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...
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...
1. 금본위제, 달러, 비트코인 등 돈의 흐름으로 보는 세계사 2. 사람은 어떻게 생각하고 행동하는가 ? (행동경제학, 비선형성) 3. 돈에 대한 생각, 행동, 습관을 바꾸어보자. (부자들은 무엇이 다른가 ? 지금부터 준비해보자.) 4. 주식, 부동산 등 자산관리 [...
We proved the codimension three conjecture that says the micro-local perverse sheaves extend if it is defined outside odimension three (counting from Lagrangian subvarity). It is a joint work with Kari Vilonen.
Black holes are perhaps the most celebrated predictions of general relativity. Miraculously, these complicated spacetimes arise as explicit (i.e., exact expression can be written down!) solutions to the vacuum Einstein equation. Looking thes...
Since Belavin, Polyakov, and Zamolodchikov introduced conformal field theory as an operator algebra formalism which relates some conformally invariant critical clusters in two-dimensional lattice models to the representation theory of Viraso...
For each natural number k, the C^k diffeomorphisms of the circle form a group with function compositions. This definition even extends to real numbers k no less than one by Hölder continuity. We survey algebraic properties of this grou...
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...
Free boundary problems arising from mathematical finance
Many problems in financial mathematics are closely related to the stochastic optimization problem because the optimal decision must be made under the uncertainty. In particular, optimal stopping, singular control, and optimal switching prob...
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-...
In this talk, we investigate some regularity results for non-uniformly elliptic problems. We first present uniformly elliptic problems and the definition of non-uniform ellipticity. We then introduce a double phase problem which is characte...
Mathematical Models and Intervention Strategies for Emerging Infectious Diseases: MERS, Ebola and 2009 A/H1N1 Influenza
Emerging infectious diseases have long been recognized as a continuous, inevitable, unpredictable threat to the global public health. Hence, understanding the underlying dynamics why they spread and what causes epidemics gives key ideas of i...
The spaces admitting a rational parameterization are called rational. In particular plane conics, including circles, are rational. We will explain a few interesting applications of the rational parameterization of a circle. Also several exam...
Concordance is a relation which classifies knots in 3-space via surfaces in 4-space, and it is closely related with low dimensional topology. Satellite operators are one of the main tools in the study of knot concordance, and it has been wi...
