An international team of researchers including Ryan Fortenberry, an astrochemist at the University of Mississippi, and Ralf Kaiser, professor of chemistry at the University of Hawaii at Mānoa and Samer Gozem, computational chemist at Georgia State University, published their research in the journal Nature Communications.

“Hydrogen sulfide is everywhere: it’s a product of coal-fired power plants, it has an effect on acid rain, it changes the pH levels of oceans and it comes out of volcanoes,” Fortenberry said. “If we gain a better understanding of what the chemistry of sulfur can do, the technological commercialization that can come from that can only be realized with a foundation of fundamental knowledge.”

Sulfur is the 10th most abundant element in the universe and is considered a vital chemical element for planets, stars and life. The lack of molecular sulfur in space has been a mystery for years.

“The observed amount of sulfur in dense molecular clouds is less – compared to predicted gas-phase abundances- by three orders of magnitude,” Kaiser said.

The answer might lie in interstellar ice.

In cold regions of space, sulfur can form two distinct, stable configurations: octasulfur crowns, which are a group of eight sulfur atoms configured in ring-like crowns, and polysulfanes, chains of sulfur atoms that are bonded by hydrogen. These molecules can form on icy dust grains, locking sulfur into solid forms.

“If you use, for instance, the James Webb Space Telescope, you get a specific signature at specific wavelengths for oxygen and carbon and nitrogen and so forth,” Fortenberry said. “But when you do that for sulfur, it’s out of whack, and we don’t know why there isn’t enough molecular sulfur.

“What this work is showing is that the most common forms of sulfur that we already know about are probably where the sulfur is hiding.”

Kaiser and Fortenberry’s research showed that these sulfur-rich molecules may be abundant in icy regions of interstellar space, giving astronomers a potential road map to solving the sulfur puzzle.

“Laboratory simulations of interstellar conditions such as this study discover possible inventories of sulfur-containing molecules that can be formed on interstellar ices,” Kaiser said. “Astronomers can then utilize the results and look for these polysulfane molecules in the interstellar medium via radio telescopes once sublimed into the gas-phase in star forming regions.”

The reason sulfur has been so difficult to find is that the bonds it forms are always changing, going from crowns to chains and a variety of other formulations.

“It never maintains the same shape,” Fortenberry said. “It’s kind of like a virus – as it moves, it changes.”

The researchers’ work identifies possible stable configurations that astronomers can search for in the universe.

“The thing that I love about astrochemistry is that it forces you to ask hard questions, then forces you to come up with creative solutions,” Fortenberry said. “And those hard questions and creative solutions can have significant, unintended positive consequences.”

Michael Hill, a professor of chemistry at Occidental College, will present his team’s results at the fall meeting of the American Chemical Society (ACS). ACS Fall 2025 is being held Aug. 17-21; it features about 9,000 presentations on a range of science topics.

Human corneas are dome-shaped, clear structures that sit at the front of the eye, bending light from surroundings and focusing it onto the retina, where it’s sent to the brain and interpreted as an image. But if the cornea is misshapen, it doesn’t focus light properly, resulting in a blurry image. With LASIK, specialized lasers reshape the cornea by removing precise sections of the tissue. This common procedure is considered safe, but it has some limitations and risks, and cutting the cornea compromises the structural integrity of the eye. Hill explains that “LASIK is just a fancy way of doing traditional surgery. It’s still carving tissue — it’s just carving with a laser.”

But what if the cornea could be reshaped without the need for any incisions?

This is what Hill and collaborator Brian Wong are exploring through a process known as electromechanical reshaping (EMR). “The whole effect was discovered by accident,” explains Wong, a professor and surgeon at the University of California, Irvine. “I was looking at living tissues as moldable materials and discovered this whole process of chemical modification.”

In the body, the shapes of many collagen-containing tissues, including corneas, are held in place by attractions of oppositely charged components. These tissues contain a lot of water, so applying an electric potential to them lowers the tissue’s pH, making it more acidic. By altering the pH, the rigid attractions within the tissue are loosened and make the shape malleable. When the original pH is restored, the tissue is locked into the new shape.

Previously, the researchers used EMR to reshape cartilage-rich rabbit ears, as well as alter scars and skin in pigs. But one collagen-rich tissue that they were eager to explore was the cornea.

In this work, the team constructed specialized, platinum “contact lenses” that provided a template for the corrected shape of the cornea, then placed each over a rabbit eyeball in a saline solution meant to mimic natural tears. The platinum lens acted as an electrode to generate a precise pH change when the researchers applied a small electric potential to the lens. After about a minute, the cornea’s curvature conformed to the shape of the lens — about the same amount of time LASIK takes, but with fewer steps, less expensive equipment and no incisions.

They repeated this setup on 12 separate rabbit eyeballs, 10 of which were treated as if they had myopia, or nearsightedness. In all the “myopic” eyeballs, the treatment dialed in the targeted focusing power of the eye, which would correspond to improved vision. The cells in the eyeball survived the treatment, because the researchers carefully controlled the pH gradient. Additionally, in other experiments, the team demonstrated that their technique might be able to reverse some chemical-caused cloudiness to the cornea — a condition that is currently only treatable through a complete corneal transplant.

Though this initial work is promising, the researchers emphasize that it is in its very early stages. Next up is what Wong describes as, “the long march through animal studies that are detailed and precise,” including tests on a living rabbit rather than just its eyeball. They also plan to determine the types of vision correction possible with EMR, such as near- and far-sightedness and astigmatism. Though the next steps are planned, uncertainties in the team’s scientific funding have put them on hold. “There’s a long road between what we’ve done and the clinic. But, if we get there, this technique is widely applicable, vastly cheaper and potentially even reversible,” concludes Hill.

Title Electrochemical corneal refraction

Abstract The cornea is a transparent, highly organized anatomical structure that is responsible for ~2/3 of the refractive power of the eye. The corneal stroma consists of orthogonally stacked collagen- fibril lamellae whose molecular composition and precise macromolecular geometry eliminate backscattered light and maintain the shape of the cornea. Anatomical variation, birth defects, trauma, and various pathologies can alter the shape, structural stability, and transparency of the cornea, thus affecting vision. Surgical interventions to treat myopia, hyperopia, and astigmatism include laser-assisted in situ keratomileusis (LASIK) and photorefractive keratectomy (PRK). Despite their popularity, these procedures are expensive and permanently lower the biomechanical strength of the cornea. Here we report our efforts to apply electromechanical reshaping (EMR) as a molecular- based, non-ablative/non-incisional alternative to laser vision refraction, using ex vivo rabbit globes. EMR relies on short electrochemical pulses to electrolyze interstitial water, with subsequent diffusion of protons into the extracellular matrix of collagenous tissues; protonation of immobilized anions within this matrix disrupts the ionic-bonding network that provides structural integrity. This leaves the tissue transiently responsive to mechanical remodeling; subsequent re-equilibration to physiological pH restores the ionic matrix, resulting in persistent shape change of the tissue. Optical coherence tomography (OCT), second-harmonic generation (SHG), and confocal microscopy suggest that EMR enables control over corneal contouring while maintaining the underlying macromolecular collagen structure and stromal cellular viability.

This research was funded by the National Eye Institute of the National Institutes of Health and the John Stauffer Charitable Trust.

To the point:

• Bridging mathematics and physics: The study explores how algebraic and one of the key players in the flourishing field of positive geometry unify physics from subatomic particles to galaxies.
• Beyond Feynman diagrams: Positive geometry offers a complementary perspective to traditional quantum field theory methods — providing a geometric framework for describing particle interactions alongside Feynman diagrams.
• From particle collisions to the Big Bang: Tools from algebraic geometry, D-module theory, and combinatorics drive this interdisciplinary progress — helping to decode the fundamental structures of particle interactions and the universe’s earliest states.

Mathematics and physics share a close, reciprocal relationship. Mathematics offers the language and tools to describe physical phenomena, while physics drives the development of new mathematical ideas. This interplay remains vital in areas such as quantum field theory and cosmology, where advanced mathematical structures and physical theory evolve together.

In their article, the authors explore how algebraic structures and geometric shapes can help us understand phenomena ranging from particle collisions such as happens, for instance, in particle accelerators to the large-scale architecture of the cosmos. Their research is centered around algebraic geometry. Their recent undertakings also connect to a field called positive geometry – an interdisciplinary and novel subject in mathematics driven by new ideas in particle physics and cosmology. This field was inspired by the geometrical concept of positive geometry which expands the standard Feynman diagram approach in particle physics by representing interactions as volumes of high-dimensional geometric objects, such as the amplituhedron, as introduced by the theoretical physicists Nima Arkani-Hamed and Jaroslav Trnka in 2013. It carries a rich combinatorial structure and offers an alternative, potentially simpler way to compute scattering amplitudes, from which one can derive probabilities of scattering events.

This approach has far-reaching implications that go beyond particle physics. In cosmology, scientists are using the faint light of the cosmic microwave background and the distribution of galaxies to infer what shaped the early universe. Similar mathematical tools are now being applied. For instance, cosmological polytopes, which are themselves positive geometries, can represent correlations in the universe’s first light and help reconstruct the physical laws that governed the birth of the cosmos.

A Geometry for the Universe

The article highlights that positive geometry is not a niche mathematical curiosity but a potential unifying language for form branches of theoretical physics. These geometric frameworks naturally encode the transfer of information between physical systems, for example, by mapping concrete, sensory-based concepts to abstract structures, a process that mirrors how humans metaphorically understand the world.

The mathematics behind this is sophisticated and spans multiple disciplines. The authors draw on algebraic geometry, which defines shapes and spaces through solutions to systems of polynomial equations, algebraic analysis, which studies differential equations through mathematical objects called D-modules, and combinatorics, which describes the arrangements and interactions within these structures.

The formal objects under consideration, such as Feynman integrals, generalized Euler integrals, or canonical forms of positive geometries, are not merely mathematical abstractions. They correspond to observable phenomena in high-energy physics and cosmology, enabling precision computations of particle behavior and cosmic structures alike.

Bridging Scales with Mathematics

The study presents an approach with broad applicability and scalability. Scattering processes are often illustrated using Feynman diagrams. Feynman’s approach in the study of scattering amplitudes boils down to the study of intricate integrals associated to such diagrams. Algebraic geometry provides a range of tools for systematically investigating these integrals.

The graph polynomial of a Feynman diagram is defined in terms of the spanning trees and forests of the underlying graph. The associated Feynman integral can be expressed as a Mellin transform of a power of this graph polynomial, interpreted as a function of its coefficients. These coefficients, however, are constrained by the underlying physical conditions. Feynman integrals are therefore closely connected to generalized Euler integrals, specifically through restrictions to the relevant geometric subspaces. One way to study these holonomic functions is via the linear differential equations they satisfy, which are D-module inverse images of hypergeometric D-modules. Constructing these differential equations explicitly, however, remains challenging. In theoretical cosmology, correlation functions in toy models also take the form of such integrals, with integrands arising from hyperplane arrangements.

The complement of the algebraic variety defined by the graph polynomial in an algebraic torus is a very affine variety, and the Feynman integral can be viewed as the pairing of a twisted cycle and cocycle of this variety. Its geometric and (co-)homological properties reflect physical concepts such as the number of master integrals. These master integrals form a basis for the space of integrals when the kinematic parameters vary, and the size of this basis is, at least generically, equal to the signed topological Euler characteristic of the variety.

A Field in Motion

Fevola and Sattelberger’s work reflects a growing international effort, supported by the ERC synergy grant UNIVERSE+ of Nima Arkani-Hamed, Daniel Baumann, and Johannes Henn, Bernd Sturmfels. It brings together mathematics, particle physics, and cosmology focusing on precisely these connections between algebra, geometry, and theoretical physics. “Positive geometry is still a young field, but it has the potential to significantly influence fundamental research in both physics and mathematics,” the authors emphasize. “It is now up to the scientific community to work out the details of these emerging mathematical objects and theories and to validate them. Encouragingly, several successful collaborations have already laid important groundwork.”

The recent developments are not only advancing our understanding of the physical world but also pushing the boundaries of mathematics itself. Positive geometry is more than a tool. It is a language. One that might unify our understanding of nature at all scales.