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The Grobner basis for a zero-dimensional polynomial ideal comprises a univariate polynomial in the least variable. The elimination process in Buchberger's algorithm unnecessarily involves the least va...
For any θ<1/3 , we show that very weak solutions to the two-dimensional Monge–Ampère equation with regularity C1,θ are dense in the space of continuous functions. This result is shown by a convex inte...
We define a higher-dimensional analogue of symplectic Khovanov homology. Consider the standard Lefschetz fibration of a 2n-dimensional Milnor fiber of the A_{k-1} singularity. We represent a link by a...
Using the results presented in the previous lecture, namely the generalization of the Tsirelson's theorem [2] to mixed volumes, we calculate the mixed volume of the closed convex hulls of the two orth...
Let K be a convex compact subset of a separable Hilbert space H. One of the most important geometric characteristics of K is its intrinsic volumes. In the finitedimensionalcase (K ? R^d), the intrinsi...
In his pioneering work in 1860, Riemann proposed the Riemann problem and solved it for isentropic gas in terms of shocks and rarefaction waves. It eventually became the foundation of the theory of one...
Higher dimensional Heegaard Floer homology (HDHF) is a higher dimensional analogue of Heegaard Floer homology in dimension three. It's partly used to study contact topology in higher dimensions. In a ...
This talk will survey some results for the two- or three-space dimensional compressible Euler equations. We shall present non-uniqueness results of weak entropy solutions using convex integration and ...
We explore time-varying networks for high-dimensional locally stationary time series, using the large VAR model framework with both the transition and (error) precision matrices evolving smoothly over...
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 ...
Hypothesis testing on high-dimensional fixed effects is indispensable for investigating the utility of the predictors on response. In this case, the conventional frequentist methods designed for cases...
We will discuss two special cases of the three-dimensional Kakeya conjecture: SL_2 Kakeya and a refined Wolff's hairbrush result. As an application of the refined Wolff's hairbrush result, we will dis...
In recent years there has been an explosion of complex data-sets in areas as diverse as Bioinformatics, Ecology, Epidemiology, Finance, subsurface Geophysics, Meteorology, and Population genetics. In ...
The program aims at showing the role of modern statistical methods in complex data and serves to support interactions among mathematicians, statisticians, engineers and scientists working in the inter...
In genetical genomics studies, it is important to jointly analyze gene expression data and genetic variants in exploring their associations with complex traits, where the dimensionality of gene expres...

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