Tom Hutchcroft demonstrates hierarchical models of critical connections to provide optimal estimates for long-range percolation models.
MELVILLE, N.Y., May 16, 2023 – The Journal of Mathematical Physics has selected Tom Hutchcroft for the 2022 JMP Young Researcher Award. Hutchcroft’s winning publication, “Sharp hierarchical upper bounds on the critical two-point function for long-range percolation on ℤ𝑑,” demonstrated that hierarchical percolation models provide good quality estimates when compared to Euclidean models.
A panel of expert judges selected Hutchcroft for the $3,000 prize, which recognizes JMP authors within eight years of receiving their Ph.D. His paper will be highlighted on the journal’s website.
Originally from Glastonbury in South West England, Hutchcroft graduated from the University of Cambridge with degrees in mathematics in 2013. He obtained his Ph.D. in mathematics in 2017 from the University of British Columbia in Vancouver and served as a Herchel Smith Postdoctoral Research Fellow at the University of Cambridge from 2017 to 2020. In 2021, Hutchcroft became a professor of mathematics at the California Institute of Technology.
“I always found mathematics to be the most enjoyable subject I studied growing up,” Hutchcroft said. “I appreciate its problem-solving, puzzle-like nature, and I think that many of the most enticing problems in contemporary mathematics are found in mathematical physics!”
Hutchcroft is interested in phase transitions and critical phenomena in systems with interacting components governed by continuously varying parameters, such as temperature or pressure. When such a parameter passes a critical value, the system undergoes a phase transition, altering the system’s properties. These systems exhibit rich behavior at or near the critical values, which Hutchcroft investigates using probability models.
In particular, Hutchcroft focuses on critical phenomena in intermediate dimensions, including three and four, which are less understood than two dimensions or much higher dimensions. His prize-winning publication uses “long-range” percolation models to understand intermediate dimension critical phenomena.
“These models involve an extra parameter (describing the decay of the long-range interaction) that is closely analogous to the dimension of the lattice but is not restricted to integer values and can therefore be varied continuously,” said Hutchcroft. “Since the work of Freeman Dyson in the late 1960s, we have understood these models partly by studying hierarchical models, which are simplified versions of the same models that are significantly easier to understand.”
Previously, hierarchical models have been applied as rough, simplified approximations for real Euclidean models. Hutchcroft’s work proved these models produce high-quality estimates and are optimal in many cases.
“This paper revolutionized our understanding of long-range percolation,” said JMP editor-in-chief Jan Philip Solovej. “We might hope that the original methodology introduced in the paper can be adapted in greater generality and lead to novel understanding of short-range percolation models.”
Winning this award, Hutchcroft feels, validates his decision to pursue the interdisciplinary field of mathematical physics. He will continue his work by applying these results to other models.
The article, “Sharp hierarchical upper bounds on the critical two-point function for long-range percolation on ℤ𝑑,” is authored by Tom Hutchcroft. It published in the Journal of Mathematical Physics on November 4, 2022 (DOI: 10.1063/5.0088450). It can be accessed at https://doi.org/10.1063/5.0088450.
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