2025 MPS Annual Meeting

Ruth Baker
University of Oxford

What Is Parameter Identifiability, Why Do We Need Identifiable Models, and What Can Identifiable Models Tell Us About Regulation of the Cell Cycle?

Mathematical modelling is increasingly integral to the interpretation of experimental data across applied mathematics, particularly in the life sciences where complex dynamical systems are prevalent. Accurate parameter estimation is central to this endeavor: model parameters are used not only to fit observed data but also to infer latent biological processes and generate predictive simulations. A fundamental issue is parameter identifiability—the extent to which model parameters can be uniquely or reliably estimated given the available data. This becomes especially challenging in the context of nonlinear, high-dimensional models that are common in systems biology because many existing identifiability tools are either underutilized or not well-adapted to such models. In this talk, I will outline recent progress in developing methods to assess parameter identifiability. I will illustrate these approaches using models of cell cycle regulation and demonstrate how identifiability analysis can shed light on the influence of regulatory mechanisms on collective cell migration.

Ruth E. Baker is a professor of applied mathematics and an affiliated principal investigator at the Institute of Developmental and Regenerative Medicine at the University of Oxford. She holds a D.Phil. in mathematics from Oxford and has developed a research program at the interface of applied mathematics, statistical inference, and the life sciences. Her work focuses on the development of mathematical and computational tools to extract biological insights from complex models and data, with particular emphasis on parameter identifiability and the integration of models with experimental observations. Her contributions have been recognized through numerous awards, including the Whitehead Prize of the London Mathematical Society and a Royal Society Wolfson Research Merit Award. Beyond her research, she plays a leading role in the international mathematical biology community, having served on the Board of Directors of the Society for Mathematical Biology and currently chairing the SIAM Life Sciences Activity Group.
 

Emanuele Berti
Johns Hopkins University

Black Hole Demography and Black Hole Spectroscopy with Gravitational Waves

As the LIGO-Virgo-KAGRA gravitational-wave detector network improves in sensitivity, observations of binary black hole mergers are growing in number and quality. With each new observation, we are building a census of black hole masses, spins, and redshifts. In the first part of their talk, Emanuele Berti will discuss our current understanding of the population of astrophysical black holes and of their formation channels, and how future detectors (the Einstein Telescope, Cosmic Explorer, and the space-based interferometer LISA) will extend this “black hole demography” program to a whole new mass and redshift range.

Gravitational-wave observations are also testing general relativity in the strong gravity regime. According to Einstein’s theory, as the remnant of a binary black hole merger settles to the stationary, rotating solution found by Roy Kerr, it emits characteristic “ringdown” waves—a superposition of damped exponentials with frequencies and damping times that depend only on the mass and spin of the black hole. In the second part of their talk, Berti will explain how these measurements can be used to do “black hole spectroscopy” and provide direct evidence of black holes, just like the 21-cm line identifies interstellar hydrogen.

Emanuele Berti’s research focuses on black holes, neutron stars, gravitational-wave astronomy, and tests of general relativity. After his Ph.D. from the University of Rome, he held postdoctoral positions at the Aristotle University of Thessaloniki, the Institut d’Astrophysique de Paris, Washington University in Saint Louis, and JPL/Caltech. He joined the faculty at the University of Mississippi in 2009, and he moved to Johns Hopkins University in 2018. Berti served as chair of the American Physical Society’s Division of Gravitational Physics and as president of the International Society on General Relativity and Gravitation. His research has been supported by awards from the National Science Foundation, NASA, the Templeton Foundation, and the Simons Foundation.
 

Ivan Corwin
Columbia University

Extreme Diffusion

Two hundred years ago, Robert Brown observed the statistics of the motion of grains of pollen in water. It took almost one hundred years for Einstein and others to develop an effective theory describing this motion as that of a random walker. In this talk, Ivan Corwin challenges a key implication of this well-established theory. When studying systems with very large numbers of particles diffusing together, Corwin will argue that the Einstein random walk theory breaks down when it comes to predicting the statistical behavior of extreme particles—those that move the fastest and furthest in the system. In its place, Ivan will describe a new theory of extreme diffusion which captures the effect of the hidden environment in which particles diffuse together and allows us to interrogate that environment by studying extreme particles. He will highlight one piece of mathematics that led us to develop this theory—a non-commutative binomial theorem—and hint at other connections to integrable probability, quantum integrable systems and stochastic PDEs.

Ivan Corwin is a professor of mathematics at Columbia University. Prior to arriving there in 2013, he did a postdoc at MIT and Microsoft Research and received his Ph.D. in 2011 from the Courant Institute. His research is at the interface of probability, integrable systems, and mathematical physics. He is currently a Simons Investigator in mathematics, a fellow of the American Mathematical Society and of the Institute for Mathematical Statistics; has held fellowships or chairs from the Simons Foundation, Packard Foundation, Clay Mathematics Institute, Institut Henri Poincaré, and Miller Institute; and is a recipient of the Loève prize, Alexanderson award, Rollo Davidson prize, and a Blavatnik National Award finalist.
 

Zaher Hani
University of Michigan

Hilbert’s Sixth Problem: From Particles to Waves

In his sixth problem, Hilbert called for the derivation of the equations of fluid mechanics—such as the Euler and Navier-Stokes equations—by way of rigorously justifying Boltzmann’s kinetic theory for particle systems. The scope of this program, now known as Hilbert’s program, was precisely framed in the mid-20th century through the works of Grad and Cercignani, who identified the correct limiting process involved: the Boltzmann-Grad limit. In his celebrated work, Lanford (1975) gave the first rigorous derivation of Boltzmann’s equations, albeit only valid for short times. However, Hilbert’s sixth problem requires a long-time extension of Lanford’s result, which remained open for decades. In recent joint work with Yu Deng (University of Chicago) and Xiao Ma (University of Michigan), we extend Lanford’s theorem to long times—specifically for as long as the solution of Boltzmann’s equation exists. This allows for the full execution of Hilbert’s program and the derivation of the fluid equations in the Boltzmann-Grad limit. The underlying strategy follows an earlier joint work with Yu Deng that resolved a parallel problem, in which colliding particles are replaced by nonlinear waves; thus, establishing the mathematical foundations of wave turbulence theory. In this talk, we will review this progress and discuss some future directions.

Zaher Hani is the Frederick W. and Lois B. Gehring Professor of Mathematics at the University of Michigan, Ann Arbor. He works in the field of nonlinear PDE and mathematical physics. Before moving to Michigan in 2018, Hani held positions at Georgia Tech (2014-2018), and the Courant Institute of Mathematical Sciences, NYU (2011-2014). He graduated with a Ph.D. from the University of California, Los Angeles in 2011 under the supervision of Terence Tao.
 

Hee Oh
Yale University

A Traveler’s Journey in a Hyperbolic World

In this lecture, we will explore the journey of a traveler moving along a straight (Euclidean) path in a variety of geometric worlds. In a Euclidean torus world, she enjoys the sights of a subtorus, a phenomenon explained by Kronecker’s 1884 theorem showing that the closure of any line in the Euclidean torus is always a subtorus. But what happens when she ventures into closed hyperbolic manifolds or even hyperbolic manifolds of infinite volume? We will describe what she encounters, accompanied by numerous illustrations to bring these geometric concepts to life.

Hee Oh is the Abraham Robinson Professor of Mathematics at Yale University. Her work bridges dynamics, Lie groups, geometry, and number theory, showing how symmetry and motion of shapes in curved spaces uncovers hidden patterns—even when those spaces stretch out endlessly. After earning her Ph.D. from Yale in 1997, she held faculty appointments at Princeton, Caltech, and Brown before returning to Yale in 2013. Her contributions have been recognized with the AMS Satter Prize (2015), a Guggenheim Fellowship (2017), the Ho-Am Prize in Science (2018), and election to the American Academy of Arts and Sciences (2024). She previously served as a vice president of the American Mathematical Society.
 

Amit Singer
Princeton University

Mathematics of Cryo-Electron Microscopy

Single particle cryo-EM is an increasingly popular technique for determining 3-D molecular structures at high resolution. The 2017 Nobel Prize in Chemistry was awarded to three of the pioneers of cryo-EM, and already in the early stages of the global pandemic, cryo-EM was successfully applied to image the SARS-CoV-2 spike protein. We will discuss the mathematical principles and computational methods for reconstruction using cryo-EM, focusing on the challenges of reconstructing small size molecules and the reconstruction of flexible molecules.

Amit Singer is a professor of mathematics, the director of the Program in Applied and Computational Mathematics (PACM), and a member of the Executive Committee for the Center for Statistics and Machine Learning (CSML) at Princeton University. He joined Princeton as an assistant professor in 2008. From 2005 to 2008, he was a Gibbs Assistant Professor in Applied Mathematics at the Department of Mathematics, Yale University. Singer received the B.Sc. degree in physics and mathematics and the Ph.D. degree in Applied Mathematics from Tel Aviv University (Israel), in 1997 and 2005, respectively. His list of awards includes a SIAM Fellowship (2022), Simons Math+X Investigator Award (2017), National Finalist Blavatnik Award for Young Scientists (2016), Moore Investigator in Data-Driven Discovery (2014), Simons Investigator Award (2012), Presidential Early Career Award for Scientists and Engineers (2010), an Alfred P. Sloan Research Fellowship (2010), and the Haim Nessyahu Prize for Best Ph.D. in Mathematics in Israel (2007). His current research in applied mathematics focuses on theoretical and computational aspects of data science, and on developing computational methods for structural biology.
 

John Voight
University of Sydney

Ranks of Elliptic Curves

Elliptic curves lie at the intersection of many areas of mathematics and remain central to modern number theory. The rank of an elliptic curve over the rational numbers measures the size of its group of rational points; intuitively, it counts the number of independent points needed to generate all rational solutions up to torsion. A fundamental question, going back to Poincaré, remains unresolved: can the rank be arbitrarily large? In this talk, we present computations and data, a statistical model and heuristic framework to guide our expectations, and outliers that challenge these assumptions. This is joint work with Jennifer Park, Bjorn Poonen, and Melanie Matchett Wood.

John Voight is professor of mathematics at the University of Sydney, where he leads the Magma Computational Algebra group and works in arithmetic geometry. He earned his Ph.D. from the University of California, Berkeley in 2005 and then held faculty positions at the University of Vermont and Dartmouth College. He is a recipient of an NSF CAREER award and in 2025 was named a fellow of the American Mathematical Society. Voight’s research aims to make structures in algebra and number theory explicit. Motivated by the Langlands program, he develops algorithms that bring abstract objects—such as modular forms, elliptic curves, Galois representations, and L-functions—within computational reach. His work enables large-scale computations and new experimental approaches in number theory, with a view to solve concrete problems as well as reveal patterns and conjectures that illuminate the landscape of modern arithmetic.
 

Norman Yao
Harvard University

A Universal Theory of Spin Squeezed Entanglement

Quantum metrology makes use of structured entanglement to perform measurements with greater precision than would be possible with only classically correlated particles. One of the most paradigmatic examples of such entanglement is known as “spin squeezing”, which is known to arise in bespoke systems exhibiting all-to-all interactions. In this talk, Norman Yao will provide evidence for the following conjecture: that there exists a one-to-one correspondence between spin squeezing and a particular type of magnetic order (i.e. an easy-plane ferromagnet). If true, this would suggest that spin squeezed entanglement can naturally be generated in a wide variety of physical systems, including quantum dipoles.

Norman Yao is Professor of Physics at Harvard University. His research interests lie at the interface between AMO physics, condensed matter, and quantum information science. A recurring theme in his research program is that much of the power of quantum mechanics remains concealed if one focuses solely on systems in thermal equilibrium. Norm earned both his undergraduate degree (2009) and his Ph.D. (2014) from Harvard. Following a Miller postdoctoral fellowship, he joined the UC Berkeley physics faculty in 2017 and returned to Harvard in 2022. He is a recipient of the Breakthrough Foundation’s New Horizons Prize, a Simons Investigator (2023-2028), a Brown Investigator and has been awarded the I. I. Rabi Prize and the George E. Valley Prize from the American Physical Society.

Watch a playlist of all presentations from this meeting here.