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In recent work with Will Johnson, we have shown that given a curve C over the rational number field Q with genus at least 2 and C(Q) is empty, the class of fields K of characteristic 0 such that C(K) ...
By using direct N-body numerical simulations, we model the dynamical coevolution of two supermassive black holes (SMBHs) and the surrounding stars in merging galaxies. In order to investigate how diff...
How does animal behavior emerge from networks of connected neurons? How are these incredible nervous systems and behaviors actually generated by evolution? Are there principles shared by all nervous s...
An LG model (M, f) is given by a noncompact complex manifold M and the holomorphic function f defined on it, which is an important model in string theory. Because of the mirror symmetry conjecture, th...
Generalized pairs are a natural structure in birational geometry that first appeared in Kodaira’s canonical bundle formula for elliptic fibrations. They were formally introduced by Birkar and Zhang in...
Liouville quantum gravity (LQG) is a theory of random surfaces that originated from string theory. Schramm Loewner evolution (SLE) is a family of random planar curves describing scaling limits of many...
In this talk, we first review some related progresses on one dimensional shallow water models. Then we introduce the derivation of a new nonlocal shallow water model from the 3D Euler system with free...
We develop the Double Principal Component Analysis (DPCA) based on a dual factor structure for high-frequency intraday returns contaminated by microstructure noise. The dual factor structure allows a ...
In this talk I will review the developments of homogenization theory for a front propagation model. It is described by a first order Hamilton-Jacobi equation with a Hamiltonian that grows linearly wit...
When two black holes collide into each other to form a new bigger black hole, they violently roil spacetime around them, sending ripples called gravitational waves outward in all directions. Previous ...
In this talk, we present numerical approximations of a phase-field model for two-phase ferrofluids, which consists of the Navier-Stokes equations, the Cahn-Hilliard equation, the magnetostatic equatio...
In this talk, we investigate a stochastic nutrient-phytoplankton model which incorporates the effect of white noise on phytoplankton growth. The global existence and uniqueness of a positive solution,...
How to select the active variables which have significant impact on the event of interest is a very important and meaningful problem in the statistical analysis of ultrahigh-dimensional data. In many ...
The pathogenesis of breast cancer is not the same in all countries and regions; therefore, some existing breast cancer risk assessment models are not well adapted to all countries and regions, includi...
In this talk, we first briefly review history of the geometric singular perturbation theory, then talk about the traveling pulses for a diffusive Rosenzweig MacArthur model. We show the existence of t...

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