Student Committee

Gwyn Bellamy is an expert on symplectic singularities and their applications in geometric representation theory and symplectic algebraic geometry. He is currently PI on an EPSRC standard grant and was previously CoI on the EPSRC programme grant “Enhancing Representation Theory, Noncommutative Algebra And Geometry Through Moduli, Stability And Deformations”. He loves exploring the Scottish wilderness, ideally by trying to race others to the top of mountains. 

I am a second year PhD student working with Antony Maciocia on computing the walls and moduli spaces for Bridgeland stability in higher dimensions.

I am interested in symplectic geometry and other closely related topics. My work is focused on quantitative symplectic geometry, particularly symplectic embedding problems.  Currently, I am looking at the question of existence of “infinite staircases”, a phenomenon which arises in some instances of this kind of problems. Some other tools that are useful in this context and which I am interested in include almost toric fibrations (ATFs) and embedded contact homology (ECH).

 My research interests are in low dimension topology, quantum invariants, group theory, and representation theory. I am interested in areas where these topics come together in various ways.
At the moment I’m looking into Thompson knot theory, and I am always happy to talk about different topics in math!

I am working in representation theory, specifically, my project is focused on solvable lattice models and similar combinatorial tools that are used to study various objects in connection to geometry, mathematical physics and number theory. At the moment, I am interested in crystal graphs, specifically Demazure crystals

I am a final year PhD student working with Lotte Hollands. My current project tries to understand the role of spectral networks in 2d conformal field theory. This has deep connections to 4d supersymmetric field theories, quantum topology and exact WKB analysis.

I am interested in the geometry of moduli spaces of vector bundles and Higgs bundles, and nonabelian Hodge theory.

I am currently interested in the Morse boundary and constructing Coxeter groups whose Morse boundaries exhibit specific topological properties. In particular, I am working with the Sierpiński carpet and the Menger curve, which are fractal-like topological spaces that arise as Morse boundaries. I am also broadly interested in quantitative and probabilistic methods in geometric group theory. Previously, I worked on a quantitative version of guessing geodesics, a set of conditions ensuring that a given metric space is hyperbolic, and obtained an explicit hyperbolicity constant.

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.