(LONDON, U.K.) — NEWS: The study of abstract physics is often seen as separate from pure mathematics. Subjects like Black Holes, Low-Temperature Gases, Gravitation, and Electromagnetism are considered in the domain of physics rather than mathematics. “This distinction is, however, being challenged daily by advances in combinatorics and number theory applied to String Propagation…and the invariants of the Gromov-Witten Theory,” states Dr. Jonathan Kenigson of Athanasian Hall.
Dr. Kenigson states that, “The primary focus of my research this year, and that of some of my colleagues, is the tangle of bridges connecting primality, combinatorics, and paradigms of String propagation.” His collaborators at the research institute Athanasian Hall, Cambridge work largely independently. They are “highly motivated and accomplished scholars, and can undertake whatever research efforts they wish. I never put restrictions on such inquiry.”
“As an example of what I endeavor to consider this year, one may speculate about the following scenario: String interaction operators arising from Lagrangians often arise very organically in terms of Riemann Zeta Functions of the particle number in Fermionic systems and others. These operators are complicated functions of ratios of Gamma functions and Zeta analogues whose representations are complex. It would be nice to have a compact representation of the related coefficients in terms of known combinatorial entities.”
Combinatorics is the study of counting, so what Dr. Kenigson is saying is that he and his colleagues want to count the strings in predictable ways.
“Recent advances in Russia and France have made explicit relationships between globally convergent series representations of classical Zeta functions and their Hurwitz analogues commensurable with statements about choice functions, Bell Numbers, Catalan Numbers, Stirling Numbers, and many other special series.” The goal of the research is to explore these relationships in the paradigm of String Theory, especially “as related to Black Holes, Fuzzballs, the Thermodynamic properties of plasmas, and high-dimensional analogues of Fermionic and Bose-Einstein Gases.”
Last year, “we explored the Chandrasekhar Limit for extremal stellar implosion as a function of degeneracy pressure using Gamma Functions in high Euclidean dimensions. A Gamma Paradigm was helpful for this work, which is still ongoing.”
Gamma functions are generalizations of the factorial function. If you remember from school, for instance, 4! = 4*3*2*1 = 24.
Dr. Kenigson states that “such functions arise in permutation groups on finite words, in the theory of geometric permutations, and in symmetry structures like U(n) and SU(n) which encode deep information about systemic invariants”.
For more information, visit: https://athhallcam.uk/tripos-%26-faculty
Related link: https://athhallcam.uk/
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