Colloquium

Despite intensive theoretical research for several decades, the theory of quantum gravity remains elusive. I will review the obstacles that prevent from reconciling the principles of general relativity with those of quantum mechanics. It is plausible that an eventual ultraviolet completion of general relativity will require sacrificing some of these principles. I will then focus on the class of theories where the abandoned property is local Lorentz invariance, replaced by an approximate anisotropic scaling symmetry in deep ultraviolet. At low energies these theories reduce to a special type of scalar — tensor gravity. I will show that this approach allows us to construct renormalizable gravitational theories in any number of spacetime dimensions. The study of a (2+1) dimensional model reveals its asymptotic freedom and suggests that this property may be generic for gravity with anisotropic scaling. Relevance of these results for gravity in the real world will be discussed.

Hidden sector particles, with masses and couplings below those of the weak interactions, can resolve many of the outstanding questions of the Standard Model, including the identity of dark matter, the origin of the baryon asymmetry, and the physics of neutrino masses. Existing searches at colliders such as the Large Hadron Collider are, however, often insensitive to signals of hidden sectors. Using the well-motivated example of low-scale leptogenesis and neutrino masses, I will demonstrate connections between the cosmology of hidden sectors and their signatures in experiments. I will then present new experimental ideas for how to uncover the existence of hidden sectors at the LHC, as well as my role in founding and leading a joint theory-experiment initiative working to greatly expand sensitivity to long-lived particles  Finally, I will discuss my theoretical and experimental work on low-energy colliders such as B factories, which have an immense and under-utilized potential for discovering hidden particles. Given the many connections between colliders, astrophysics, cosmology, and other terrestrial experiments emerging from the study of hidden sectors, the future is bright for expanding our knowledge of the hidden universe.

Current progress in quantum field theory is largely driven by the conformal bootstrap program, which aims to classify the space and properties of conformal field theories using symmetries and other fundamental constraints. In the context of the AdS/CFT Correspondence, this increasingly sophisticated endeavor doubles as a probe of foundations of quantum gravity. I will describe the current era in the holographic application of conformal field theory methods, with particular focus on the use of the conformal bootstrap to describe the spectrum and dynamics of quantum gravity and string theory beyond the classical regime.

3d quantum gravity is a beautiful toy-model for 4d quantum gravity: it is much simpler, it does not have local degrees of freedom, yet retains enough complexity and subtlety to provide a non-trivial example of dynamical quantum geometry and open new directions of research in physics and mathematics. I will present the Ponzano-Regge model, introduced in 1968, built from tetrahedra “quantized" as 6j-symbols from the theory of recoupling of spins. I will show how it provides a discrete path integral for 3d quantum gravity, related to topological invariants and loop quantum gravity and other approaches to quantum gravity. It is also a perfect arena to investigate boundary theories and holographic dualities, with a beautiful duality with the 2d Ising model realized through a supersymmetry, and more.

Strong gravitational lenses with measured time delays between the multiple images can be used to determine the Hubble-Lemaitre constant (H0) that sets the expansion rate of the Universe. An independent determination of H0 is important to ascertain the possible need of new physics beyond the standard cosmological model, given the tension in current H0 measurements. A program initiated to measure H0 to <3.5% in precision from strongly lensed quasars is in progress, and I will present the latest results and their implications. Search is underway to find new lenses in imaging surveys. An exciting discovery of the first strongly lensed supernova offered a rare opportunity to perform a true blind test of our modeling techniques. I will outline a new research program on lensed supernovae, showing their bright prospects as a competitive and unique probe of cosmology and stellar physics.

The discovery of a Higgs like boson at LHC in 2012 was a development of fundamental importance in particle physics. With this newly discovered state included in theoretical predictions of scattering events,  the Standard Model can be extrapolated  to much higher experimental energies. This implies that a degree of scale separation will be present between the discovered particles of the Standard Model, and any new particles required to address the outstanding mysteries that the Standard Model leaves unanswered. As a result, interest in treating the Standard Model as a consistent Effective Field Theory (the SMEFT) has dramatically increased. This powerful theory is the state of the art in studying experimental results model independently, up to energies that LHC probes in a robust fashion experimentally. Rather remarkably, as interest in this theory has increased in recent years, a number of subtleties has also been discovered in the physics of the SMEFT.  In this talk, I will review this rapidly advancing area.

Applications of physics to geometry have deep historical roots going back at least to Archimedes, while recent decades have seen structures of classical and quantum gauge theory lead to enormous advances in the theory of three and four manifolds. Meanwhile, geometry provides conceptual tools for physics as foundational  as variational principles, the kinematics of spacetime, and the topological  classification of matter. This talk will describe some possibilities for bringing number theory, more specifically, *arithmetic geometry* into this interaction. After giving some examples of the suggestive interplay of  number theory and physics, I will speculate somewhat on how ideas of quantum field theory may elucidate some of the deepest and hardest problems of number theory, especially the effective Mordell conjecture and the Hasse-Weil conjecture.

Many of the rich interactions between mathematics and physics arise using general mathematical frameworks that describe a host of physical phenomena: from differential equations, to algebra, to topology and geometry. On the other hand, mathematics also possesses many examples of "exceptional objects": they constitute the finite set of leftovers that appear in numerous classification problems. For example, groups of symmetries in three dimensions appear in two infinite families (cyclic groups and dihedral groups of n-sided polygons) and the symmetry groups of the five Platonic solids--- the 'exceptional' structures. 

The mathematical subject of moonshine refers to surprising relationships between other kinds of special/exceptional objects that arise from the theory of finite groups and from number theory. Increasingly, string theory has been a source of insights in and explanations for moonshine. It is even the source of new examples of moonshine that further implicate special objects in geometry. We will review moonshine, survey these developments, and highlight some of the (many!) exciting mysteries that remain.

The cosmic microwave background radiation has been an indispensable tool for learning about the origins and evolution of our Observable Universe. Satellites and ground based experiments measuring the temperature and polarization anisotropies with ever increasing angular resolution and sensitivity have established the standard cosmological model, LCDM, and constrained or ruled out a huge variety of theoretical models of the early Universe. Most of this cosmological information has thus far been derived from the primary CMB, anisotropies largely sourced during the epoch of recombination some 380,000 years after the Big Bang. However, experiments are achieving the sensitivity and resolution necessary to access a whole new treasure-trove of cosmological information: secondary temperature and polarization anisotropies induced by photons scattering from mass (CMB lensing) and free electrons (the Sunyaev Zel'dovich effect). Unlike the primary CMB, where cosmological information is contained in the pattern of fluctuations in statistically isotropic temperature/polarization anisotropies, the secondary CMB encodes cosmological information in the statistical anisotropies of non-gaussian temperature/polarization fields on the sky. In this talk, I will describe the possibilities for future CMB experiments, in concert with large galaxy surveys, to reconstruct the cosmological information contained in the statistics of the secondary CMB anisotropies. In particular, I will describe the information that can be reconstructed from kinetic/polarized Sunyaev Zel'dovich effect, CMB lensing, and the moving lens effect. I speculate on what we might learn from future measurements, and conclude by discussing several projects in progress.

Sexual harassment and sexual assault in the workplace is almost always a severe betrayal of trust.  I will describe research and theory that my students and I have developed over the last 25 years regarding interpersonal and institutional betrayals of trust.  My presentation will include an explanation of betrayal trauma theory and information about institutional betrayal.   I will present data from some of our research studies, including results from a study of sexual harassment of graduate students.   Included will be research-based recommendations for how to respond well to disclosures of harassment and sexual violence as well as steps individuals and institutions can take to constructively address sexual violence and promote institutional courage.  

Jennifer J. Freyd, PhD, is a Fellow at the Center for Advanced Study in the Behavioral Sciences at Stanford University and a Professor of Psychology at the University of Oregon.

From earliest infancy, we live in and learn to function in a world of causes and effects. Yet science has had an ambivalent, even hostile attitude toward causation for more than a century. Statistics courses teach us that “correlation is not causation,” yet they are strangely silent about what is causation.

A central reason for this silence is that causation does not reside in data alone, but in the process that generates the data. In order to answer causal questions, like “What would happen if we lowered the price of toothpaste?” or “Should I brake for this object?” we need a model of causes and effects. Judea Pearl has developed a simple calculus for expressing our cause-effect knowledge in a diagram and using that diagram to tell us how to interpret the data we gather from the real world. His methods are already transforming the practice of statistics and could equip future artificial intelligences with causal reasoning abilities they currently lack.

This talk is largely based on Mackenzie’s book co-written with Pearl, The Book of Why.