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Along with the rapid development of artificial intelligence (AI) technology, scientific research enters a new era of AI. Topology optimization (TO) and AI technology are recently showing a growing tre...
Modern algebraic topology sees equivariance arising in unexpected context. Equivariant cohomology carries rich structures but is much harder to compute. In 2009, Hill, Hopkins, and Ravenel solved the ...
Topology and entanglement are two powerful principles for characterizing the structure of complex quantum states. In a new paper in the journal Physical Review X, researchers from the University of Pe...
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 ...
This is the seventh annual Tech Topology Conference. It brings together established and beginning researchers from around the country for a weekend of mathematics in Atlanta. Check back soon for more ...
Computer experiments and calculations have had a profound influence on many areas covered by this Symposium. In 3-manifold theory the program SnapPea has been widely used to explore the landscape of 3...
An interesting example of a compact Hausdorff space that is often presented in beginning courses in topology is the unit square [0, 1]× [0, 1] with the lexicographic order topology. The closed subspac...
Modern spaceborne SAR sensors like TerraSAR-X offer ground resolution of up to one meter in range and azimuth direction. Buildings, roads, bridges, and other man-made structures appear in such data of...
This paper is a follow-up to the author's work "Topology of probability measure space, I" devoted to investigation of the functors $\hat P$ and $P_\tau$ of spaces of probability $\tau$-smooth and Rado...
For a non-empty set $X$, the collection $Top(X)$ of all topologies on $X$ sits inside the Boolean lattice $\PP(\PP(X))$ (when ordered by set-theoretic inclusion) which in turn can be naturally identif...
Abstract: We present Nonstandard Analysis by three axioms: the {\em Extension, Transfer and Saturation Principles} in the framework of the superstructure of a given infinite set. We also present sever...
Reducing interference is one of the main challenges in wireless communication. To minimize interference through topology control in wireless sensor networks is a well-known open algorithmic problem. I...
Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic words in the generators of the fundamental group and their inverses.
Topological spaces - such as classifying spaces, configuration spaces and spacetimes - often admit extra temporal structure.
Let A+ denote the set of Laplace transforms of complex Borel measures μ on [0,+1) such that μ does not have a singular non-atomic part. In [1], an extension of the classical -metric of Vinnicombe was...

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