The aim of the presentation is to review the beautiful geometry underlying the standard model of particle physics, as captured by the framework of "SO(10) grand unification." Some new observations related to how the Standard Model (SM) gauge group sits inside SO(10) will also be described.

I will start by reviewing the SM fermion content, organising the description in terms of 2-component spinors, which give the cleanest picture.

I will then explain a simple and concrete way to understand how spinors work in 2n dimensions, based on the algebra of differential forms in n dimensions.

This will be followed by an explanation of how a single generation of standard model fermions (including the right-handed neutrino) is perfectly described by a spinor in a 10 ("internal") dimensions.

I will review how the two other most famous "unification" groups -- the SU(5) of Georgi-Glashow and the SO(6)xSO(4) of Pati-Salam -- sit inside SO(10), and how the SM symmetry group arises as the intersection of these two groups, when they are suitably aligned.

I will end by explaining the more recent observation that the choice of this alignment, and thus the choice of the SM symmetry group inside SO(10), is basically the choice of two Georgi-Glashow SU(5) such that the associated complex structures in R^{10} commute. This means that the SM gauge group arises from SO(10) once a "bihermitian" geometry in R^{10} is chosen. I will end with speculations as to what this geometric picture may be pointing to.

In quantum many-body physics, we aim to understand and predict the exciting phenomena emerging from the interactions of many quantum particles. In this talk I will use the paradigmatic Fermi-Hubbard model, a conceptually simple model of interacting fermionic particles, as an example to highlight different approaches to gain insights into quantum many-body problems. I will describe a semi-analytical theory, established numerical methods, machine learning techniques, as well as quantum simulation experiments, which provide detailed information about the quantum state of the system. A particular focus will be on how to combine these different approaches to learn as much as possible about the system of interest, for example through new observables and modified microscopic models.

In 2008 Masahiro Hotta proposed a protocol for transporting energy between two localized observers A and B without any energy propagating from A to B. When this protocol is applied to the vacuum state of a quantum field, the local energy density in the field achieves negative values, violating energy conditions

We will explore the protocol of quantum energy teleportation and show how quantum information techniques can be used to activate thermodynamically passive states. We will review the first experiment showcasing the local activation of ground state energy (carried out in 2022), and we will discuss the potential of this relativistic quantum information protocol to create exotic distributions of stress-energy density in a quantum field theory, and how spacetime might react to them.

In this talk, I will discuss our work on using models inspired by natural language processing in the realm of many-body physics. Specifically, I will demonstrate their utility in reconstructing quantum states and simulating the real-time dynamics of closed and open quantum systems. Finally, I will show the efficacy of using these models for combinatorial optimization, yielding solutions of exceptional accuracy compared to traditional simulated and simulated quantum annealing methods.

The importance of the tenfold way in physics was only recognized in this century. Simply put, it implies that there are ten fundamentally different kinds of matter. But it goes back to 1964, when the topologist C. T. C. Wall classified the associative real super division algebras and found ten of them. The three 'purely even' examples were already familiar: the real numbers, complex numbers and quaternions. The rest become important when we classify representations of groups on Z/2-graded Hilbert spaces. We explain this classification, its connection to Clifford algebras, and some of its implications.

I will introduce asymptotically safe quantum gravity, which is based on the quantum realization of scale invariance, as one candidate theory to describe nature at all scales. I will discuss the concept of an asymptotically safe fixed point, and how the realization of scale invariance at high energies might provide a predictive and UV-complete description of nature. In particular, I will focus on the interplay of gravity and matter, and highlight mechanisms how this interplay might lead to constraints and predictions of asymptotically safe gravity-matter systems.

I will introduce the QAOA and discuss some recent developments. These might include the application of the QAOA to the Sherrington-Kirkpatrick model, landscape independence, and the odd behavior when starting in a good place.

A quantum computer is a new type of computer based on quantum physics. When it comes to certain computational objectives, the computational ability of quantum computers is much stronger than that of the familiar digital computers, and their construction will enable us to factor large integers and to break most of the current cryptosystems.

The question of whether quantum computation is possible is one of the fascinating clear-cut open scientific questions of our time. In my lecture I will explain theoretical discoveries from the 1990s that suggested that quantum computation is possible and present my theory as to why quantum computation is nevertheless impossible.

At the crux of the matter is the study of noisy intermediate scale quantum (NISQ) computers. Based on the mathematical notions of "noise sensitivity vs noise stability" (Benjamini, Kalai, and Schramm 1999, Kalai and Kindler 2014), we identify the inherent noise sensitivity of probability distributions arising from NISQ computers. This leads to a very low complexity class of probability distributions that can be robustly described by such quantum computers; consequently, NISQ computers will not allow good-quality quantum error-correction which are the necessary building blocks for larger quantum computers.

The lecture will be self-contained and will start with a gentle explanation of some basic notions about computation, and quantum computers.

A fundamental aspect of a random walk is determining when it reaches a specified threshold position for the first time. This first-passage time, and more generally, the distribution of first passage times underlies many non-equilibrium phenomena, such as the triggering of integrate and fire neurons, the statistics of cell division, and the execution of stock options. The computation of the first-passage time and its distribution is both simple and beautiful, with profound connections to electrostatic potential theory. I will present some aspects of these fundamentals and then discuss applications of first-passage ideas to diverse phenomena, including stochastic search processes and a toy model of wealth sharing.

I will present recent progress in building a rigorous theory to understand how scientists, machines, and future quantum computers could learn models of our quantum universe. The talk will begin with an experimentally feasible procedure for converting a quantum many-body system into a succinct classical description of the system, its classical shadow. Classical shadows can be applied to efficiently predict many properties of interest, including expectation values of local observables and few-body correlation functions. I will then build on the classical shadow formalism to answer two fundamental questions at the intersection of machine learning and quantum physics: Can classical machines learn to solve challenging problems in quantum physics? And can quantum machines learn exponentially faster than classical machines?

Over the last decade, there have been many Perimeter efforts in the realm of EDI, and they have unquestionably enhanced the Institute’s culture. Paradoxically, some of these efforts have illuminated areas where we can do more, and there are still others to be addressed.

In Perimeter’s short life, we’ve built a unique institution, with a culture characterized by intellectual fearlessness and excellence. Yet we can do even better. Our culture is connected to our research. We’re here to make breakthroughs in our understanding of our universe – and breakthroughs are made by thinking in new ways. We can’t afford to leave any great thinkers, or any great ideas, behind.

In 2020, we embarked on a project to develop a coherent, concrete strategic plan to guide Perimeter’s efforts in EDI, in partnership with experts at Shift Health and the Laurier Centre for Women in Science. All members of the Perimeter community have been consulted to ensure that the final strategy is reflective of our whole community.

Our actions to date are a step in an intentional and comprehensive effort to make Perimeter an institute where everyone can thrive and find a sense of belonging.