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Lee Sang Gak Telescope (LSGT): A Remotely Operated Robotic Telescope for Education and Research at Seoul National UniversityOct 12 2015We introduce the Lee Sang Gak Telescope (LSGT), a remotely operated, robotic 0.43-meter telescope. The telescope was installed at the Siding Spring Observatory, Australia, in 2014 October, to secure regular and exclusive access to the dark sky and excellent ... More

Intra-night optical variability of AGN in the COSMOS field with the KMTNetSep 05 2018Active Galactic Nucleus (AGN) variability can be used to study the physics of the region in the vicinity of the central black hole. In this paper, we investigated intra-night optical variability of AGN in the COSMOS field in order to understand the AGN ... More

Development of SED Camera for Quasars in Early Universe (SQUEAN)May 30 2016We describe the characteristics and performance of a camera system, Spectral energy distribution Camera for Quasars in Early Universe (SQUEAN). It was developed to measure SEDs of high redshift quasar candidates (z $\gtrsim$ 5) and other targets, e.g., ... More

Camera for QUasars in EArly uNiverse (CQUEAN)Jun 13 2012We describe the overall characteristics and the performance of an optical CCD camera system, Camera for QUasars in EArly uNiverse (CQUEAN), which is being used at the 2.1 m Otto Struve Telescope of the McDonald Observatory since 2010 August. CQUEAN was ... More

The Very Early Light Curve of SN 2015F in NGC 2442: A Possible Detection of Shock-Heated Cooling Emission and Constraints on SN Ia Progenitor SystemOct 07 2015The main progenitor candidate of Type Ia supernovae (SNe Ia) is white dwarfs in binary systems where the companion star is another white dwarf (double degenerate system) or a less evolved non-degenerate star with R* >~ 0.1 Rsun (single degenerate system), ... More

Seoul National University Camera II (SNUCAM-II): The New SED Camera for the Lee Sang Gak Telescope (LSGT)Jul 27 2017We present the characteristics and the performance of the new CCD camera system, SNUCAM-II (Seoul National University CAMera system II) that was installed on the Lee Sang Gak Telescope (LSGT) at the Siding Spring Observatory in 2016. SNUCAM-II consists ... More

Distance and properties of NGC 4993 as the host galaxy of a gravitational wave source, GW170817Oct 16 2017Recently, the optical counterpart of a gravitational wave source GW170817 has been identified in NGC 4993 galaxy. Together with evidence from observations in electromagnetic waves, the event has been suggested as a result of a merger of two neutron stars. ... More

Optical Multi-Channel Intensity Interferometry - or: How To Resolve O-Stars in the Magellanic CloudsOct 23 2014Intensity interferometry, based on the Hanbury Brown-Twiss effect, is a simple and inexpensive method for optical interferometry at microarcsecond angular resolutions; its use in astronomy was abandoned in the 1970s because of low sensitivity. Motivated ... More

"Visible" 5d orbital states in a pleochroic oxychlorideApr 12 2019Transition metal compounds sometimes exhibit beautiful colors. We report here on a new oxychloride Ca3ReO5Cl2 which shows unusually distinct pleochroism; that is, the material exhibits different colors depending on viewing directions. This ple-ochroism ... More

The Infrared Medium-deep Survey. VI. Discovery of Faint Quasars at $z\sim5$ with a Medium-band-based ApproachNov 21 2018Nov 22 2018The faint quasars with $M_{1450}>-24$ mag are known to hold the key to the determination of the ultraviolet emissivity for the cosmic re-ionization. But only a few have been identified so far because of the limitations on the survey data. Here, we present ... More

Measurable Relationship Between Bright Galaxies and Their Faint Companions in WHL J085910.0+294957, a Galaxy Cluster at z = 0.30: Vestiges of Infallen Groups?Jun 25 2014The properties of satellite galaxies are closely related to their host galaxies in galaxy groups. In cluster environments, on the other hand, the interaction between close neighbors is known to be limited. Our goal is to examine the relationships between ... More

The Infrared Medium-deep Survey. III. Survey of Luminous Quasars at 4.7 $\leq$ z $\leq$ 5.4Jun 26 2017We present our first results of the survey for high redshift quasars at $5 \lesssim {\rm z} \lesssim 5.7$. The search for quasars in this redshift range has been known to be challenging due to limitations of filter sets used in previous studies. We conducted ... More

Discovery of A Faint Quasar at z~6 and Implications for Cosmic ReionizationNov 05 2015Recent studies suggest that faint active galactic nuclei may be responsible for the reionization of the universe. Confirmation of this scenario requires spectroscopic identification of faint quasars ($M_{1450}>-24$ mag) at $z \gtrsim6$, but only a very ... More

The Infrared Medium-deep Survey. IV. Low Eddington Ratio of A Faint Quasar at $z\sim6$: Not Every Supermassive Black Hole is Growing Fast in the Early UniverseFeb 08 2018To date, most of the luminous quasars known at $z\sim6$ have been found to be in maximal accretion with the Eddington ratios, $\lambda_{\rm{Edd}}\sim1$, suggesting enhanced nuclear activities in the early universe. However, this may not be the whole picture ... More

The Infrared Medium-Deep Survey II: How to Trigger Radio-AGN? Hints from Their EnvironmentsOct 15 2014Oct 20 2014Activity at the centers of galaxies, during which the central supermassive black hole is accreting material, is nowadays accepted to be rather ubiquitous and most probably a phase of every galaxy's evolution. It has been suggested that galactic mergers ... More

Variability at the Edge: Optical Near/IR Rapid Cadence Monitoring of Newly Outbursting FU Orionis Object HBC 722Dec 11 2012We present the detection of day-timescale periodic variability in the r-band lightcurve of newly outbursting FU Orionis-type object HBC 722, taken from > 42 nights of observation with the CQUEAN instrument on the McDonald Observatory 2.1m telescope. The ... More

Phase transition of quantum corrected Schwarzschild black holeJul 23 2012Nov 07 2012We study the thermodynamic phase transition of a quantum-corrected Schwarzschild black hole. The modified metric affects the critical temperature which is slightly less than the conventional one. The space without black holes is not the hot flat space ... More

Unavoidable Subtournaments in Tournaments with Large Chromatic NumberApr 13 2018For a set H of tournaments, we say H is heroic if every tournament, not containing any member of H as a subtournament, has bounded chromatic number. Berger et al. explicitly characterized all heroic sets containing one tournament. Motivated by this result, ... More

Sequential Learning of Visual Tracking and Mapping Using Unsupervised Deep Neural NetworksFeb 26 2019We proposed an end-to-end deep learning-based simultaneous localization and mapping (SLAM) system following conventional visual odometry (VO) pipelines. The proposed method completes the SLAM framework by including tracking, mapping, and sequential optimization ... More

Simplicial volume of Q-rank one locally symmetric manifolds covered by the product of R-rank one symmetric spacesApr 24 2011Jan 10 2012In this paper, we show that the simplicial volume of Q-rank one locally symmetric spaces covered by the product of R-rank one symmetric spaces is strictly positive.

Moduli Spaces of Standard Holomorphic Bundles on a Noncommutative Complex TorusDec 11 2003In this paper we study the moduli space of standard holomorphic structures on a noncommutative complex two torus. It will be shown that the moduli space is naturally identified with the moduli space of stable bundles on an elliptic curve. We also propose ... More

Primitive stable representations in higher rank semisimple Lie groupsApr 30 2015Jan 10 2019We study primitive stable representations of free groups into higher rank semisimple Lie groups and their properties. Let $\Sigma$ be a compact, connected, orientable surface (possibly with boundary) of negative Euler characteristic. We first verify the ... More

Comments on the symmetry of AdS$_6$ solutions in String/M-theory and Killing spinor equationsApr 27 2016Aug 22 2016It was recently pointed out in \cite{Kim:2015hya} that AdS$_6$ solutions in IIB theory enjoy an extended symmetry structure and the consistent truncation to $D=4$ internal space leads to a nonlinear sigma model with target $SL(3,\mathbb{R})/SO(2,1)$. ... More

A Y-band look of the sky with 1-m class telescopesFeb 23 2012Y -band is a broad passband that is centered at ~ 1 micron. It is becoming a new, popular window for extragalactic study especially for observation of red objects thanks to recent CCD technology developments. In order to better understand the general ... More

$J^+$-like invariants of periodic orbits of the second kind in the restricted three body problemAug 28 2017Sep 05 2018We determine three invariants: Arnold's $J^+$-invariant as well as $\mathcal{J}_1$ and $\mathcal{J}_2$ invariants, which were introduced by Cieliebak-Frauenfelder-van Koert, of periodic orbits of the second kind near the heavier primary in the restricted ... More

Direct calculation of the strong Goos-Hänchen effect of a Gaussian light beam due to the excitation of surface plasmon polaritons in the Otto configurationJan 12 2019We study theoretically the influence of the surface plasmon excitation on the Goos-H\"{a}nchen lateral shift of a $p$-polarized Gaussian beam incident obliquely on a dielectric-metal bilayer in the Otto configuration. We find that the lateral shift depends ... More

Geometrical Interpretation of Electromagnetism in a 5-Dimensional ManifoldJul 12 2015Aug 13 2017In this paper, Kaluza-Klein theory is revisited and its implications are elaborated. We show that electromagnetic 4-potential can be considered as a shearing-like deformation of a 5-dimensional (5D) manifold along the fifth (5th) axis. The charge-to-mass ... More

Volume invariant and maximal representations of discrete subgroups of Lie groupsMay 22 2012Sep 21 2012Let $\Gamma$ be a lattice in a connected semisimple Lie group $G$ with trivial center and no compact factors. We introduce a volume invariant for representations of $\Gamma$ into $G$, which generalizes the volume invariant for representations of uniform ... More

Application of Support Vector Machine to detect an association between a disease or trait and multiple SNP variationsApr 17 2001May 22 2001After the completion of human genome sequence was anounced, it is evident that interpretation of DNA sequences is an immediate task to work on. For understanding their signals, improvement of present sequence analysis tools and developing new ones become ... More

Mirror duality and noncommutative toriOct 06 2007In this paper, we study a mirror duality on a generalized complex torus and a noncommutative complex torus. First, we derive a symplectic version of Riemann condition using mirror duality on ordinary complex tori. Based on this we will find a mirror correspondence ... More

Black holes with baryonic charge and $\mathcal{I}$-extremizationApr 10 2019We study $\mathcal{I}$-extremization of three-dimensional gauge field theories and its geometric dual, focusing in particular on a seven-dimensional Sasaki-Einstein manifold $M^{1,1,1}$. We generalize recent studies on relations among toric geometry, ... More

An lp-boundedness of stochastic singular integral operators and its application to spdesAug 31 2016Jun 08 2017In this article we introduce a stochastic counterpart of the H\"ormander condtion on the kernel $K(r,t,x,y)$: there exists a pseudo-metric $\rho$ on $(0,\infty)\times R^d$ and a positive constant $C_0$ such that for $X=(t,x), Y=(s,y), Z=(r,z) \in (0,\infty) ... More

Parabolic Littlewood-Paley inequality for $φ(-Δ)$-type operators and applications to Stochastic integro-differential equationsFeb 20 2013In this paper we prove a parabolic version of the Littlewood-Paley inequality for the operators of the type $\phi(-\Delta)$, where $\phi$ is a Bernstein function. As an application, we construct an $L_p$-theory for the stochastic integro-differential ... More

Memorization Precedes Generation: Learning Unsupervised GANs with Memory NetworksMar 05 2018Mar 10 2018We propose an approach to address two issues that commonly occur during training of unsupervised GANs. First, since GANs use only a continuous latent distribution to embed multiple classes or clusters of data, they often do not correctly handle the structural ... More

Abstractive Summarization of Reddit Posts with Multi-level Memory NetworksNov 02 2018We address the problem of abstractive summarization in two directions: proposing a novel dataset and a new model. First, we collect Reddit TIFU dataset, consisting of 120K posts from the online discussion forum Reddit. We use such informal crowd-generated ... More

1/4-BPS M-theory bubbles with SO(3) x SO(4) symmetryJun 14 2007Jul 06 2007In this paper we generalize the work of Lin, Lunin and Maldacena on the classification of 1/2-BPS M-theory solutions to a specific class of 1/4-BPS configurations. We are interested in the solutions of 11 dimensional supergravity with $SO(3)\times SO(4)$ ... More

On the largest integer that is not a sum of distinct nth powers of positive integersOct 07 2016Oct 12 2016It is known that for an arbitrary positive integer n the sequence S(x^n)=(1^n, 2^n, ...) is complete, meaning that every sufficiently large integer is a sum of distinct nth powers of positive integers. We prove that the upper bound of an integer that ... More

Quantum cohomology of flag manifolds G/B and quantum Toda latticesJul 02 1996Jan 01 1999We prove the Givental conjecture that the (equivariant) quantum cohomology of flag manifolds G/B are governed by the conservation law of Toda lattices. In addition, we find the quantum differential module structure of the flag manifolds.

A critical look at V_us determinations from hadronic tau decay dataNov 29 2010Jan 07 2011A critical review of hadronic tau decay data based determinations of |V_{us}| is given, focussing on the impact of the slow convergence of the integrated D=2 OPE series for the conventional flavor-breaking sum rule determination and the potential role ... More

A-type Supergiant Abundances in the SMC: Probes of EvolutionJan 21 1999New abundances of N, O, Na, Mg, Si, Ca, Sc, Ti, Cr, Fe, Sr, Zr, and Ba are presented for 10 A-type supergiants in the SMC, plus upper limits for C. In interpreting the CNO results for constraints on stellar evolution theories, careful attention has been ... More

Solitons of the Self-dual Chern-Simons Theory on a CylinderMay 30 2001We study the self-dual Chern-Simons Higgs theory on an asymptotically flat cylinder. A topological multivortex solution is constructed and the fast decaying property of solutions is proved

Ulrich bundles on blowupsJul 11 2016We construct an Ulrich bundle on the blowup at a point when the original variety is embedded by a sufficiently positive linear system and carries an Ulrich bundle. In particular, we describe the relation between special Ulrich bundles on the blown-up ... More

Langlands-Shahidi $L$-functions for $GSpin$ groups and the generic Arthur packet conjectureJul 26 2015Dec 09 2015We prove that $L$-functions from Langlands-Shahidi method in the case of $GSpin$ groups over a non-Archimedean local field of characteristic zero are Artin $L$-functions through the local Langlands correspondence. It has an application on the proof of ... More

Scaling Behaviour of Quiver Quantum MechanicsMar 09 2015Sep 28 2015We explore vacuum degeneracy of Kronecker quiver with large ranks, by computing Witten index of corresponding 1d gauged linear sigma model. For $(d-1,d)_k$ quivers with the intersection number $k$, we actually counted index of its mutation equivalent, ... More

Towards Predictable Real-Time Performance on Multi-Core PlatformsJul 28 2016Cyber-physical systems (CPS) integrate sensing, computing, communication and actuation capabilities to monitor and control operations in the physical environment. A key requirement of such systems is the need to provide predictable real-time performance: ... More

Distributed agent-based automated theorem proving in order-sorted first-order logicSep 08 2016This paper presents a distributed agent-based automated theorem proving framework based on order-sorted first-order logic. Each agent in our framework has its own knowledge base, communicating to its neighboring agent(s) using message-passing algorithms. ... More

The group $G_{n}^{2}$ with a parity and with pointsApr 30 2016In~\cite{Ma} Manturov studied groups $G_{n}^{k}$ for fixed integers $n$ and $k$ such that $k<n$. In particular, $G_{n}^{2}$ is isomorphic to the group of free braids of $n$-stands. In~\cite{KiMa} Manturov and the author studied an invariant valued in ... More

On the recurrence formula of the Euler zeta functionsDec 23 2015In this paper, we find a new recurrence formula fo the Euler zeta functions.

A Nonconvex Unconstrained Method for Eigenvalue Problems and A Nonsingular System for Eigenvector EstimationNov 28 2016We propose a nonconvex unconstrained minimization problem for eigenvalue problems. In this framework, given a symmetric matrix $A$, it turns out that any nonzero critical point is an eigenvector of $A$ and any local minimizer is a global minimizer, an ... More

Seesaw Scale and CP Phases in a Minimal Model of LeptogenesisNov 14 2016The seesaw mechanism to derive the light masses of left-handed neutrinos using heavy masses of right-handed neutrinos gives rise to a connection between low-energy measurables and GUT-scale mechanism. We expresses the neutrino mixing angles in terms of ... More

The Particle- and Astro-Physics of Dark MatterNov 09 1994We review some recent determinations of the amount of dark matter on galactic, cluster, and large scales, noting some puzzles and their possible resolutions. We discuss the interpretation of big bang nucleosynthesis for dark matter, and then review the ... More

On a quadratic Waring's problem with congruence conditionsJan 16 2019Jan 17 2019We say a quadratic polynomial is represented by a sum of $r$ odd squares if it is represented by $\Delta_r(y_1,...,y_r)=\sum_{i=1}^r (y_i+\frac{1}{2})^2$. For each positive integer $n$, let $g_\Delta(n)$ be the smallest positive integer $g$ such that ... More

Galois deformation theory for norm fields and flat deformation ringsMay 18 2010Let $K$ be a finite extension of $\mathbb{Q}_p$, and choose a uniformizer $\pi\in K$, and put $K_\infty:=K(\sqrt[p^\infty]{\pi})$. We introduce a new technique using restriction to $\Gal(\ol K/K_\infty)$ to study flat deformation rings. We show the existence ... More

Origin of Hawking Radiation: Firewall or Atmosphere?Apr 02 2016Apr 14 2016The Unruh vacuum not admitting any outgoing flux at the horizon implies that the origin of the outgoing Hawking radiation would be the atmosphere of a near-horizon quantum region without resort to the firewall; however, the existence of the firewall of ... More

Character design for soccer commmentaryJul 31 1998In this paper we present early work on an animated talking head commentary system called {\bf Byrne}\footnote{David Byrne is the lead singer of the Talking Heads.}. The goal of this project is to develop a system which can take the output from the RoboCup ... More

Group-theoretical vector space modelSep 20 2015This paper presents a group-theoretical vector space model (VSM) that extends the VSM with a group action on a vector space of the VSM. We use group and its representation theory to represent a dynamic transformation of information objects, in which each ... More

Origin of Hawking Radiation: Firewall or Atmosphere?Apr 02 2016Jan 16 2017The Unruh vacuum not admitting any outgoing flux at the horizon implies that the origin of the outgoing Hawking radiation is the atmosphere of a near-horizon quantum region without resort to the firewall; however, the existence of the firewall of superplanckian ... More

The Causal Effect of Answer Changing on Multiple-Choice ItemsAug 31 2018Mar 12 2019Whether examinees' answer changing behavior on multiple-choice exams is beneficial or harmful is a long-standing puzzle in the educational and psychological measurement literature. This article unravels the problem by formalizing it using the potential ... More

Rapoport-Zink spaces of Hodge typeAug 26 2013Jan 29 2018When $p>2$, we construct a Hodge-type analogue of Rapoport-Zink spaces under the unramifiedness assumption, as formal schemes parametrising "deformations" (up to quasi-isogeny) of $p$-divisible groups with certain crystalline Tate tensors. We also define ... More

Deep Neural Network Optimized to Resistive Memory with Nonlinear Current-Voltage CharacteristicsMar 30 2017Artificial Neural Network computation relies on intensive vector-matrix multiplications. Recently, the emerging nonvolatile memory (NVM) crossbar array showed a feasibility of implementing such operations with high energy efficiency, thus there are many ... More

On a p-adic interpolation function for the q-extension of the generalized Bernoulli polynomials and Its derivativeFeb 22 2005We construct the q-extension of the Hurwitz's type L-function which interpolates the q-extension of generalized Bernoulli polynomials attached to $chi$.

Deformation space of a non-uniform 3-dimensional real hyperbolic lattice in quaternionic hyperbolic planeFeb 29 2012In this note, we study deformations of a non-uniform real hyperbolic lattice in quaternionic hyperbolic spaces. Specially we show that the representations of the fundamental group of the figure eight knot complement into PU(2,1) cannot be deformed in ... More

Separated Rows structure of vortex streets behind triangular objectsJun 30 2018Aug 09 2018We discuss two distinct spatial structures of vortex streets. The `conventional mushroom' structure is commonly discuss in many experimental studies, but the exotic `separated rows' structure is characterized by a thin irrotational fluid between two rows ... More

An $L_p$-Lipschitz theory for parabolic equations with time measurable pseudo-differential operatorsJul 15 2017In this article we prove the existence and uniqueness of a (weak) solution $u$ in $L_p\left((0,T) , \Lambda_{\gamma+m}\right)$ to the Cauchy problem \begin{align} \notag &\frac{\partial u}{\partial t}(t,x)=\psi(t,i\nabla)u(t,x)+f(t,x),\quad (t,x) \in ... More

Welfare Maximization with Deferred Acceptance Auctions in Reallocation ProblemsJul 06 2015Sep 20 2015We design approximate weakly group strategy-proof mechanisms for resource reallocation problems using Milgrom and Segal's deferred acceptance auction framework: the radio spectrum and network bandwidth reallocation problems in the procurement auction ... More

Handlebody-preserving finite group actions on Haken manifolds with Heegaard genus two - IIFeb 07 2009May 25 2009Let $M$ be a closed orientable 3-manifold with a genus two Heegaard splitting $(V_1, V_2; F)$ and a non-trivial JSJ-decomposition, where all components of the intersection of the JSJ-tori and $V_i$ are not $\partial$-parallel in $V_i$ for $i=1,2$. If ... More

A note on the p-adic log-gamma functionsOct 26 2007In this paper we prove that q-Euler numbers are occured in the coefficients of some stirling type seies for p-adic analytic q-log gamma function

q-Bernoulli numbers and Stirling numbers(2)Oct 26 2007In this paper we study q-Bernoulli numbers and polynomials related to q-Stirling numbers. From thsese studying we investigate some interesting q-stirling numbers' identities related to q-Bernoulli numbers.

The Modified q-Euler numbers and polynomialsFeb 18 2007In the recent paper the interesting q-Euler numbers and polynomials introduced in JMAA. The purpose of this paper is to construct the modified q-Euler numbers and polynomiasl. Finally we will give the interesting many identities related to these numbers ... More

A note on q-Volkenborn integrationJun 01 2005In this paper, we construct the new $q$-analogue of the ordinary Euler numbers and polynomials by using the $q$-Volkenborn integrals.

A note on multiple Dirichlet's q-L--functionJun 09 2005Recently, the two variable $q$-$L$-functions which interpolate the generalized $q$-Bernoulli polynomials associated with $\chi$ are introduced and studied, cf. [2]. In this paper, we construct multiple Dirichlet's $q$-$L$-function which interpolates the ... More

Sums of powers of consecutive q-integersJan 29 2005We give the q-analogue of the sums of the n-th powers of positive integers up to k-1.

Link diagrams with low Turaev genusJul 10 2015Nov 30 2015We classify link diagrams with Turaev genus one and two in terms of an alternating tangle structure of the link diagram. The proof involves surgery along simple closed curves on the Turaev surface, called cutting loops, which have corresponding cutting ... More

p-adic L-functions and Selmer varieties associated to elliptic curves with complex multiplicationOct 28 2007We show how non-vanishing of p-adic L functions controls the dimensions of Selmer varieties associated to the complement of the origin in an elliptic curve with CM. As a corollary, one obtains a \pi_1-proof of the theorem of Siegel for such curves.

Minimal volume of complete uniform visibility manifolds with finite volumeApr 10 2012We show that complete uniform visibility manifolds of finite volume with sectional curvature $-1 \leq K \leq 0$ have positive simplicial volumes. This implies that their minimal volumes are non-zero.

$q$-Volkenborn Integration and Its ApplicationsOct 25 2005The main purpose of this paper is to present a systemic study of some families of multiple $q$-Euler numbers and polynomials. In particular, by using the $q$-Volkenborn integration on $\Bbb Z_p$, we construct $p$-adic $q$-Euler numbers and polynomials ... More

A study on the q-Euler numbers and the fermionic q-integrals of the product of several type $q$-Bernstein polynomials on ZpOct 19 2010In this paper, we investigate some interesting properties of q-Berstein polynomials realted to q-Euler numbers by using the fermionic q-integral on Zp.

Some identities of symmetry for the generalized Bernoulli numbers and polynomialsMar 17 2009In this paper, by the properties of p-adic invariant integral on Zp, we establish various identities concerning the generalized Bernoulli numbers and polynomials. From the symmetric properties of p-adic invariant integral on Zp, we give some interesting ... More

On the weighted q-Bernoulli numbers and polynomialsNov 24 2010In this paper we consider the weighted q-Bernoulli numbers and polynomials which are differnt type of Carlitz's q-Bernoulli numbers and polynomials. From these numbers and polynomials, we derive some interesting formulaes and identities.

Motivic L-FunctionsOct 27 2007This is the text of an introductory lecture delivered at the IHES summer school on motives in July, 2006.

Euler number and polynomials of higher orderJan 11 2010In this paper we study the higher-order Euler numbers and polynomials and we introduce the mutiple zeta functions which interpolate higher-order Euler polynomials and numbers at negative integers

q-Euler numbers and polynomials associated with multiple q-zeta functionsDec 24 2009The purpose this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials and we construct multiple q-zeta function which interpolates multiple q-Euler numbers at negative integers.

The fermionic p-adic integrals on Zp associated with extended q-Euler numbers and polynomialsJan 14 2009The purpose of this paper is to present a systemic study of some families of q-Euler numbers and polynomials of Norlund's type by using multivariate fermionic p-adic integral on Zp. Moreover, the study of these higher-order q-Euler numbers and polynomials ... More

Langlands-Shahidi $L$-functions for $GSpin$ groups and the generic Arthur packet conjectureJul 26 2015Dec 26 2017We prove that $L$-functions from Langlands-Shahidi method in the case of $GSpin$ groups over a non-Archimedean local field of characteristic zero are Artin $L$-functions through the local Langlands correspondence. It has an application on the proof of ... More

Comments on $AdS_2$ solutions from M2-branes on complex curves and the backreacted Kähler geometryNov 28 2013Jan 31 2014We consider $AdS_2$ solutions of M-theory which are obtained by twisted compactifications of M2-branes on a complex curve. They are of a generalized class, in the sense that the non-abelian part of the connection for the holomorphic bundle over the supersymmetric ... More

Rigidity of noncompact complete manifolds with harmonic curvatureNov 13 2009Nov 25 2009Let $(M,g)$ be a noncompact complete $n$-manifold with harmonic curvature and positive Sobolev constant. Assume that $L_2$ norms of Weyl curvature and traceless Ricci curvature are finite. We prove that $(M,g)$ is Einstein if $n \ge 5$ and $L_{n/2}$ norms ... More

Normal all pseudo-Anosov subgroups of mapping class groupsJun 20 1999Oct 14 2000We construct the first known examples of nontrivial, normal, all pseudo-Anosov subgroups of mapping class groups of surfaces. Specifically, we construct such subgroups for the closed genus two surface and for the sphere with five or more punctures. Using ... More

An alternating labeling on a spanning tree of Seifert graphs and applications in knot theoryAug 06 2011Feb 07 2014The existence of basket, flat plumbing and flat plumbing basket surfaces of a link was first proven from a braid representative of the link. In the present article, we show the existence of such surfaces from an induced graph of the link. Consequently, ... More

On a quadratic Waring's problem with congruence conditionsJan 16 2019Feb 12 2019For each positive integer $n$, let $g_\Delta(n)$ be the smallest positive integer $g$ such that every complete quadratic polynomial in $n$ variables which can be represented by a sum of odd squares is represented by a sum of at most $g$ odd squares. In ... More

The nullcone in the multi-vector representation of the symplectic group and related combinatoricsApr 25 2009Mar 18 2010We study the nullcone in the multi-vector representation of the symplectic group with respect to a joint action of the general linear group and the symplectic group. By extracting an algebra over a distributive lattice structure from the coordinate ring ... More

Hyperelliptic curves and Hitchin tangential coversAug 30 2011Oct 11 2011In \cite{kim11} we have generalized a tangency condition in the Treibich-Verdier theory \cite{trei89,tv90,trei97} about elliptic solitons to a Hitchin system. As an application of this generalization, we will define, so-called, Hitchin hyperelliptic tangential ... More

A note on a system of cubic nonlinear Klein-Gordon equations in one space dimensionJul 24 2014Feb 15 2015We study the Cauchy problem for a system of cubic nonlinear Klein-Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and decays of the order $O(t^{-1/2})$ ... More

A note on decay rates of solutions to a system of cubic nonlinear Schrödinger equations in one space dimensionAug 27 2014We consider the initial value problem for a system of cubic nonlinear Schr\"odinger equations with different masses in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the small amplitude solution exists ... More

A splitting theorem for holomorphic Banach bundlesMay 14 2008This paper is motivated by Grothendieck's splitting theorem. In the 1960s, Gohberg generalized this to a class of Banach bundles. We consider a compact complex manifold $X$ and a holomorphic Banach bundle $E \to X$ that is a compact perturbation of a ... More

Diophantine geometry and non-abelian reciprocity laws IDec 25 2013May 15 2015We use non-abelian fundamental groups to define a sequence of higher reciprocity maps on the adelic points of a variety over a number field satisfying certain conditions in Galois cohomology. The non-abelian reciprocity law then states that the global ... More

Generalized Heegaard splittings and the disk complexJul 02 2016Oct 08 2016Let $M$ be an orientable, irreducible $3$-manifold and $(\mathcal{V},\mathcal{W};F)$ a weakly reducible, unstabilized Heegaard splitting of $M$ of genus at least three. In this article, we define an equivalent relation $\sim$ on the set of the generalized ... More

Algebraic Ranks of CAT(0) GroupsOct 05 2012Aug 16 2013We study the algebraic rank of various classes of $\mathrm{CAT}(0)$ groups. They include right-angled Coxeter groups, right-angled Artin groups, relatively hyperbolic groups and groups acting geometrically on $\mathrm{CAT}(0)$ spaces with isolated flats. ... More

On critical Heegaard splittings of tunnel number two composite knot exteriorsOct 11 2012Oct 15 2012In this article, we prove that a tunnel number two knot induces a critical Heegaard splitting in its exterior if there are two weak reducing pairs such that each weak reducing pair contains the cocore disk of each tunnel. Moreover, we prove that a connected ... More

Two-sided estimates for the transition densities of symmetric Markov processes dominated by stable-like processes in $C^{1,η}$ open setsFeb 19 2014In this paper, we study sharp Dirichlet heat kernel estimates for a large class of symmetric Markov processes in $C^{1,\eta}$ open sets. The processes are symmetric pure jump Markov processes with jumping intensity $\kappa(x,y) \psi_1 (|x-y|)^{-1} |x-y|^{-d-\alpha}$, ... More

Poly-Cauchy numbers and polynomials with umbral calculus viewpointJul 19 2013In this paper, we give some interesting identities of poly-Cauchy numbers and polynomials arising from umbral calculus.