# 세미나 및 콜로퀴엄

구글 Calendar나 iPhone 등에서 구독하면 세미나 시작 전에 알림을 받을 수 있습니다.

The Hybridizable discontinuous Galerkin (HDG) methods retain the advantage of the discontinuous Galerkin (DG) methods such as flexibility in meshing and preserving local conservation of physical quantities and overcome to shortcomings of the DG by reducing the globally coupled degree of freedom. I will design a multiscale method within the HDG framework. The main concept of the multiscale HDG method is to deriving upscale structure of the method and to generate multiscale spaces defined on the coarse edges that provide a reduced dimensional approximation for numerical traces. Eigenvalue problems plays a significant role in generating a multiscale space. Also, error analysis and a representative number of numerical examples will be given.

Abstract: The large deviation problem for the spectrum of random matrices has attracted immense interest. It was first studied for GUE and GOE, which are exactly solvable, and subsequently studied for Wigner matrices with general distributions. Once the sparsity is induced (i.e. each entry is multiplied by the independent Bernoulli distribution, Ber(p)), eigenvalues can exhibit a drastically different behavior. For a large class of Wigner matrices, including Gaussian ensembles and the adjacency matrix of Erdos-Renyi graphs, dense behavior ceases to hold near the constant average degree of sparsity, p~1/n (up to a poly-logarithmic factor). In this talk, I will talk about the spectral large deviation for Gaussian ensembles with a sparsity p=1/n. Joint work with Shirshendu Ganguly.

ZOOM회의정보 link:https://zoom.us/j/94727585394?pwd=QlBSRUNTQi9UWXNLSTlPOTgrRnhhUT09 회의 ID: 947 2758 5394 암호: saarc

ZOOM회의정보 link:https://zoom.us/j/94727585394?pwd=QlBSRUNTQi9UWXNLSTlPOTgrRnhhUT09 회의 ID: 947 2758 5394 암호: saarc

The compressible Euler system was first formulated by Euler in 1752, and was complemented by Laplace and Clausius in the 19th century, by introducing the energy conservation law and the concept of entropy based on thermodynamics. The most important feature of the Euler system is the finite-time breakdown of smooth solutions, especially, appearance of a shock wave as severe singularity to irreversibility(-in time) and discontinuity(-in space). Therefore, a fundamental question (since Riemann 1858) is on what happens after a shock occurs. This is the problem on well-posedness (that is, existence, uniqueness, stability) of weak solutions satisfying the 2nd law of thermodynamics, which is called entropy solution. This issue has been conjectured as follows: Well-posedness of entropy solutions for CE can be obtained in a class of vanishing viscosity limits of solutions to the Navier-Stokes system. This conjecture for the fundamental issue remains wide open even for the one-dimensional CE. This talk will give an overview of the conjecture, and recent progress on it.

Introduction: In this lecture series, we'll discuss algebro-geometric study on fundamental problems concerning tensors via higher secant varieties.
We start by recalling definition of tensors, basic properties and small examples and proceed to discussion on tensor rank, decomposition, and X-rank
for any nondegenerate variety $X$ in a projective space. Higher secant varieties of Segre (resp. Veronese) embeddings will be regarded as a natural
parameter space of general (resp. symmetric) tensors in the lectures. We also review known results on dimensions of secants of Segre and Veronese,
and consider various techniques to provide equations on the secants.
In the end, we'll finish the lectures by introducing some open problems related to the theme such as syzygy structures and singularities of higher secant varieties.

It is a gentle introduction to the mean curvature flow and its application to knot theory for undergraduate students. J.W.Alexander discovered a knotted sphere embedded in 3-dimensional Euclidean space in 1924. This example has provoked curiosity to find simple conditions under which embedded spheres are unknotted. In this talk we will sketch theorems and conjectures in the mean curvature flow for the knot theory, in analogy to the Ricci flow for the smooth 4-dimensional Poincare conjecture.

Infinity-category theory is a generalization of the ordinary category theory, where we extend the categorical perspective into the homotopical one. Putting differently, we study objects of interest and "mapping spaces" between them. This theory goes back to Boardman and Vogt, and more recently, Joyal, Lurie, and many others laid its foundation. Despite its relatively short history, it has found applications in many fields of mathematics. For example, number theory, mathematical physics, algebraic K-theory, and derived/spectral algebraic geometry: more concretely, p-adic Hodge theory, Geometric Langlands, the cobordism hypothesis, topological modular forms, deformation quantization, and topological quantum field theory, just to name a few.
The purpose of this series of talks on infinity-categories is to make it accessible to those researchers who are interested in the topic. We’ll start from scratch and try to avoid (sometimes inevitable) technical details in developing the theory. That said, a bit of familiarity to the ordinary category theory is more or less necessary. Overall, this series has an eye toward derived/spectral algebraic geometry, but few experience in algebraic geometry would hardly matter. Therefore, everyone is welcome to join us.
This is the first in the series. We’ll catch a glimpse of infinity-category theory through some motivational examples.

Zoom ID: 352 730 6970, password: to be announced.

Zoom ID: 352 730 6970, password: to be announced.

Generative adversarial networks (GAN) are a widely used class of deep generative models, but their minimax training dynamics are not understood very well. In this work, we show that GANs with a 2-layer infinite-width generator and a 2-layer finite-width discriminator trained with stochastic gradient ascent-descent have no spurious stationary points. We then show that when the width of the generator is finite but wide, there are no spurious stationary points within a ball whose radius becomes arbitrarily large (to cover the entire parameter space) as the width goes to infinity.