Mathematical Physics Webinar

Matthew P.A. Fisher – UC Santa Barbara 

Wednesday, November 11, 2026

Zoom opens: 10:30AM EDT

Seminar begins: 10:45AM EDT

Strong-to-weak U(1) Symmetry Breaking in Open System Dynamics

In generic open quantum systems, universal dynamical processes tend to exhibit classicality - dissipation washes out quantum effects. Here I consider open quantum dynamics in the presence of a global U(1) symmetry. In mixed states, this symmetry can be either strong or weak, and distinct dynamical phases can be characterized by the spontaneous breaking of either symmetry. The strong-to-weak spontaneous symmetry breaking (SW-SSB) transition is characterized by various information theoretic quantities which are non-linear in the system's mixed state density matrix. Within a Lindblad framework for U(1) dynamics, we show that a finite-time SW-SSB transition occurs in two and three dimension, whereas in one dimension the correlation length grows linearly with time and diverges only in the in finite-time steady state. Moreover, with carefully chosen Lindblad dynamics, the SW-SSB transition signals a finite time breakdown of quantum dynamics, giving rise to classical dynamics described by a stochastic Langevin equation (Model F of Halperin-Hohenberg). When the weak symmetry is spontaneously broken, the system enters a superfluid state with classical hydrodynamics. I will describe observation of a SW-SSB phase and phase transition in cold atomic gas simulators, as revealed by an appropriately chosen quantum-classical cross-correlator

Smitha Vishveshwara – University of Illinois at Urbana-Champaign

Wednesday, November 4, 2026

Zoom opens: 10:30AM EDT

Seminar begins: 10:45AM EDT

Exploring Condensate Shells: From ground-based lattices to Space

Bose-Einstein Condensates trapped in shell-shaped geometries are expected to be found in a variety of unique settings from co-existent superfluid-Mott insulating phases in optical lattices to neutron stars. On Earth, such freely standing condensate shells generally cannot exist due to gravitational sag. Remarkably, such structures, however, are being realized in microgravity conditions in the Cold Atomic Laboratory aboard the International Space Station. Following a survey of these shells from laboratory to astrophysical settings, I describe our theoretical studies in close connection with experiments in optical lattices and in Space. I discuss the collective mode structure of shell shaped condensates and related signatures of hollowing, quantum interference effects in time-of-flight expansion, and vortex behavior. In the instance of microgravity, I present the thermodynamics of expanding shells,  parallels in cosmological scenarios, and the journey that brought these experiments to Space.

Sourav Chatterjee – Stanford University

Wednesday, October 28, 2026

Zoom opens: 10:30AM EDT

Seminar begins: 10:45AM EDT

Some exact calculations in timelike Liouville field theory

Timelike Liouville field theory is a toy model of 2D gravity that has received attention in the recent literature. Most of the conjectures about this theory are currently beyond the reach of rigorous mathematics. I will present a recent work where I was able to perform some exact calculations for certain parameter values. No background is necessary.

Lai-Sang Young - NYU

Wednesday, October 21, 2026

Zoom opens: 10:30AM EDT

Seminar begins: 10:45AM EDT

"Neuroscience meets dynamical systems: building a model of primary visual cortex"

In this talk, I would like to discuss some modeling work in which  simple mathematical ideas were used to shed light on neural mechanisms. The model in question simulates a small region of the primary visual cortex (V1) of the Macaque monkey, whose visual system is very similar to that of humans. Our model is a dynamical network of spiking neurons capable of reproducing dozens of V1 function and is (to a degree) built to "compute like the real brain". I will attempt to clarify/propose answers to some basic questions in visual neuroscience, such as how exactly orientation selectivity (OS) works, and the origin of direction selectivity (DS). OS and DS are visual functions enjoyed by neurons in V1 but not by their LGN afferents.

M. Cristina Marchetti – UC Santa Barbara

Wednesday, October 14, 2026

Zoom opens: 10:30AM EDT

Seminar begins: 10:45AM EDT

Active nematic solids and morphogenesis

Orientational order of elongated cells or muscle fibers is observed ubiquitously in biology and is known to play an important role in the organization of biological tissue. While most previous work has modeled living tissue as active fluids, in many circumstances both cell neighbor exchanges and cell divisions are suppressed and the tissue behaves more like an active solid. A striking example of this is the freshwater polyp Hydra, where topological defects in the muscle fiber orientation have been shown to localize to key features of the body plan. In this talk I will examine the behavior of active nematic solids, where the feedback between alignment, elasticity and biochemical signaling controls shape and structure.

Daniel Fisher – Stanford University

Wednesday, October 7, 2026

Zoom opens: 10:30AM EDT

Seminar begins: 10:45AM EDT

Eco-Evo Dynamics, Diversification, and Red Queen Phases Near a Snowy Fitness Peak

The caricature of evolution in a fitness landscape with trajectories approaching a fitness peak is very misleading., especially if drawn in two-dimensions.   The dimensionality of both organismic phenotype spaces and environmental spaces are very large, and they are inextricably coupled by evolution changing the environment:  A better caricature is a fitness snowscape.  We show that near a high-dimensional snowy peak, multiple distinct eco-evolutionary phases exist, including a diverse Red Queen phase with continual turnover of strains but no overall individual or community improvement.  

Nigel Goldenfeld – University of California San Diego

Wednesday, September 30, 2026

Zoom opens: 10:30AM EDT

Seminar begins: 10:45AM EDT

Emergence and Generalization in Machine Learning

The remarkable ability of modern neural networks to generalize improves with increasing network capacity, even when the number of model parameters or effective degrees of freedom exceeds the number of training data points.   Here we use dynamical mean field theory to show, in a simple setting of linear regression, that this surprising behavior is the outcome of a phase transition in the stochastic field theory describing the training process.  We calculate the critical exponents and scaling function of the double descent phase transition, and show that it is marked by a breakdown of the fluctuation-dissipation theorem associated with broken ergodicity. We describe how this phenomenon is an example of emergent behavior, and that the appropriate response function has the same functional form as the simple London model of the superconducting transition, with the rigidity of the wave function corresponding to the neural network's ability to generalize accurately. Our results are distinct from earlier work, because we calculate the time-dependence specifically, not just the least norm equilibrium solutions.  This is what enables us to identify the origin of the emergent behavior.  Our work provides a specific framework with which to understand emergent behavior in artificial neural networks, and I outline some future directions.

Work performed in collaboration with Chan Li.

Alberto Maspero – SISSA Trieste

Wednesday, September 23, 2026

Zoom opens: 10:30AM EDT

Seminar begins: 10:45AM EDT

Transfer of energy for pure-gravity water waves with constant vorticity

We prove growth of Sobolev norms for the two-dimensional periodic gravity water waves with constant nonzero vorticity, in infinite depth and with periodic boundary conditions. Precisely we construct weakly turbulent solutions exhibiting arbitrary large growth of high Sobolev norms, while having lower-order norms of small size, yielding the first rigorous construction of weakly turbulent solutions for the water waves equations. The proof relies on a new mechanism for generating energy cascades in quasilinear dispersive PDEs with sublinear dispersion and a nonlinear transport structure. A central ingredient is to exploit quasi-resonances from 2-wave interactions to produce a resonant transport operator that drives energy to high modes and causes Sobolev norm growth.

Arup K Chakraborty – MIT

Wednesday, September 9, 2026

Zoom opens: 10:30AM EDT

Seminar begins: 10:45AM EDT

How the Immune System Learns

The humoral immune system, comprised of B cells and their antibody and memory B cell products, plays an important role in protecting us from infection. This system is also a learning algorithm. Antibodies and memory B cells are produced by a Darwinian evolutionary process. This is a non-equilibrium stochastic dynamic process that allows the immune system to learn about a new antigen (pathogen or vaccine component). I will first describe results obtained from statistical physics-based models of these processes and complementary data from animals and humans. These studies show that the human immune system has a remarkable ability to learn to develop responses that can respond to previously unseen variant antigens upon “training” with only a few exposures to the same antigen. The mechanism underlying this ability to generalize will be discussed. I will then discuss how exploring and exploiting analogies between how the immune system learns and how machines learn is now enabling us to address basic scientific questions that can potentially guide better strategies to cure and prevent disease. Finally, I will comment on similarities and differences between learning in the immune system and deep learning networks.

Eduardo Fradkin – University of Illinois at Urbana Champaign

Wednesday, September 2, 2026

Zoom opens: 10:30AM EDT

Seminar begins: 10:45AM EDT

The Quantum Roughening Problem revisited

In 1978 Andreev and Parshin conjectured that the surface of a quantum crystal would become rough due to effects of quantum fluctuations. Two papers published in 1983,  one by Daniel Fisher and John Weeks and another one by me, showed that quantum fluctuations make these surfaces smooth and are not rough. In my talk I will revisit these arguments and sinus some interesting connections between this problem and other problems of interest such as quantum dimer models and Josephson junction arrays. In particular I will discuss the case of a model  with a  global conservation law in its quantum dynamics and the existence of two types of smooth phases in this case.

Karin Dahmen – University of Illinois at Urbana Champaign

Wednesday, August 26, 2026

Zoom opens: 10:30AM EDT

Seminar begins: 10:45AM EDT

Universal Avalanches and Prediction: from Nanoindentation and the Brain to Earthquakes and Stars?

Slow nanoindentation, or slow compression of nano-crystals, bulk metallic glasses, rocks, granular materials, and the earth all show intermittent slips or “quakes”. We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with a stress-dependent cutoff, indicating an underlying nonequilibrium phase transition. A simple model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stress-dependent cutoff function. The analysis draws on tools from statistical physics and the renormalization group. The results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes. Connections to neuron avalanches in the brain and recent observations on stars will also be discussed, extending the range of scales to 16 decades in length.

Cris Moore–  Santa Fe Institute

Wednesday, August 19, 2026

Zoom opens: 10:30AM EDT

Seminar begins: 10:45AM EDT

Which links matter most? Sparsifying network dynamics with effective resistance

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“Sparsification” is the act of reducing a network to a subset of its edges while approximately preserving its properties: either to reduce the computational cost of solving problems about it, or to identify which edges are the most important in some sense. Computer scientists have developed beautiful techniques for sparsifying a graph using physics-related ideas like the effective resistance. However, while these methods preserve the spectral properties of the Laplacian, it is not obvious to what extent they preserve the behavior of nonlinear dynamical systems. Using a mobility network from the United States as an example, I’ll show that they do very well for the SIR epidemic model, including the probability each node becomes infected and its distribution of arrival times, even when the sparse network includes less than 10% of the original edges. Choosing edges using purely topological methods, or by thresholding edge weights, does not perform nearly as well. I will end by discussing the possibility of using sparsification to “denoise” networks from bioinformatics, and present some preliminary results on the Kuramoto model of coupled oscillators.

This is joint work with Alexander Mercier (Harvard School of Public Health), Emmie Fitz-Gibbons (Brown), and Sam Scarpino (Northeastern).

Christopher Jarzynski – University of Maryland

Wednesday, July 29, 2026

Zoom opens: 10:30AM EDT

Seminar begins: 10:45AM EDT

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Estimating free energy differences with virtually escorted trajectories

The convergence of numerical free energy estimation methods can be accelerated using artificial fields that “escort” simulated trajectories along near-equilibrium paths.  Unfortunately, designing such fields is not easy.  Taking a cue from the mathematics behind diffusion models – a class of generative models in machine learning – we introduce a method based on virtual escorting.  This method adopts a post-processing approach.  Given a fixed set of nonequilibrium trajectories, a parameter-dependent virtual escorting field is constructed, possibly using a neural network.  This field is used in combination with the trajectories to produce an estimate of the desired free energy difference.  The parameters are then adjusted to optimize the convergence of the estimate.  I will describe the method, and will discuss conditions under which it produces a zero-variance estimator of the free energy difference.

Uri Alon  - Weizmann Institute

Wednesday, July 22, 2026

Zoom opens: 10:30AM EDT

Seminar begins: 10:45AM EDT

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Why is the upper tail of human lifespan so rigid? Insights from Langevin threshold-crossing models of aging

Human life expectancy has doubled over the last two centuries, yet the upper tail of human lifespan has barely moved. Why is median lifespan so plastic while extreme longevity remains so rigid? I will present a stochastic threshold-crossing view of aging, in which physiological damage follows time-dependent Langevin dynamics and death occurs as a first-passage event across a critical threshold. In this framework, the exponential increase in mortality with age corresponds to escape from a linearly declining barrier. The model separates two classes of parameters: **robustness parameters**, such as noise amplitude and threshold height, which affect the probability of crossing the barrier, and **senogenic parameters**, which govern the deterministic damage production and removal. Changes in robustness can improve median survival while preserving extreme-lifespan distributions, whereas changes in senogenic parameters shift extreme longevity. I will discuss how this distinction helps interpret historical mortality improvements, lifestyle and socioeconomic effects, which all seem to only affect robustness parameters, as well as familial longevity, and progeroid diseases. 

Larry Abbott  - Columbia University

Wednesday, July 15, 2026

Zoom opens: 10:30AM EDT

Seminar begins: 10:45AM EDT

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Biological Systems for Spatial Orientation

I will discuss several topics related to how animals represent and update their sense of orientation in the world.  In flies, this is done with a set of neurons that collectively form a ring-attractor network.  Activity in this system indicates the azimuthal orientation of the fly.  I will discuss how the polarization pattern of the sky is used as keep this encoded angle aligned with the physical world.  Vertebrates have an analogous system for head orientation, but it is more complex.  I will discuss various ways that a ring-attractor could be embedded in a large population of neurons, with results relevant for studies of the synaptic connections in these circuits.  Finally, in both flies and vertebrates, these systems have been studied primarily in two dimension (that is, considering only yaw rotations).  I will discuss different ideas about how they might respond to three-dimensional rotations.

Itamar Procaccia - Weizmann Insitute Wednesday, July 8, 2026 Zoom opens: 10:30AM EDT Seminar begins: 10:45AM EDT Amorphous Solids: More than Meets the Eye Understanding the mechanical response of amorphous solids, like glasses and granular media, requires considerations that go

Michael Shelley - Flatiron Institute & NYU Wednesday, July 1, 2026 Zoom opens: 10:30AM EDT Seminar begins: 10:45AM EDT Modeling chromatin as an active polymer melt In this talk I'll discuss a line of work wherein chromatin in the nucleus

Robert McCann – University of Toronto Wednesday, June 24, 2026 Zoom opens: 10:30AM EDT Seminar begins: 10:45AM EDT Trading linearity for ellipticity: a low regularity Lorentzian splitting theorem While Einstein's theory of gravity is formulated in a smooth setting, the

Doyne Farmer – Oxford University Wednesday, June 17, 2026 Zoom opens: 10:30AM EDT Seminar begins: 10:45AM EDT Quantitative complexity economics: A revolution in the making Mainstream economic theory follows a standard template that I will review in this talk. Complexity