The MathNet Korea
Information Center for Mathematical Science

세미나

Information Center for Mathematical Science

세미나

한국고등과학원 세미나

Little Higgs models are a class of models to solve the hierarchy problem by protecting the Higgs mass at one loop with the help of global symmetries. We were studying the constraints by recasting the most prominent SUSY signatures like jets (and leptons) plus missing transverse energy. In order to relax bounds from direct detection searches for dark matter we also consider the collider phenomenology for the case of T-parity violation. Furthermore, we give prospects for the high-luminosity runs of the LHC.

한국고등과학원 세미나

We consider charged Q-ball dark matter scenario, which is realized after the Affleck-Dine baryogenesis through the partial decay of Q-balls. We focus on the fact that these objects are detectable by the usual electromagnetic processes, unlike the ordinary neutral Q-balls. We apply the most stringent constraint from the MICA experiment to the model where the charged Q-balls are realized. We find that the MICA constraint is severer than those from IceCube, which probe neutral Q-ball process, leading to the smaller allowed parameter region.

2018 연세대학교 수학과 콜로퀴움

The (classical) braid groups Bn(R2) have many aspects in topology and geometry, group theory, cryptography and so on, and since 1920's when Artin rstly introduced braids as mathematical objects, they have been generalized in many di erent ways for their own purpose such as braid groups on surfaces and higher dimensional manifolds, and singular braid groups by allowing double points. Most of the studies of these generalizations have been done by using the con guration spaces|the collection of some number of points in the given space|introduced by Fadell and Neuwirth in 1960's. Rather recently, in the end of 20's century, Ghrist published a pioneering paper about braid groups on graphs, which are non-collision motions of points on the graphs. Typically it can describe the motions of robots in a factory, trains on rails, or any number of particles on a given trajectory in general. In this talk, we will focus on the homotopy invariant for braid groups on graphs. In particular, for con guration spaces of graphs, we will see chain-level module structures coming from certain stabilization processes, and de ne a sequence of topological invariants of graphs related with the growth of betti numbers. If time permits, we will also discuss further algebraic structures on the chain complexes of con guration spaces of graphs. This is a joint work with Gabriel C. Drummond-Cole (IBS-CGP) and Ben Knudsen (Harvard University).

2018 연세대학교 수학과 콜로퀴움

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 problem becomes more intriguing since there is no canonical way to sum (and integrate) Fourier series (and integrals, respectively), and convergence of the multidimensional Fourier series and integrals is related to complicated phenomena which can not be understood in perspective of convergence in one dimension. The Bochner-Riesz conjecture may be regarded as an attempt to understand multidimensional Fourier series and integrals. Even though the problem is settled in two dimensions, it remains open in higher dimensions. In this talk we review developments in the Bochner- Riesz conjecture and discuss its connection to the related problems such as the restriction and Kakeya conjectures.

2018 연세대학교 수학과 콜로퀴움
  • Title : The cut-off phenomenon
  • Speaker : Insuk Seo
  • Data : 2018-09-27 17:00:00
  • Host : Yonsei University
  • Place :

The general theory implies that the distribution of an irreducible Markov chain converges to its stationary distribution as time diverges to infinity. The speed of corresponding convergence is a significant issue in the study of mathematical physics or statistical technique known as MCMC. In particular, this speed is exponentially slow under the presence of metastability. In this presentation, we shall focus on the other case; absence of metastability. We will observe a peculiar behavior known as the cut-off phenomenon.

2018 연세대학교 수학과 콜로퀴움

We present mathematical analysis on fluid and its interaction with rigid body or particles. We review several kinds of fluids, for example, Newtonian and non- Newtonian. We also mention their interaction with rigid body or particles, which are observed in various phenomena including airplane in the sky and mosquito spray. We introduce their mathematical models and problems. We also mention their application to finance.

2018 아주대학교 수학과 colloquium

2018 아주대학교 수학과 colloquium

A graph is k-colorable if each vertex receives a color from 1 to k so that no vertex receives the same color with one of its neighbors. Hence, the maximum degree ∆G of a graph G is an important quantity for chromatic graph theory. A simple greedy algorithm enables us to color a graph G with ∆G+1 colors. The well-known Brooks' theorem actually characterizes when we need all ∆G+1 colors. The square of a graph G is formed from G by adding extra edges uv whenever u and v have distance two in G. Since each closed neighborhood of a vertex forms a clique in the square of a graph G, the number of colors required must be at least ∆G+1. In fact, Wegner constructed a graph G that requires roughly 1.5∆G colors, and moreover G is planar! Sparked by a conjecture of Wang and Lih, researchers were able to prove that for each g≥5 there exist tight constants D_g and C_g such that if a planar graph G has minimum cycle length at least g and ∆G≥g , then the square of G is ∆G+C_g-colorable. Instead of asking for the threshold on the minimum cycle length, we extend the question and ask which cycle lengths must be forbidden in order to obtain a bound of the form maximum degree plus a constant. We completely solve this question when we consider the class of planar graphs with a forbidden set of cycle lengths. Namely, we prove the following: For a finite set S, there exists a constant C_S such that the square of a planar graph G without cycle lengths in S is ∆G+C_S-colorable if and only if 4∈S.

2018 아주대학교 수학과 colloquium

The human brain can be understood as a complex system or network, where brain functions emerge from the interaction between neurons at multiple levels. Connectomics is a research field that seeks to collect and analyze such information about neural interaction, which has greatly advanced our understanding of the brain. This talk will introduce how the brain network can be constructed using neuroimaging techniques and characterized using various methodological approaches for investigating brain functions.

2018 고려대학교 수학과 Colloquium

Reaction-diffusion systems with a Lotka-Volterratype reaction term, also known as competition-diffusion systems, have been used to investigate the dynamics of the competition among m ecological species for a limited resource necessary to their survival and growth. Even though they have a rather simple mathematical structure, such systems may display quite interesting behaviors. In particular, while for m=2 no coexistence of the two species is usually possible, if m is larger or equal to 3 we may observe coexistence of all or a subset of the species, sensitively depending on the parameter values. Such coexistence can take the form of very complex spatio-temporal patterns and oscillations. In this talk, we will present some criteria for the non-coexistence of species, motivated by the ecological problem of the invasion of an ecosystem by an exotic species. We will show that when the environment is very favorable to the invading species the invasion will always be successful and the native species will be driven to extinction. On the other hand, if the environment is not favorable enough, the invasion will always fail. This is joint work with Lorenzo Contentoand MasayasuMimura.

2018 고려대학교 수학과 Colloquium
  • Title : Tangle and Knot theory
  • Speaker : 권보현
  • Data : 2018-10-26 16:30:00
  • Host : KOREA University
  • Place :

In this talk, we introduce general knot which is related to the 3-dimensional topology. As one of the nice tools to analyze knot types, we introduce the tangle theory, which is meaningful study itself. We will give some applications to use the tangle theory which is related to our current research studies.

2018 고려대학교 수학과 Colloquium

Meta-material, which is a material made of artificially designed atom, is an emerging field between physics and material science. It has many exciting new applications such as optical computing, super-resolutio n imaging and invisibility cloaks. The rational design of meta-material requires to solve interesting mathematical problems involving PDEs, spectral geometry, operator theory and topology. In this talk, we shall discuss our recent works on the mathematics of meta-materials based on surface plasmonsand acoustic bubbles. This talk is based on joint works with Prof. Habib Ammari(ETH Zurich).

2018 고려대학교 수학과 Colloquium
  • Title : Omega surfaces
  • Speaker : Mason Pember
  • Data : 2018-09-21 16:30:00
  • Host : KOREA University
  • Place :

Omega surfaces are a classical surface class discovered by Demoulinin 1911. This class includes well known surfaces such as isothermicsurfaces, Guichardsurfaces, L-isothermicsurfaces and linear Weingarten surfaces. They have recently received attention because they form an integrablesystem and thus possess a rich transformation theory. In this talk we shall explore this class using their characterisationin Laguerre geometry.

2018 고려대학교 수학과 Colloquium

Compressible flow motion is governed by the Euler system which is a PDE system describing the conservations of mass, momentum and energy. Due to the nonlinear feature of compressible flow, a jump transition, such as a shock or a contact discontinuity, can occur depending on the geometry of a domain, or initial/boundary condition of a flow. In this talk, I will explain physical background of shock phenomena, and how to formulate a shock problem into a mathematical problem. Then, I will discuss about my recent results on a detached shock problem.

고려대학교 수학과 세미나

Timelikethomsensurfaces are timelikeminimal surfaces that are also affine minimal. In this talk, we utilize both the Lorentz conformal coordinates and the null coordinates (and their respective representation theorems) to characterize and classify timelikeThomsen surfaces. Furthermore, we reveal a surprising relationship between timelikeThomsen surfaces, and timelikeminimal surfaces with planar curvature lines.

2018 서울대학교 수리과학부 세미나

The least square Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz is the most widely used method for pricing options with early exercise features. The LSM estimator contains look-ahead bias, and the conventional technique of removing it necessitates an independent set of simulations. This study proposes a new approach for effciently eliminating look-ahead bias by using the leave-one-out method, a well-known cross-validation technique for machine learning applications. The leave-one-out LSM (LOOLSM) method is illustrated with examples, including multi-asset options whose LSM price is biased high. The asymptotic behavior of look-ahead bias is also discussed with the LOOLSM approach.

2018 서울대학교 수리과학부 세미나

2018 서울대학교 수리과학부 세미나

It is well known that a bounded operator with dense range has a nontrivial invariant subspace if and only if its Aluthge transform does. Recently, R. Curto and Jasang Yoon have introduced the toral and spherical Aluthge transforms for commuting pairs and studied their basic properties. In this talk, we talk about nontrivial common invariant subspaces between the toral (resp. spherical) Aluthge transform and the original n-tuple of bounded operators with dense ranges.

한국고등과학원 세미나

Miyawaki type lifts are kinds of Langlands functorial lifts and a special case was first conjectured by Miyawaki and proved by Ikeda for Siegel cusp forms under the assumption of non-vanishing of certain integrals. I will explain Miyawaki lifts and show infinitely many examples which satisfy the non-vanishing assumption. This is a joint work with T. Yamauchi.

한국고등과학원 세미나

The Gross-Keating invariant of a quadratic form over p-adic integers is a relatively recent but fundamental concept in the study of quadratic forms. I will explain how it is related to some classical topics of number theory, such as the representation of integers by quadratic forms and the classical modular polynomials for the j-invariant. The rest of the talk will be devoted to a computer program that computes the Gross-Keating invariant of a quadratic form over Zp, and other related quantities.