The main topic of the talk is a determinantal formula for high dimensional tree numbers of acyclic complexes via combinatorial Laplace operators . This result is a generalization of Temperley's tree number formula for graphs, motivated by a ...
Contact topology of singularities and symplectic fillings
For an isolated singularity, the intersection with a small sphere forms a smooth manifold, called the link of a singularity. It admits a canonical contact structure, and this turns out to be a fine invariant of singularities and provides an...
Normal form reduction for unconditional well-posedness of canonical dispersive equations
Normal form method is a classical ODE technique begun by H. Poincare. Via a suitable transformation one reduce a differential equation to a simpler form, where most of nonresonant terms are cancelled. In this talk, I begin to explain the not...
2000년 국제수학교육위원회( International Commission on Mathematical Instruction)는 수학교육연구에 탁월한 업적을 이룬 학자에게 수여하는 Freudenthal 메달과 Klein메달을 제정하여, 2003년 부터 홀수 해에 수상하고 있다. 이 강연에서는 2012년 서울에...
In this talk I will talk about existence and regularity for solutions to the compressible viscous Navier-Stokes equations on nonsmooth domains, especially with corners. The solution is constructed by the decomposition of the corner singulari...
Weyl character formula and Kac-Wakimoto conjecture
The character of the finite-dimensional irreducible modules over a finite-dimensional simple Lie algebra is given by the celebrated Weyl character formula. However, such a formula does not hold in general for finite-dimensional irreducible m...
We will introduce the behavior of zeros of linear combinations of zeta functions. Those linear combinations are related to the Riemann zeta function, the Eisenstein series, Periods, etc.
Noise-induced phenomena in stochastic heat equations
Stochastic heat equations (SHE) usually refer to heat equations perturbed by noise and can be a model for the density of diffusing particles under a random potential. When the irregularity of noise is dominating the diffusion, SHE exhibits ...
On classification of long-term dynamics for some critical PDEs
This talk concerns the problem of classifying long-term dynamics for critical evolutionary PDEs. I will first discuss what the critical PDEs are and soliton resolution for these equations. Building upon soliton resolution, I will further in...
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...
We rely on intuition every day, and we use mathematics every day. Intuition is fast, powerful and omniapplicable, but sometimes wrong. Mathematics is efficient, powerful and correct, when applicable. Whenever there is an uncertainty, a proof...
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...
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...
