Recently it has been reported that certain compounds under high pressure exhibit a conventional Migdal-Eliashberg-BCS type of superconductivity, with remarkably high critical temperatures for the superconducting transition. Practically this has kindled new interest in room-temperature superconductors; more fundamentally it has put renewed focus on the physics controlling the critical temperature for the superconducting transition. This presentation will argue that there are two principles governing the critical temperature in a given system: (1) The intrinsic strength of the pair-binding, and (2) the (potentially large) effect of the many-body environment on the efficiency of the transition. Understanding the interplay of these effects is crucial to charting a path to the highest-temperature superconductors. Most discussions take into account only the first principle, but this talk will argue that the essential properties of unconventional superconductors are governed more by the second. As illustration, I will demonstrate systematically that an SU(4) fermion dynamical symmetry accounts naturally for all the essential properties of cuprate high-temperature superconductors, and show that this SU(4) symmetry implies an intrinsic mechanism whereby its Mott-insulator, antiferromagnetic ground state at zero doping undergoes a spontaneous (quantum phase) transition upon infinitesimal doping to a singlet d-wave superconducting state, with almost no change in entropy. I will argue that this transition is the essential physics of the "high" in high-Tc for unconventional superconductors (and superfluids, in all fields of physics), with the type and strength of the pairing affecting only details.

Mike Guidry is the author of more than 200 journal publications and invited conference presentations, and 5 published textbooks. These address a range of topics in nuclear physics, computational science, advanced educational technology, programming mobil devices, astronomy, astrophysics, cosmology, general relativity, the mathematics of symmetry in physics, elementary particle physics, relativistic quantum field theory, and condensed matter physics. His published textbooks include:
1. Gauge Field Theories: An Introduction with Applications – Mike Guidry (Wiley Interscience, 1991)
2. Online Journey through Astronomy – Mike Guidry and Tina Riedinger (Brooks-Cole, Cengage, 2000)
3. Virtual Astronomy Laboratories – Mike Guidry and Kevin Lee (Brooks-Cole, Cengage, 2004)
4. Stars and Stellar Processes – Mike Guidry (Cambridge University Press, 2019)
5. Modern General Relativity: Black Holes, Gravitational Waves, and Cosmology – Mike Guidry (Cambridge University Press, 2019)
A sixth textbook, Symmetry and Broken Symmetry: Groups, Algebras, and Topologies in Modern Physics is currently in preparation for Cambridge University Press. He previously held the role of lead technology developer for several major college textbooks in introductory physics, astronomy, biology, genetics, and microbiology. He has won multiple teaching awards and is responsible for a variety of important science outreach initiatives. His current research centers on development of new algorithms for solving large coupled sets of differential equations in astrophysics and other scientific applications, developing new symmetry-based techniques for understanding high-temperature superconductors and other strongly-correlated electron systems, and development of new symmetry-based approaches to quantum Hall physics in graphene.