Phylogenetic tree reconstruction is a main task in evolutionary biology.Traditional MCMC methods may suffer from the curse of dimensionality and the local-trap problem. Firstly,we introduce a new combinatorial SMC method, with a novel and efficient proposal distribution. We also explore combining SM...

In a joint work with Davesh Maulik and Yukinobu Toda, we proposed a conjectural Gopakumar-Vafa type formula for the generating series of stable pair invariants on Calabi-Yau 4-folds. In this talk, I will present a joint work with Yukinobu Toda on how to give an interpretation of the above GV type fo...

Common and oft-observed assumption for high-dimensional datasets is that they sample (possibly with added noise) a low-dimensional manifold embedded in a high-dimensional space. In this situation, Non-linear Dimensional Reduction (NLDR) offers to find a low-dimensional embedding of the data (i.e., u...