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The Prandtl equation introduced by Prandtl in 1904 is a basic equation describling the behavior of the fluid near the boundary at high Reynolds number regime. In this talk, I will first introduce some...
In this talk, we present recent progress on holomorphic Morse inequalities. We first review the history and motivation. Then we introduce recent results on CR manifolds. Finally we give a uniform proo...
In this talk, we report several very recent asymptotic results on certain classical geometric quantities viewed as random variables on the moduli space of Riemann surfaces for large genus (and many cu...
In this talk, I will describe an elliptic PDE that models electric conduction, and the electric field concentration phenomenon between closely spaced inclusions of high contrast. In the first part, I ...
In this talk we review some recent results on the multi-bubble blow-ups and multi-solitons to the focusing stochastic nonlinear Schr鰀inger equations. We will show the corresponding construction and co...
In this talk we review some recent results on the multi-bubble blow-ups and multi-solitons to the focusing stochastic nonlinear Schr鰀inger equations. We will show the corresponding construction and co...
We will survey some recent existence theory of closed constant mean curvature hypersurfaces using the min-max method. We hope to discuss some old and new open problems on this topic as well.
Research published in the journal Physical Review Letters conducted by an international team of scientists including Joshua Klein, the Edmund J. and Louise W. Kahn Term Professor in the School of Arts...
We report 3 recent works along this direction: (A) The nature of L1, L21 error function robustness, using an outlier regularization framework.(B)Labeled robust principal component analysis (RPCA), by ...
Manakov equations play a key role in understanding nonlinear coupling in many physical contents with different scales in time and space, including optics, cold atoms, crossing seas, and even financial...
Sea level rise causes devastating effects on coastal habitats. For example, coastal erosion and saltwater intrusion are major threats for the Black Sea coasts. So, determining sea level changes in the...
Sea level rise causes devastating effects on coastal habitats. For example, coastal erosion and saltwater intrusion are major threats for the Black Sea coasts. So, determining sea level changes in the...
The study of Hamiltonian dynamical systems plays a fundamental role in many different contexts, both in pure and applied mathematics. Indeed, most of the physical laws ruling our everyday lives --the ...
Convexity is omnipresent in mathematics and the mathematical sciences. During the past ten years, there has been intensive research in convex geometry. Methods and techniques from different fields hav...
It was August 25, and Hurricane Harvey's intensifying winds were moving onshore in South Texas, bringing torrential rains. No one yet knew that Harvey would eventually swamp Houston in flood waters. N...

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