Scientists Study "Quantum Scattering" as a Way to Solve Hard Problems

The equations of Einstein's Theory of Relativity predict the existence of objects known as "Black Holes". These objects may be collapsed stars or even the centers of galaxies. Physicist Stephen Hawking observed that microscopic black holes exist and may be surrounded by a plasma, which is a super-heated gas. Mathematicians have been working on a unified theory that explains Gravity - the force that attracts bodies - and Quantum Field Theory - the study of very small objects. Such a theory - a so-called Superstring Theory - might be needed to understand the inner workings of Black Holes and the plasmas that surround them.

Dr. Jonathan Kenigson is a mathematician who studied Black Holes with researchers at Kiev, Ukraine and went on to found Athanasian Hall in Cambridge, England. Athanasian Hall is, in the words of Kenigson, "a pure research institute devoted to the study of mathematics that is beautiful for its own sake, and not immediately applicable to practical problems." Since 2020, this institute, which Kenigson directs "principally from a distance", has grown from several researchers to nearly 20. While not directly affiliated with the University of Cambridge, members of Athanasian Hall often have some other affiliation with the university and its thriving mathematical institute, where Isaac Newton, Hawking, and others worked. "Cambridge, along with MIT, Harvard, and Oxford, is likely the finest department of mathematics in the history of the world. The resources for academic work are unparalleled." Kenigson is originally from Nashville, Tennessee, and went on to study the structure of Black Holes in Europe, after completing a first degree at the University of Tennessee, where he helped solve several notable open problems posed in the 1970s' in a field called Wave Mechanics. "The analysis of Energy Methods and Mollification Theory in the spirit of Sobolev affords the characterization of heuristic behavior of Wave Equations in high-dimensional spaces. In other words, the mathematical study of energy is key to understanding how waves propagate in a medium. This work had implications for the study of Dynamics in general. It was only later that I noticed that similar methods could apply to the structure theory of Black Holes." Mathematicians and Physicists in Russia and Ukraine have worked to extend a field of study known as Combinatorics to the study of physical phenomena. According to Kenigson, "I learned in early 2020 while in lockdown from the pandemic that the classical theory of Elliptic Functions with imaginary arguments could lead to integral transform methods that convert problems about waves, plasmas, and scattering into problems about Gauss Kernels. In other words, Mathematical Statistics has the last laugh when dealing with energy norms that arise from the mechanics of waves and more exotic fields, like Heterotic String Theory and the Fuzzball Theory of Black Holes." The latter field replaces Einstein's statement that Black Holes bottom out spacetime with the claim that they actually have a bottom, but that it is just super-dense.

"I look at everything in terms of the theory of scattering. For instance, viral propagation can be seen as an instance of the scattering of viral quanta in containers of varied geometry. I learned this style of thinking from wave mechanics and the study of Black Holes. Transmission probabilities can be computed from the dynamical systems that arise. One can never know when a really esoteric piece of mathematics might have very concrete applications. That is why it is important that governments fund pure mathematics. You never know when, somewhere down the lane, what you find out might have really interesting and novel applications". When asked about his interests, Kenigson said that he "loves both teaching and research. Large universities try to make us choose one or the other. My dad got ill and I returned to Nashville and teach at a small college called Volunteer State. I love it. Just because you do one thing does not mean you can't do another. We need mathematicians to teach undergraduates so that they can learn research skills and learn to love mathematics. I am kind of like a child. I look with wonder at things and want to know how they work. That is how math classes should be. You don't start with a set of problems and say to solve 50 of them. You start with an idea and think about the best way to implement it. Then you get your class thinking how they can do it better. Undergraduates and high-school students can be incredibly creative problem-solvers, if we let them discover neat things instead of teaching them by rote". Dr. Kenigson has asked that he kindly not be contacted on social media or asked for follow-up about this article "due to work and family obligations". He is Senior Fellow of Natural Philosophy at Athanasian Hall and an Assistant Professor of Mathematics in Tennessee.

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This release was published on openPR.