# 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**

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**

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**

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.