Potential flow theory has been well-known in fluid mechanics for over a century, and one may think there is not much left to say about it. And yet, advances in microfluidic technologies invite us to revisit this established theory with a contemporary lens. In this talk, I show how classic tools of mathematical analysis can be exploited to model transport in modern microfluidic systems. Using conformal maps, I build a toolbox for the analytical understanding of flow and diffusion in 2D geometries of arbitrary complexity. These theoretical models can find use in a number of technological sectors, but this sort of approach can also give us a scaffolding to start approaching contemporary problems in the physics of complex systems, particularly for flow in disordered media.
We live in an era when quantum computers are becoming a reality. As these devices grow in size and capability, the central challenge becomes understanding what computational tasks they can perform efficiently. I will discuss how quantum measurements and feedforward, an ingredient already available in current hardware but largely absent from the theoretical toolkit, can drastically alter the complexity of quantum algorithms. Incorporating measurements into the algorithmic framework leads to provable — sometimes doubly exponential — speedups for a broad class of tasks, from preparing quantum states to implementing unitaries.
Tensor networks are a mathematical framework for efficiently representing quantum many-body states. After a brief introduction from scratch, I will briefly discuss their correlation structure, how tensor networks relate to classifying phases of matter, and some no-go results from computational complexity theory.
Quantum computers require several distinct resources to solve computational tasks faster than classical computers. Entanglement is one such resource, but by itself it is not sufficient to guarantee a quantum advantage. Nonstabilizerness, colloquially known as magic, quantifies the departure of a quantum state from the class of stabilizer states and captures the non-Clifford resources required for universal quantum computation. Understanding how magic builds up and propagates in many-body quantum systems is therefore a fundamental question, with direct implications for quantum chaos, classical simulability, and near-term quantum devices. In this talk, I will discuss the spreading of magic under unitary dynamics. I will consider both Haar-random brick-wall circuits and Hamiltonian dynamics, with particular emphasis on the role of conservation laws. In U(1)-symmetric systems, I will compare the growth of stabilizer Rényi entropy and participation entropy across different dynamical regimes. Participation entropy becomes closely connected to symmetry-compatible notions of magic, allowing resource growth to be related to transport properties. I will show that the buildup and saturation of magic distinguish ballistic, superdiffusive, and diffusive regimes, revealing dynamical information beyond that captured by entanglement alone.
A distinctive feature of many biological systems is their ability to adapt to persistent stimuli or disturbances that would otherwise drive them away from a desirable steady state. This resulting stasis enables reliable function across a wide range of external environments. We focus on a stringent form of this behavior—robust perfect adaptation (RPA)—which remains resilient to certain network and parameter perturbations. As in engineered control systems, RPA is not incidental: it requires the regulating network to satisfy specific, unavoidable structural constraints. Using examples from systems biology and synthetic biology, we show how these constraints arise in natural and engineered circuits. We argue that identifying the structural basis of RPA allows us to move beyond implementation details and provides a principled lens for understanding regulatory complexity and information processing in biological systems
Over the past decades, statistical physics has provided a powerful framework for analyzing learning in high-dimensional models, revealing phase transitions, fundamental limits on generalization, and the role of algorithms and architectures. In this talk, I will discuss how these ideas are now being extended beyond classical perceptron-type models to attention-based architectures that process sequences of tokens, opening a path toward a statistical physics theory of transformers.
It has long been understood that the exact (“fundamental”) gauge symmetry of the electromagnetic fields plays an important role in the theory of quantum materials. What has come into focus more recently is that there exist essential properties of quantum phases of matter that are best understood in terms of an effective field theory with emergent gauge fields, rather than (or in addition to) in terms of broken symmetries. Here, gauge invariance is not a symmetry of the microscopic problem but is rather an efficient representation of the low energy physics. As time permits, I will discuss recent theoretical results that suggest that exotic “resonating valence-bond” fluids, describable by emergent gauge theories, might exist in a much broader range of experimentally accessible platforms than has been previously appreciated.
In fractional quantum Hall states, electrons self-organize into a strongly interacting fluid with nontrivial emergent properties. It has recently been understood that fractional quantum Hall fluids accommodate one or several spin-2 excitations, which have been argued to be condensed-matter analogues of the graviton. In this talk we will review the origin of the idea of the graviton and the basic physics of the fractional quantum Hall effect. We then discuss a recent experiment claiming observation of a graviton-like mode in fractional quantum Hall effect and its broader implications.