Cohort 2

My field of interest is Geometric Group Theory. In particular, I would like to understand the action of Artin groups on certain geometric spaces to try and prove some properties of these groups.   If I am not at work, I am probably playing guitar, playing cards or on a walk.

My general interest lies in geometric representation theory and algebraic geometry. In particular, I am studying moduli spaces of sheaves and derived equivalences.

Fun Fact: I enjoy baking in my spare time and am trying to become a decent bartender.

The field of mathematics I am interested in is geometric group theory. In particular, in my project I will be thinking about boundaries of hyperbolic groups; these are groups that act nicely on a space with hyperbolic structure. More specifically, I will focus on relatively hyperbolic groups and their boundaries. 

I am working on geometric problems in physics, mainly relating to the mathematical description of black holes inside of general relativity and related theories.

I am currently learning Higher Topos theory. I’m excited to work with the language of categories in general. Fun fact: I love dancing. I learned Bharatanatyam in school and have enjoyed dance ever since.

I am broadly interested in the overlap of algebra and quantum physics. In particular, I am interested in the representation theory of Hecke algebras (and their double affine versions) with a  view towards understanding special functions and integrable quantum systems with long-range interacting spins.

I am interested in contact structures and their interactions with open books, Anosov flows, and foliations. I am also interested in moduli spaces of non-orientable hyperbolic surfaces.

The aim of my research is to understand thermal phenomena in QFT, such as the emergence of fluid dynamics, using the AdS/CFT correspondence as well as other field-theoretic methods. Another topic I am passionate about is the study of entanglement in QFT and holography.

My research interests are primarily on topological solitons in 2+1 dimensional field theories describing condensed matter systems. At the moment, I am particularly interested in the dynamics and quantisation of magnetic Skyrmions.

My research interests are in non-commutative geometry, and in particular quantum groups. One of my current goals is to understand how self-similarity properties of classical groups translate to the context of quantum groups.

I’m interested in C*-algebras in general, and during my PhD I will focus on their connections with groupoids. At the moment, I’m studying techniques related to non-Hausdorff étale groupoids. Fun fact: the first time I ever travelled by plane was when I moved to Scotland.

My research interests can roughly be described by the motto that “Geometry determines Arithmetic”. More specifically, at the moment I am interested in Manin’s conjecture, which links the distribution of rational points on an algebraic variety to a geometric invariant called the Picard rank.

I am currently working on understanding the Rauzy Gasket, how it can be interpreted as a hyperbolic analog to the Sierpinski Gasket, and the relationship to the Minkowski question mark function. Broadly speaking, this can be seen as a more complicated case of relating dyadic expansions of numbers (a parabolic representation) to the corresponding continued fraction expansions (a hyperbolic representation).

Research Interests: My primary research interests are universal algebra and category theory.

I am interested in low-dimensional topology and contact topology. Currently, I am learning about 4-manifolds and Heegaard Floer homology, with a focus on understanding intersection forms, Seiberg-Witten gauge theory, and Donaldson’s diagonalisation theorem.