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...
Circular maximal functions on the Heisenberg group
The spherical average has been a source of many problems in harmonic analysis. Since late 90's, the study of the maximal spherical means on the Heisenberg group $mathbb{H}^n$ has been started to show the pointwise ergodic theorems on the gro...
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...
A modified separation method to solve a heat-transfer boundary value problem
We derive a general solution of the heat equation through two modied separation methods. The obtained solution is expressed as linearly combined kernel solutions in terms of Hermite polynomials, which appears to provide an explanation of non...
Elliptic curves defined over the rationals satisfy two finiteness properties; its group of rational points is a finitely generated abelian group and it has only finitely many points with integral coordinates. Bhargava and his collaborators e...
<학부생을 위한 ɛ 강연> Convergence of Fourier series and integrals in Lebesgue spaces
Convergence of Fourier series and integrals is the most fundamental question in classical harmonic analysis from its beginning. In one dimension convergence in Lebesgue spaces is fairly well understood. However in higher dimensions the probl...
Trends to equilibrium in collisional rarefied gas theory
Dynamics of many particle system can be described by PDE of probability density function. The Boltzmann equation in kinetic theory is one of the most famous equation which describes rarefied gas dynamics. One of main property of the Boltzman...
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...
Lagrangian Floer theory in symplectic manifold associate a category (A infinity category) to a symplectic manifold. More than 20 years ago a relation of a relation between Lagrangian Floer theory and Gauge theory was studied by Floer himself...
CategoryMath ColloquiaDept.Simons Center for Geometry and PhysicsLecturerKenji Fukaya
Weak and strong well-posedness of critical and supercritical SDEs with singular coefficients
In this talk I will first give a survey of recent recent results SDEs with singular coefficients. Then I will report some recent results, jointly with Longjie Xie, on critical and supercritical SDEs with singular coefficients.
CategoryMath ColloquiaDept.University of IllinoisLecturerRenming Song
We introduce the notion of congruences (modulo a prime number) between modular forms of different levels. One of the main questions is to show the existence of a certain newform of an expected level which is congruent to a given modular form...
A W-algebra is introduced as a symmetry algebra in 2-dimensional conformal field theory. Mathematical realization of a W-algebra was introduced by the theory of vertex algebras. Especially, W-algebras related to Lie superalgebras have been s...
On function field and smooth specialization of a hypersurface in the projective space
In this talk, we will discuss two interesting problems on hypersurfaces in the projective space. The first one is the absolute Galois theory on the function field of a very general hypersurface in the projective space. The other one is the c...
We discuss how the closed connected 1-dimensional manifold, namely the circle, can help understanding 3-manifolds. We describe so-called the universal circle proposed by a lengendary mathematician, William Thurston, and discuss certain gene...