Abstract:
This is a summary of the talks I gave at Korean Physical Society meeting (April 26, 2012, Daejeon, Korea) and the 4th Asian Triangle Heavy Ion Conference (ATHIC) (November 14, 2012, Pusan, Korea). They are based on the series of work done at Hanyang University in the World Class University III Program under the theme of "From Dense Matter to Compact Stars." The program was conceived and executed to understand highly compressed baryonic matter in anticipation of the forthcoming RIB machine "RAON" which is in construction in the Institute for Basic Science (IBS) in Korea. The problems treated ranged from the origin of the proton mass, topological structure of barynic matter, chiral symmetry and conformal symmetry to the EoS of nuclear matter and dense neutron-rich matter and to the maximum mass of neutron stars. The results obtained are new and intriguing and could have an impact on the novel structure of dense matter to be probed in the accelerators "RAON," FAIR etc. and in compact stars.

Abstract:
The emergence and importance of hidden local symmetry in the structure of hadrons under extreme conditions is discussed. The topics covered are the potentially important role played by an infinite tower of vector mesons encoded in holographic dual QCD (or AdS/QCD) in chiral dynamics of mesons and baryons, in the vector dominance and its violation in EW response functions and the presence of the vector manifestation fixed point and its influence on the properties of hadrons in hot temperature (i.e., in relativistic heavy ion collisions) and in dense matter (i.e., in compact stars). Also discussed are the natural emergence of instantons/skyrmions from the infinite tower of vector mesons coupled to pions in AdS/QCD and their (speculated) role in chiral restoration at high density.

Abstract:
The infinite tower of vector mesons encoded in holographic dual QCD bring drastic changes to the soliton structure of the nucleon. The nucleon is given by a point-like instanton in 5D surrounded by a vector meson cloud with the vector dominance restored by the infinite tower. I discuss the possible relevance of this structure in hot and dense hadronic matter.

Abstract:
I discuss in this lecture how to make a connection between effective chiral Lagrangians -- low-energy effective theory of QCD -- and Landau Fermi liquid theory extended by Migdal to nuclear matter. The practical purpose of such a connection is to provide a link between certain observables in relativistic heavy-ion processes and those in low-energy spectroscopy, giving a new insight into how chiral dynamics manifests itself in nuclear systems.

Abstract:
The changes of hadron properties in dense and/or hot matter are discussed in terms of effective chiral Lagrangians with the parameters of the theory scaled in a simple way. The phenomenologically successful Walecka model is identified as a mean field chiral Lagrangian with the scaled parameters. Kaon condensation and chiral restoration transitions can be described within the same mean field framework.

Abstract:
I describe a novel phase structure of cold dense baryonic matter predicted in a hidden local symmetry approach anchored on gauge theory and in a holographic dual approach based on the Sakai-Sugimoto model of string theory. This new phase is populated with baryons with half-instanton quantum number in the gravity sector which is dual to half-skyrmion in gauge sector in which chiral symmetry is restored while light-quark hadrons are in the color-confined phase. It is suggested that such a phase that aries at a density above that of normal nuclear matter and below or at the chiral restoration point can have a drastic influence on the properties of hadrons at high density, in particular on short-distance interactions between nucleons, e.g., multi-body forces at short distance and hadrons -- in particular kaons -- propagating in a dense medium. Potentially important consequences on the structure of compact stars will be predicted.

Abstract:
Based on BHHRS and further sharpened by discussions with Gerry Brown that I had in October 2008, we arrive at the present assessment of the dilepton saga, namely, that dileptons become "blind" to changes in the vacuum structure of chiral symmetry (such as, e.g., BR scaling at high temperature and/or at high density and hence are {\em not} an appropriate probe for a signal for partial or complete chiral restoration, contrary to what has been widely believed. There, however, are a variety of indirect indications that the scaling notion is qualitatively, if not quantitatively, valid and should work in various low-energy nuclear phenomena, and it is fair to conclude that while there is no direct evidence for the scaling notion, there is {\em none against} it either, in a strong disagreement with what was claimed in CERN Courier November 2009. I will touch briefly on certain observables that could give a clear-cut litmus signal for the vacuum structure of chiral symmetry modified by temperature and/or density.

Abstract:
Hadron structure and nuclear structure are discussed from the common ground of effective chiral Lagrangians modeling QCD at low energy. The topics treated are the chiral bag model in large $N_c$ QCD, its connection to heavy-baryon chiral perturbation theory (HB\chpt),\ the role of nonabelian Berry gauge connections for baryon excitations and the application of HB\chpt \ to the thermal $n+p\rightarrow d +\gamma$ process and to the axial-charge transitions in heavy nuclei.

Abstract:
I discuss recent work done with Gerry Brown on chiral phase transition at high temperature and/or density described in terms of Georgi's vector limit. The notion of ``mended symmetry" is suggested to play an important role in understanding the properties of hadrons in dense and/or hot matter before reaching the phase transition. It is shown that while the QCD vacuum in baryon-free space is resistant to ``melting" up to the critical temperature, baryon-rich medium can induce the vacuum to become softer in temperature: the hadron masses drop faster in temperature when baryon matter is present.

Abstract:
The role of chiral symmetry in nuclear physics is summarized. The topics treated are the chiral bag model for nucleon structure resulting from large $N_c$ QCD, the pion cloud in chiral perturbation theory for low-energy electroweak nuclear response functions, ``swelled hadrons" in nuclear matter, chiral symmetry restoration in terms of the Georgi vector limit and pseudo-Goldstone meson condensation in nuclear medium.