Many aspects of the differential geometry of embedded Riemannian manifolds, including curvature, can be formulated in terms of multi-linear algebraic structures on the space of smooth functions. For matrix analogues of embedded surfaces, one...
Among many different ways to introduce derived algebraic geometry is an interplay between ordinary algebraic geometry and homotopy theory. The infinity-category theory, as a manifestation of homotopy theory, supplies better descent results ...
※ 강연 뒷부분이 녹화되지 않았습니다. A symplectic manifold is a space with a global structure on which Hamiltonian equations are defined. A classical result by Darboux says that every symplectic manifold locally looks standard, so it has be...
In this talk, I will talk about the definition Q-curvature and some of its properties. Then I will talk about the problem of prescribing Q-curvature, especially I will explain the ideas of studying the problem using flow approach.
행렬, 행렬함수 그리고 행렬방정식 (Matrix, Matrix Functions and Matrix Equations)
In this presentation, we introduce how matrices appeared in the history of mathematics and how they are used in today's fields. Also, we consider the necessary mathematics concepts to define the matrix functions. and the existence and conver...
The 21st century is the age of life science. Two issues in the life sciences are that humans live long, healthy lives and maintain a steady state of the earth's ecosystems despite disturbances. In this talk, we will look at how mathematics i...
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...
Global result for multiple positive radial solutions of p-Laplacian system on exterior domain
Global result for multiple positive radial solutions of p-Laplacian system on exterior domain In this talk, we consider p-Laplacian systems with singular indefinite weights. Exploiting Amann type three solutions theorem for the singular syst...
Fixed points of symplectic/Hamiltonian circle actions
A circle action on a manifold can be thought of as a periodic flow on a manifold (periodic dynamical system), or roughly a rotation of a manifold. During this talk, we consider symplectic/Hamiltonian circle actions on compact symplectic mani...
I will tell two interrelated stories illustrating fruitful interactions between combinatorics and Hodge theory. The first is that of Lorentzian polynomials, based on my joint work with Petter Brändén. They link continuous convex...
CategorySpecial ColloquiaDept.미국 프린스턴대 교수, 한국 고등과학원 석학교수Lecturer허준이
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.