2024 MPS Annual Meeting

Richard Carthew
Northwestern University

Predictability in Phenotypic Variation of Organismal Form
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Living systems exhibit remarkable fidelity in form (morphology) when comparing individual organisms from the same species or closely related species. And yet variation in form exists between individuals, enabling evolution by selection. However, geometric study of form has been limited by the quantitative measures of morphology that typically rely on a sparse number of handpicked anatomical landmarks. We have developed an application of Riemann’s mapping theorem to measure variation in morphology of the common fruit fly wing. 2D images of wings are conformally mapped to a unit disc and aligned with one another to produce a global registration of wing images. Studying an outbred population of the fruit fly Drosophila melanogaster, we find natural variation is spatially extended across the wing and is strongly correlated along a single mode of variation as determined by PCA.

Remarkably, minute perturbations in environment or genome sequence shift the population’s average wing morphology along the 1D manifold regardless of the qualitative features of the perturbation. The average wing phenotypes of three other species in the melanogaster clade are also positioned along the manifold, and the distances between one another and D. melanogaster strongly reflect their inferred phylogenetic relationships. Theoretical work suggests that evolvable variation in wing morphology might be driven by a “soft mode” in the dynamical system that corresponds to wing development. Carthew will also discuss recent topological analysis of wing form that provides a different perspective to the correlated variation.

Richard Carthew is the Owen L. Coon Professor of Molecular Biosciences at Northwestern University. Born and raised in Toronto Canada, he received a Ph.D. in biology at MIT. After a postdoctoral stint at University of California, Berkeley, he held a faculty position at University of Pittsburgh before joining the faculty at Northwestern University in 2001. He is the inaugural director of the NSF-Simons National Institute for Theory and Mathematics in Biology, which was established in 2023 and is located in Chicago. His primary research focus is on the patterns of shape and form in complex animals. More specifically, the self-organization of cells during development that create complex forms with remarkable predictability. He was also a pioneer in elucidating the mechanisms whereby small RNA molecules are capable of regulating gene expression across the Eukaryota (nucleus-bearing cellular life). Carthew is a Helen Hay Whitney Fellow and a Pew Biomedical Scholar.
 

Jonathan Feng
University of California, Irvine

The Fall and Rise of Forward Physics
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Particle colliders have been the workhorse tool for particle physics since they were invented over 60 years ago. Forward particles are those that are produced at colliders and then travel in a direction close to the beamline. For decades, forward particles were largely ignored, and all of the large detectors currently operating at colliders are blind to them. In the last few years, however, our understanding of the forward region has been transformed and we now know that this region contains a treasure trove of physics, including the most energetic neutrinos ever produced by humans, possible evidence for dark matter, milli-charged particles, and new forces, and a wealth of other valuable information. To capture some of this potential, the Forward Search Experiment (FASER) has been operating in the forward region of the Large Hadron Collider since 2022. FASER’s latest results will be described, along with their implications for the future of particle physics.

Jonathan Feng is Distinguished Professor of Physics and Astronomy at University of California, Irvine. His research spans topics in particle and astroparticle physics, and he is known as a central figure in the theoretical study of particle dark matter and searches for new particles. In recent years, he has also led an experiment at CERN, the Forward Search Experiment (FASER), which he founded in 2018. Feng received degrees in physics and mathematics from Harvard, Cambridge, and Stanford. He joined the UC Irvine faculty in 2002 and became Professor and Chancellor’s Fellow in 2006. Feng’s research has been supported by awards from the National Science, Sloan, Guggenheim, Heising-Simons, and Simons Foundations.
 

Aaron Lauda
University of Southern California

New Interactions Between Topology and Quantum Computation
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The field of topological quantum computation promises to provide scalable and robust models for quantum computation, leveraging the unique properties of topological phases of matter. Central to this approach is the existence of exotic particles known as anyons, which exhibit non-Abelian exchange statistics. These particles offer a pathway to fault-tolerant quantum computing, where information is stored and manipulated in a way that is inherently protected from local perturbations.

This talk will introduce the interplay between topology and quantum computation, focusing on how recent advances in our understanding of topology can provide new theoretical techniques for quantum computation. We will delve into the rich mathematical framework that predicts the existence of anyons and their associated braiding operations, which form the foundation of topological quantum gates. Additionally, we will discuss how advances in topology, such as the study of knot invariants and topological quantum field theories, have provided new tools and insights for quantum computation.

Aaron Lauda is a professor of mathematics at the University of Southern California, studying representation theory, low-dimensional topology and their applications in mathematics and theoretical physics. He holds a joint appointment in the Department of Physics and Astronomy and is a member of the USC Center for Quantum Information Science and Technology. He completed his Ph.D. in pure mathematics in 2006 at Cambridge University, following a master’s degree in Physics from University of California, Riverside. He spent five years as a Ritt Assistant Professor at Columbia University before joining USC in 2011. Lauda is a recipient of the Sloan Research Fellowship and an NSF CAREER award and is a Fellow of the American Mathematical Society and the Simons Foundation. From 2017–2020, he directed an NSF Focused Research Grant supporting a collaboration involving a team from USC, UCLA, Caltech and Columbia. In 2021, he was awarded a D.Sci from Cambridge University. Currently, he is directing the Simons Collaboration in Mathematical and Physical Sciences New Structures in Low-Dimensional Topology.
 

Lin Lin
University of California, Berkeley

Quantum Advantage in Scientific Computation?
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The advent of error-corrected quantum computers is anticipated to usher in a new era in computing, with Shor’s algorithm poised to demonstrate practical quantum advantages in prime number factorization. However, cryptography problems are typically not categorized as scientific computing problems. This raises the question: which scientific computing challenges are likely to benefit from quantum computers? Lin Lin will first discuss some essential criteria and considerations towards realizing quantum advantages in these problems. Lin will then introduce some recent advancements in quantum algorithms, especially for simulating open quantum system dynamics. The first half of the presentation is intended to be accessible to a broad audience without prior background in quantum computation.

Lin Lin is a professor in the Department of Mathematics at University of California, Berkeley and a faculty scientist in the Mathematics Group at Lawrence Berkeley National Laboratory. His research centers on solving quantum many-body problems by employing both classical and contemporary methods. These techniques prove valuable across various domains, including quantum chemistry, quantum physics, materials science and quantum information theory. He has received the Sloan Research Fellowship (2015), the National Science Foundation CAREER award (2017), the Department of Energy Early Career award (2017), the (inaugural) SIAM Computational Science and Engineering (CSE) early career award (2017), the Presidential Early Career Awards for Scientists and Engineers (PECASE) (2019), the ACM Gordon Bell Prize (Team, 2020) and the Simons Investigator in Mathematics award (2021).
 

Joel Moore
University of California, Berkeley

The Evolving Boundary Between Classical and Quantum Hardware for Studying Low-Dimensional Quantum Matter

One of the first nontrivial examples of quantum matter to be understood at equilibrium was the behavior of a chain of two-state spins, or qubits, entangled by nearest-neighbor interactions. Hans Bethe’s solution of the ground state in 1931 eventually led to the concept of Yang-Baxter integrability, and the thermodynamics were fully understood in the 1970s. However, the dynamical properties of this spin chain at any nonzero temperature remained perplexing until some unexpected theoretical and experimental progress beginning around 2019. Starting from this and other spin models, which appear in magnetic solids known as “Mott insulators,” Joel Moore will talk about how new atomic emulators and quantum computers are beginning to complement solid-state experiment and theory. Moore will also explain why computer scientists, physicists and mathematicians all have their own reasons to care about the dynamics of simple arrangements of quantum spins.

Joel Moore is Chern-Simons Professor of Physics at the University of California, Berkeley, and a senior faculty scientist at Lawrence Berkeley National Laboratory. His work in theoretical physics studies quantum matter with a focus on the remarkable phenomena that emerge as consequences of entanglement and topology. He received his A.B. in physics from Princeton University in 1995 and spent a Fulbright year abroad before graduate studies at MIT. He then was a postdoc at Bell Labs before joining the Berkeley faculty in 2002. He is an elected member of the National Academy of Sciences (2022), a Simons Investigator (2013–2023) and a Fellow of the American Physical Society (2013). He previously served as member and chair of the advisory board of the Kavli Institute for Theoretical Physics.
 

Elizabeth Paul
Columbia University

Advances in Optimization for Stellarator Design
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A stellarator confines plasma with asymmetric toroidal magnetic fields for fusion energy applications. The immense freedom in the stellarator design space provides opportunities for reducing engineering complexity and improving performance. Although the magnetic field may be far from symmetric, modern stellarators take advantage of “hidden symmetries” for enhanced confinement. This talk will provide an overview of recent advances in stellarator optimization and their application to the design of new experiments in the Columbia Plasma Laboratory. The Columbia Stellarator eXperiment (CSX) will build on the success of the Columbia Non-neutral Torus (CNT) to confine a small aspect ratio quasisymmetric plasma with two shaped interlinked coils. Using this device, we will explore the physics of quasiaxisymmetry and demonstrate non-insulated HTS technology for non-planar magnets.

Elizabeth Paul joined the Department of Applied Physics and Applied Mathematics at Columbia University as an assistant professor in 2023. She leads a group of postdocs and students in stellarator theory and computation. Her team works to develop software for numerical optimization of new devices and advance modeling of energetic particles in 3D magnetic fields. Paul received her A.B. in astrophysical sciences with concentrations in applied and computational mathematics and applications of computing from Princeton University in 2015. In 2020, she received her Ph.D. in physics from the University of Maryland, College Park. In 2021, Dr. Paul received the Marshall N. Rosenbluth Award from the American Physical Society in recognition of her doctoral work, “For pioneering the development of adjoint methods and application of shape calculus for fusion plasmas, enabling a new derivative-based method of stellarator design.” Prior to joining Columbia University, she was a Presidential Postdoctoral Research Fellow at Princeton University. In 2023, she received the DOE Early Career Research Award.
 

Richard Schwartz
Brown University

The Optimal Paper Moebius Band

A paper Moebius band is made by taking a 1 x L rectangular strip of paper, giving it an odd number of twists, and joining the ends together. The question is: How small can you make L? Richard Schwartz will explain why L>sqrt(3) is a necessary and sufficient condition. This resolves a question about the optimal paper Moebius band raised in 1962 by W. Wunderlich, and confirms the more specific conjecture made in 1977 by B. Halpern and C. Weaver.

Richard Evan Schwartz (b. 1966) is the Chancellor’s Professor of Mathematics at Brown University. He received a math B.S. from University of California, Los Angeles in 1987 and a math Ph.D. from Princeton University in 1991. He spoke at the International Congress of Mathematicians in 2002 and 2022. He wrote and illustrated a number of picture books, one of which (You Can Count on Monsters) briefly made it to number one on Amazon.com. Schwartz is happiest when he has a lot of free time. His hobbies include drawing, coding, cycling and yoga.
 

Daniel Tataru
University of California, Berkeley

Global Solutions for Nonlinear Dispersive Waves
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The key property of linear dispersive flows is that waves with different frequencies travel with different group velocities, which leads to the phenomena of dispersive decay. Nonlinear dispersive flows also allow for interactions of linear waves, and their long time behavior is determined by the balance of linear dispersion on one hand, and nonlinear effects on the other hand.

The first goal of this talk will be to present a new set of conjectures which aim to describe the global well-posedness and the dispersive properties of solutions in the most difficult case when the nonlinear effects are dominant, assuming only small initial data. This covers many interesting physical models, yet, as recently as a few years ago, there was no clue even as to what one might reasonably expect. The second objective of the talk will be to describe some very recent results in this direction, in joint work with my collaborator Mihaela Ifrim from University of Wisconsin, Madison.

Tataru’s work on nonlinear waves has been deep and influential. He proved difficult well-posedness and regularity results for many new classes of equations. This includes geometric evolutions such as wave and Schrödinger maps, quasilinear wave equations, some of which are related to general relativity, as well as other physically relevant models.