Stockholm Mathematics Centre Prizes for Excellent Doctoral Dissertation and Master Theses 2016/2017
Excellent Doctoral Dissertation
To be announced in November.
Excellent Master Theses
Carolina Fransson's thesis concerns properties of stochastic epidemics spreading on certain random graph structures. The analysis is carried out by using coupling arguments which link the original stochastic process with a multi-type branching process. Not only does the thesis provide an excellent introduction to random graphs, coupling techniques and multi-type branching processes, but it also contains new original results concerning the epidemic process being studied. These results cannot be obtained without an exceptional understanding of the topic.
Viktor Qvarfordt's impressive and well-written thesis is devoted to the analysis of a class of two-dimensional quantum particles known as anyons; the rich structural properties of these particles is related to the nature of representation theory of the braid group. Qvarfordt's thesis contains a lucid introduction to the mathematical background needed to understand the basics of anyon theory and extends known results on abelian anyons to the non-abelian case. Qvarfordt illustrates the general theory by examining a special class of particles, dubbed Fibonacci anyons, in detail, obtaining explicit results and pointing out intriguing connections with topological quantum computing.
Innokentij Zotov’s thesis is a detailed analysis of properties of modular forms reduced modulo a prime. The thesis is very well-written, and shows a mastery of a wide range of advanced techniques in algebraic geometry, complex functions theory, representation theory and number theory. It gives a detailed exposition of a result of Serre, which says that systems of Hecke eigenvalues arising from modular forms modulo p coincide with those arising from super-singular modular forms. The work is motivated by the Geometric Langlands Program. It brings the author to the state-of-the-art of current research, and shows that he is in an excellent position to approach difficult and important problems at the intersection of algebraic geometry and representation theory.