as specific elements in spaces of conformal blocks.

Can machines generate music? Recent deep learning-driven systems have made breakthroughs on this topic. Some famous among them are Coconet, DeepBach, GLSR-VAE, C-RNN-GAN, etc. However the generated music is still not satisfying based on the feedbacks from different music communities.

In this talk, we will consider an interacting particle system on the unit circle with stronger repelling than that of Circular beta ensemble. I will prove the Gaussian approximation of the distribution of the particles in this model. This is joint work with Alexander Soshnikov.​​​