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In his May 5 Perimeter Public Lecture webcast, Harvard professor L. Mahadevan will take viewers on a journey into the mathematical, physical, and biological workings of morphogenesis to demonstrate how scientists are beginning to unlock many of the secrets that have vexed scientists since Darwin.

I will present a single idea about representation which allows several recent advances in neural networks  to be combined into an imaginary system called GLOM.  GLOM answers the question: How can a neural network with a fixed architecture parse an image into a part-whole hierarchy which has a different structure for each image? The idea is simply to use islands of identical vectors to represent the nodes in the parse tree. The talk will discuss the many ramifications of this idea.  If GLOM can be made to work, it should significantly improve the interpretability of the representations produced by neural nets when applied to vision or language.  

The remarkable properties of electrons moving through crystalline lattices continue to surprise us. Recently, electrons in artificial moiré lattices have emerged as an extraordinary new platform. The simplest such moiré material consists of a pair of graphene sheets twisted relative to one another. At a  "magic" angle of about 1 degree, a variety of phenomena, including strong-coupling superconductivity, is observed. In this talk, I will review this rapidly moving field and describe our theoretical ideas that invoke the geometry of quantum states and topological textures like skyrmions. Finally, I will explain how these insights indicate a promising new family of moiré materials, twisted trilayer graphene, which is currently under active experimental study.

Quantum computers need to manipulate quantum states, and the only ways we know of doing this are inherently noisy. Thus, if we are ever to be able to do long computations on quantum computers, we need to make them fault tolerant. The way we know how to do this currently is to use quantum error correcting codes. We will introduce error correcting codes and explain how they can be used to provide fault tolerance for quantum computers.
 

Indigenous wellness and higher education in Canada, through the creation of Indian Residential Schools, has a dark history and has left a legacy of intergenerational trauma for Indigenous peoples. Currently, the Truth and Reconciliation Commission’s Final Report (2015) provides  a timely context for systemic change that can improve the lives of Indigenous individuals and provide healing to Indigenous communities. This presentation addresses Indigenous academic strengths and challenges in Canada and provides practical implications of implementing decolonial change in higher education settings. Examples from Dr. Stewart’s community-based Indigenous ethics and educational research provide concrete illustrations of issues such as racism, oppression, cultural identity, tensions between Western and Indigenous worldviews, and the importance of traditional knowledges.

We will discuss the recent advances involving programmable, coherent manipulation of quantum many-body systems using atom arrays excited into Rydberg states. Specifically, we will describe our recent technical upgrades that now allow the control over 200 atoms in two-dimensional arrays. Recent results involving the realization  of exotic phases of matter, study of quantum phase transitions and  exploration of  their non-equilibrium dynamics will be presented. In particular, we will report on realization and probing of quantum spin liquid states - the exotic states of matter have thus far evaded direct experimental detection. Finally,  realization and testing  of quantum optimization algorithms using such systems will be discussed.

Statistical mechanics is the branch of physics that explains how macroscopic properties of matter emerge from the behavior of its microscopic constituents. Population ecology studies how and why populations change over time and space, primarily due to the interaction among individuals and between individuals and the environment where they thrive. Although seemingly very different, both disciplines aim to explain large-scale phenomena based on a description of their underlying drivers, and statistical mechanics tools have been largely used to formalize population ecology. For over 100 years, however, mathematical models in population ecology have relied on very strong and unrealistic assumptions about the way individuals move and get to interact with each other and with the environment. Specifically, they assume that individuals behave like the molecules of an ideal gas: following completely random trajectories through the entire area occupied by the population and only interacting with each other when their trajectories intersect. 

In this presentation, I will first discuss why mathematical models are powerful tools to understand ecological processes. Then, I will show how traditional models of population dynamics emerge from ideal gas assumptions for individual movement and briefly touch on our recent efforts to refine those models combining more elaborated tools from statistical physics, random walk theory, and GPS tracking data of natural populations.

In this lecture we will show that the E8 and Leech lattices minimize energy of every potential function that is a completely monotonic function of squared distance (for example, inverse power laws or Gaussians). This theorem implies recently proven optimality of E8 and Leech lattices as sphere packings and broadly generalizes it to long-range interactions. The key ingredient of the proof is sharp linear programming bounds. To construct the optimal auxiliary functions attaining these bounds, we prove a new interpolation theorem. This is the joint work with Henry Cohn, Abhinav Kumar, Stephen D. Miller, and Danylo Radchenko.

I describe recent progress on a program of research aimed at finding a simultaneous completion of quantum mechanics and general relativity, while also addressing the question of how the universe chose its effective laws out of a vast landscape of possible laws.    This is based on a few principles:   time in the sense of causation is fundamental, as are events, and the views  of events (their backward celestial spheres.) Further the view of every event must be distinct from that of every other.  This is enforced by a choice for potential energy that maximizes the diversity of views of events, called the variety.    Given these postulates, everything else emerges dynamically, including space, spacetime, and quantum dynamics; as the variety turns out to reduce appropriately to Bohm’s quantum potential, which in turn is responsible for quantum non-locality, entanglement etc.  

A consequence of these ideas is that the effective low energy laws, including the values of the dimensionless constants of the standard model,  should evolve dynamically.    I present three realizations of this idea: cosmological natural selection (1992), the principle of precedence (2005), and the hypothesis that the universe may learn how to choose its vacuum out of a landscape of possible vacua through a process formally analogous to machine learning (2021).   I discuss the prospects for observational tests of these ideas.

At the technical level,  some of these ideas are related through the use of matrix modes whose actions are cubic in the matrices, which are tied to topological and gravitational theories.  At a methodological level, issues involving an interplay of reductionist and functionalist reasoning may be discussed.  

Collaborators on recent work include Stephon Alexander, Marina Cortes, William Cunningham,  Stuart Kauffman, Jaron Lanier,  Andrew Liddle,  Joao Magueijo,   Stefan Stanojevic,  Michael W. Toomey, Clelia Verde and Dave Wecker.

The understanding of strongly-correlated quantum matter has challenged physicists for decades. The discovery three years ago of correlated phases and superconductivity in magic angle twisted bilayer graphene led to the emergence of a new materials platform to investigate strongly correlated physics, namely moiré quantum matter. These systems exhibit a plethora of quantum phases, such as correlated insulators, superconductivity, magnetism, Chern insulators, and more. In this talk I will review some of the recent advances in the field, focusing on the newest generation of moiré quantum systems, where correlated physics, superconductivity, and other fascinating phases can be studied with unprecedented tunability. I will end the talk with an outlook of some exciting directions in this emerging field.

There has been much theorizing on the question of how the procedures of quantum theory might modify general relativity, perhaps leading to a resolution of the problem of the space-time singularities of gravitational collapse. However, I shall argue that these procedures cannot, alone, resolve the space-time singularity issue. Instead, I shall maintain that considerations of relativity, both special and general, could well provide pointers to how the major conundrum of quantum mechanics—the collapse of the wave-function—may eventually be resolved, via curious retro-active aspects of quantum and classical reality.

An important and unresolved question in cosmology today is whether there is new physics that is missing from our current standard Lambda Cold Dark Matter (LCDM) model. A current discrepancy in the measurement of the Hubble constant could be signaling a new physical property of the universe or, more mundanely, unrecognized measurement uncertainties. I will discuss two of our most precise methods for measuring distances in the local universe: Cepheids and the Tip of the Red Giant Branch (TRGB). I will present new results from the Carnegie-Chicago Hubble Program (CCHP), the goal of which is to independently measure a value of the Hubble constant to a precision and accuracy of 2%. Using the Hubble Space Telescope Advanced Camera for Surveys,  we are  using the TRGB to calibrate Type Ia supernovae. I will  address the uncertainties,  discuss the current tension in Ho, and whether there is need for additional physics beyond the standard LCDM model.