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In this talk,we discuss the finite time blow up phenomena of smooth solutions to the compressible Navier-Stokes system when the initial data contain vacuums. It is proved that any classical solutions ...
A class of nonlinear integrable PDEs admit non-smooth solitary wave solutions as certain special weak solutions. These solutions can be used to capture main attributes of solutions of these PDEs, e.g....
Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In this talk, we will first review recent progress in singu...
Nematic liquid crystals (NLCs) are anisotropic material intermediate that combine the fluidity of liquids with the orientational order of solids. NLCs are best known for their applications in the thri...
The moduli space of a smooth manifold X is defined to be the classifying space of its diffeomorphism group. Understanding the cohomology group of this space is important because elements in this group...
Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this talk, we will present a ...
Hash proof systems or smooth projective hash functions (SPHFs) have been proposed by Cramer and Shoup (Eurocrypt'02) and can be seen as special type of zero-knowledge proof system for a language. Whil...
Oblivious transfer is an important tool against malicious cloud server providers. Halevi-Kalai OT, which is based on smooth projective hash(SPH), is a famous and the most efficient framework for 11-ou...
Oblivious transfer (OT) is a fundamental primitive in cryptography. Halevi-Kalai OT (Halevi, S. and Y. Kalai (2012), Journal of Cryptology 25(1)), which is based on smooth projective hash(SPH), is a f...
Motivated by the revelations of Edward Snowden, post-Snowden cryptography has become a prominent research direction in recent years. In Eurocrypt 2015, Mironov and Stephens-Davidowitz proposed a novel...
The cartographic 3D visualization of urban areas has experienced tremendous progress over the last years. An increasing number of applications operate interactively in real-time and thus require advan...
Lossy trapdoor functions (LTDFs), proposed by Peikert and Waters (STOC'08), are known to have a number of applications in cryptography. They have been constructed based on various assumptions, which i...
Theoretical chemists at Princeton University have pioneered a strategy for modeling quantum friction, or how a particle’s environment drags on it, a vexing problem in quantum mechanics since the birth...
In 1849, Dirichlet[5] proved that the probability that two positive integers are relatively prime is 1/zeta(2). Later, it was generalized into the case that positive integers has no nontrivial kth pow...
Smooth projective hashing has proven to be an extremely useful primitive, in particular when used in conjunction with commitments to provide implicit decommitment. This has lead to applications pro...

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