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Information Center for Mathematical Science

### 세미나

Information Center for Mathematical Science

#### 세미나

##### 한국고등과학원 세미나

We present a transfer operator approach to study of distribution of modular symbols, motivated by the work of Baladi-Vall?e on dynamics of continued fractions. The approach leads to a few applications. We show an average version of Mazur-Rubin conjectures about statistical properties of modular symbols and further obtain the quantitative non-vanishing mod p of modular L-values with Dirichlet twists. (joint with Hae-Sang Sun)

##### 한국고등과학원 세미나

We consider a system of $N$-Bosons with a two-body interaction potential in three-dimensional space. It is known that the difference between the many-body Schr{\"o}dinger evolution in the mean-field regime and the corresponding Hartree dynamics at time $t$ is less or equal to $Ce^{Kt}/N$ for Coulomb potential, and it is also known that the $N$-dependency of the bound is optimal. We prove that similar result holds for all interaction potential $V \in L^2(\mathbb{R}^3)+L^\infty (\mathbb{R}^3)$ which covers more singular potentials than Coulmomb potential. Moreover, we investigate the time dependency of the difference. To have sub-exponential bound, we use the results of time decay estimate for small initial data. For time dependency, we consider the interaction potential $V(x)$ of type $\lambda \exp(?\mu |x|)|x|^{-\gamma}$ for $\lambda\in\mathbb{R}$, $\mu \geq 0$, and $0<\gamma<3/2$, which covers Coulomb and Yukawa potential.

##### 한국고등과학원 세미나

The set of zeroes of a bihomogeneous polynomial of degree (2,2) is an elliptic curve (a genus 1 Riemann surface) in the product of two copies of the complex projective line. The coefficients of the polynomial form a 3x3 matrix. I will discuss how algebraic properties of this matrix are related to the geometry of the elliptic curve. This example relates to the type of duality arising in Le Potier's "strange duality" conjecture. No prior knowledge of algebraic geometry will be assumed.

##### 한국고등과학원 세미나

The jellium is a model, introduced by Wigner, for a gas of electrons moving in a uniform neutralizing background of positive charge. In two dimensions, the model is closely related to random matrices while in one dimension the model is used to study dimerization and crystallization. For the quantum jellium, Brascamp and Lieb (1975) proved crystallization (non-ergodicity of the Gibbs measures) at low densities of electrons. Using tools from probability theory we prove crystallization for the quantum one-dimensional jellium at all densities as well as similar behavior for quasi-1d systems. This talk is based on joint work with M. Aizenman and S. Jansen.

##### 한국고등과학원 세미나

In this talk we will give some boundedness results of pseudo-differential operators of type (0,0) on Triebel-Lizorkin spaces. Our results are sharp and a counter example for the sharpness will be provided by using a randomization method.

##### 한국고등과학원 세미나

In this talk, we first review nonlinear elliptic equations when the right-hand side is a finite measure. We discuss global gradient estimates of a solution for such measure data problems in bounded nonsmooth domains. We provide proper solutions and conditions which guarantee the regularity results. If time permits, we will consider parabolic problems with measure data.

##### 한국고등과학원 세미나

In this talk we will present that global Kato type smoothing estimates are essentially equivalent to local ones.

##### 한국고등과학원 세미나
• Speaker : Arthur Parzygnat
• Data : 2018-11-21 16:00:00
• Host : KIAS
• Place :

What does it mean for a theory to admit a probabilistic analogue? We will explore the Giry/Radon monads on categories of measurable/topological spaces and measurable/continuous maps. Then, we will construct the associated Kleisli category of the monad. This category defines a probabilistic analogue of the original category. No knowledge of probability theory, monads, and Kleisli categories will be assumed in this talk.

##### 한국고등과학원 세미나

Classical conditional probabilities and disintegrations can be formulated diagrammatically in a category of stochastic matrices. Combining this with the functor taking stochastic matrices to positive operators on C*-algebras, a notion of non-commutative disintegration and conditional probability can be made for states on C*-algebras. The existence and uniqueness of conditional probabilities is an important fact in probability theory. However, unlike the classical case, the existence of non-commutative disintegrations is not guaranteed even on finite-dimensional matrix algebras. We will state some general existence and uniqueness results as well as illuminating examples. This is joint work with Benjamin P. Russo (Farmingdale State College SUNY).

##### KAIST 수리과학과 세미나

We discuss a sensitivity analysis of long-term cash flows. The price of the cash flow at time zero is given by the pricing operator of a Markov diffusion acting on the cash flow function. We study the extent to which the price of the cash flow is affected by small perturbations of the underlying Markov diffusion. The main tool is the Hansen--Scheinkman decomposition, which is a method to express the cash flow in terms of eigenvalues and eigenfunctions of the pricing operator. By incorporating techniques of Malliavin calculus, the sensitivities of long-term cash flows can be represented via simple expressions in terms of the eigenvalue and the eigenfunction.

##### KAIST PDE 세미나

Direct sampling method (DSM) is a well-known, non-iterative imaging technique in inverse scattering problem. Throughout various researches, DSM has been applied various research area e.g., diffusion tomography, electrical impedance tomography, source detection in stratified ocean waveguide, etc.; however, due to the small number of incident fields or sources, further improvements are still required. In this presentation, we carefully identify mathematical structure of indicator function of DSM to show the feasibilities and limitations, design a method of improvement, and apply in real-world microwave imaging. Simulations results with synthetic and experimental data are shown for supporting identified structure.

##### 서울대학교 지구환경과학부 세미나

High-temperature molten silicates are critical parts of geological processes ranging

##### 서울대학교 지구환경과학부 세미나

Identication of seismogenic faults is of the topmost importance in seismic hazard assessment. However most of earthquakes occur on poorly constrained or unknown subsurface faults, which makes seismic hazard assessment dicult. Unlike earthquake-prone regions such as Japan and Taiwan, damaging earth-quake has not been so frequent in Korea which is classified into the intraplate seismicity region. Establishing the relationship between the contemporary seis-micity and its causative faults explicitly is a challenging issue mainly due to the long recurrence intervals between large events and the rare occurrence of surface expression from the earthquake activity in this region. Compared to the large infrequent earthquakes, microearthquakes are in a more continual process. In crustal faults, these microearthquakes appear to be distributed over the large fault plane. A dramatic case of microearthquake cluster deciphering the fault geometry is the aftershock sequence following a large earthquake. Recent dense permanent and temporary seismic monitoring networks of Korea produce plenty of information on earthquake activity of the country allowing detection of much lower magnitude events than ever. Moreover the earthquake locations can be highly constrained when combined with an appropriate relocation algorithm such as double-difference approaches. Since the mainshock-aftershock sequence is maintained, the fault geometry can be uncovered by accurately locating large number of aftershocks. The present study addresses the seismic activity and its monitoring in Korea to reveal the subsurface fault geometry in depth of which relation with the mapped faults is not known or at least unclear. A series of the precise locations of individual microearthquake in a larger fault system is a key to the characterization of seismogenic fault to be considered in the future seismic hazard assessment of the region.

##### 서울대학교 지구환경과학부 세미나

The areal extent and thickness of the Arctic sea ice have significantly decreased during recent decades, apparently increasing heat and moisture fluxes from the ocean to the atmosphere in particular in autumn and early winter. These changes may locally increase air temperature, moisture, and cloud cover, and in turn remotely cause anomalous climate and weather, such as cold and snowy winters, in the subarctic and mid-latitude terrestrial regions. As a consequence, changes in the hydrological regime and its thermal conditions may occur. The changes were assessed by the statistical analysis using observational records and modeling results in the Arctic regions. In reality, the analyses have identified permafrost warming, in which changes in snow cover play a forcing role in additional global warming effects. The warmed permafrost was also subsequently implicated to the alternation of seasonality, variability, and magnitude of Arctic river discharges, leading to an earlier occurrence of peak in spring and an increase in the amount of the discharges. At the same time, the warming climate also increased river water temperature, resulting in a larger heat flux into the Arctic Ocean when combined with the increased discharge, and then contributing to sea ice melt. These studies suggest that the Arctic water cycle can be further intensified by sea ice retreat in a warming climate. Here, I will give a review presentation that introduces the results confirming the above findings, based on field observation and modeling study.