Spectral Analysis for the Anomalous Localized Resonance by Plasmonic Structures
We present a mathematical justification of cloaking due to anomalous localized resonance (CALR). We consider the dielectric problem with a source term in a structure with a layer of plasmonic material. Using layer potentials and symmetrizati...
Structural stability of meandering-hyperbolic group actions
Sullivan sketched a proof of his structural stability theorem for differentiabl group actions satisfying certain expansion-hyperbolicity axioms. We relax Sullivan’s axioms and introduce a notion of meandering hyperbolicity for group a...
Fitch is a formal proof system recently gaining momentum in logic education due to its structural similarity to human reasoning. We introduce Fitch via its web-implementation at http://www.proofmood.com. Then we compare Fitch with more well-...
Study stochastic biochemical systems via their underlying network structures
When a biological system is modeled using a mathematical process, the following step is normally to estimate the system parameters. Despite the numerous computational and statistical techniques, estimating parameters for complex systems can...
The mapping class group of a surface S is the component group of orientation-preserving homeomorphisms on S. We survey geometric and algebraic aspects of this group, and introduce a technique of using right-angled Artin groups to find geomet...
Subword complexity, expansion of real numbers and irrationality exponents
We introduce and study a new complexity function in combinatorics on words, which takes into account the smallest return time of a factor of an infinite word. We characterize the eventually periodic words and the Sturmian words by means of t...
It is usually a difficult problem to characterize precisely which elements of a given integral domain can be written as a sum of squares of elements from the integral domain. Let R denote the ring of integers in a quadratic number field. Thi...
Symplectic Geometry, Mirror symmetry and Holomorphic Curves
Symplectic geometry arose from the study of classical mechanics, and later many interesting symplectic invariants has been found since Gromov introduced techniques of J-holomorphic curves. Miraculously, such invariants are closely related wi...
Symplectic topology and mirror symmetry of partial flag manifolds
Soon after Gromov’s applications of pseudo-holomorphic curves to symplectic topology, Floer invented an infinite-dimensional Morse theory by analyzing moduli spaces of pseudo-holomorphic curves to make substantial progress on Arnold&r...
The Lagrange and Markov Spectra of Pythagorean triples
The Lagrange spectrum is the set of approximation constants in the Diophantine approximation for badly approximated numbers. It is closely related with the Markov spectrum which corresponds the minimum values of indefinite quadratic forms ov...
The Mathematics of the Bose Gas and its Condensation
Since Bose and Einstein discovered the condensation of Bose gas, which we now call Bose-Einstein condensation, its mathematical properties have been of great importance for mathematical physics. Recently, many rigorous results have been obta...
In many applications such as X-ray Crystallography, imaging, communication and others, one must construct a function/signal from only the magnitude of the measurements. These measurements can be, for example, the Fourier transform of the den...
Category수학강연회소속Hong Kong University of Science and Technology강연자Yang Wang
The process of mathematical modelling for complex and stochastic biological systems
The revolution of molecular biology in the early 1980s has revealed complex network of non-linear and stochastic biochemical interactions underlying biological systems. To understand this complex system, mathematical models have been widely ...
Creating information and knowledge from large and complex data sets is one the fundamental intellectual challenges currently being faced by the mathematical sciences. One approach to this problem comes from the mathematical subdiscipline cal...
Category수학강연회소속Stanford University강연자Gunnar E. Carlsson
Theory and applications of partial differential equations
I will talk in general about theory and applications of partial differential equations. A recent progress in the regularity theory for nonlinear problems will be also discussed, including uniform estimates of solutions in various function sp...
Topological aspects in the theory of aperiodic solids and tiling spaces
After a review of various types of tilings and aperiodic materials, the notion of tiling space (or Hull) will be defined. The action of the translation group makes it a dynamical system. Various local properties, such as the notion of "Finit...
Category수학강연회소속Georgia Institute of Technology, School of Mathematics and School of Physics강연자Jean V. Bellissard
Topological surgery through singularity in mean curvature flow
The mean curvature flow is an evolution of hypersurfaces satisfying a geometric heat equation. The flow naturally develops singularities and changes the topology of the hypersurfaces at singularities, Therefore, one can study topological pr...