#### Faculty

Alex Bartel | |

My interests lie between number theory and representation theory. At the moment, my main number theoretic interest is in the area called Arithmetic Statistics, in particular in the Cohen-Lenstra heuristics on ideal class groups and its many generalisations and variants. I also think about the arithmetic of elliptic curves over number fields, and about the Galois module structure of arithmetic objects, such as rings of integers of number fields, their units, and their higher K-groups. In Representation Theory I think about rational and integral representations of finite groups. Recently, I have also done some research on group actions on the cohomology of low-dimensional manifolds. | |

Jim Belk | |

My research interests include geometric group theory, dynamical systems, and fractal geometry. Within group theory, I am especially interested in discrete groups of homeomorphisms such as Thompson's groups and self-similar groups, and associated questions about computability, finiteness properties, and embeddings. Within dynamical systems my main interest is complex dynamics, including Thurston equivalence of branched covers, connections to mapping class groups and Teichmüller theory, and the topology and quasiconformal geometry of Julia sets. I am also interested in dynamics of homeomorphisms more broadly, including symbolic dynamics, as well as homeomorphism groups of fractals. See my web page for more information. | |

Gwyn Bellamy | |

I am interested in representation theory and its interaction with geometry. In particular, I am interested in anything that is even remotely related to symplectic reflection algebras (and especially rational Cherednik algebras). To date, "anything" includes symplectic algebraic geometry, D-modules, Calogero-Moser systems, algebraic combinatorics and the representation theory of certain objects of Lie type such as Hecke algebras. I am especially interested in the relationship between symplectic reflection algebras and sheaves of deformation-quantization algebras on symplectic manifolds. My papers can be found on my webpage or on the arXiv. | |

Rachael Boyd | |

I am interested in developing new methods to study algebraic objects through the lenses of geometry and topology. Some topics I'm interested in are Artin and Coxeter groups and monoids, classifying spaces of groups and group homology, topological invariants of diagram algebras and corresponding applications to low-dimensional topology, and low-dimensional embedding spaces. The majority of my work consists of building geometric models to study groups and algebras, such as semi-simplicial spaces, cube complexes and embedding spaces. | |

Tara Brendle | |

My main research interests involve the interplay between algebra and topology. The automorphism group of a surface is a fundamental object in geometric and combinatorial group theory, low-dimensional topology, and algebraic geometry, for example. My research focuses on how these mapping class groups of surfaces are related to other important classes of groups such as braid groups and Coxeter groups, arithmetic groups, and automorphism groups of free groups, as well as the role played by these groups in determining the structure of 3- and 4-manifolds via constructions such as Heegaard splittings and Lefschetz fibrations. | |

Ruadhaí Dervan | |

I research complex geometry, which is roughly the intersection of algebraic geometry and differential geometry. My current work lies in between the two areas, using ideas and tools from both sides: in practice much of my work asks analytic questions about projective varieties. Most of my work is motivated by the "Yau-Tian-Donaldson conjecture", which links the existence of Kähler metrics with special curvature properties on a projective variety (which is the analytic, PDE side) with a purely algebro-geometric condition called K-stability; this is a rich area with deep links to moduli theory, birational geometry, geometric analysis along with many others, and I also have interests in these adjacent areas. | |

Vaibhav Gadre | |

My research is broadly in geometry, topology and dynamics, specifically in the field of Teichmuller dynamics. | |

Damián Gvirtz-Chen | |

I investigate questions in higher-dimensional arithmetic geometry, which employs a wide range of methods at the intersection of algebraic geometry and number theory. Much of what I do tries to follow and establish the mantra "geometry determines arithmetic", according to which we can control the behaviour of rational points on algebraic varieties by their underlying geometry. A particular focus of my activities have been conjectures about rational points on K3 surfaces, which roughly occupy a similar place in two dimensions as elliptic curves do in one dimension, from the point of view of Brauer-Manin obstructions as well as the Hilbert Property. | |

Ana Lecuona | |

My main research interests lie in the field of low dimensional topology. I try to understand the relationship between knots and 3 and 4 dimensional manifolds. This is mainly done by computing, defining and studying invariants. I find the invariants sensitive to the difference between the topological and smooth categories particularly fascinating. | |

Xin Li | |

I am working on C*-algebras and their connections to other mathematical disciplines such as topological dynamics, group theory or number theory. My research interests include semigroup C*-algebras, K-theory, Cartan subalgebras of C*-algebras, continuous orbit equivalence, and topological full groups. | |

Dinakar Muthiah | |

My interests lie in Representation Theory and Algebraic Geometry. Specifically, I am interested in loop groups and double loop groups. This involves many aspects: affine Grassmannians, p-adic groups, Hecke algebras, and recently quiver varieties and Coulomb branches to name a few. Through p-adic groups, many of these topics make contact with number theory and the Langlands program. | |

Brendan Owens | |

My research is in low-dimensional topology. I am interested in smooth 3-manifolds, 4-manifolds and knots, and in the use of gauge-theoretic invariants of manifolds, especially Floer homology groups. | |

Mark Powell | |

I work in algebraic and geometric topology, especially on the topology of manifolds. I specialise in low dimensional topology, i.e. 3- and 4-manifolds, both smooth and topological. I'm also fascinated by higher dimensions, and often seek to apply high dimensional methods to 4-manifolds. I'm interested in classifying manifolds, understanding their symmetries, and studying embeddings. For this I've employed a range of methods from surgery theory, Morse theory, homotopy theory, Floer theory, and point set topology to homological algebra, number theory, group theory, functional analysis, and more. | |

Anna Puskás | |

I work at the intersection of number theory, representation theory, and algebraic combinatorics. Most of my research concerns reductive groups over a non-archimedean field, and corresponding Hecke algebras. More specifically, generalisations of this topic to the context of metaplectic covering groups or to infinite-dimensional Kac-Moody groups. I especially enjoy applying tools from algebraic combinatorics to describe the behaviour of objects from representation theory. Recently, I have also become interested in questions concerning the arithmetic geometry of character varieties. | |

Efthymios Sofos | |

My work lies in analytic number theory and arithmetic geometry. I have worked on Manin's conjecture on counting rational points, Schnizel's Hypothesis (H) on prime values of polynomials, Serre's problem on random Diophantine equations and Sarnak's problem on almost prime solutions of Diophantine equations. Lately, I have been looking at connections of these areas with Brownian motion. My papers are on my webpage, arXiv, or Google Scholar. | |

Christian Voigt | |

My research area is noncommutative geometry, with connections to classical disciplines like number theory, topology and mathematical physics. I work in particular on problems in operator K-theory, cyclic cohomology and the theory of quantum groups. | |

Andy Wand | |

My research is in contact and symplectic topology and geometry, mostly focused on the low-dimensional setting. | |

Michael Wemyss | |

My main research interests are in algebraic geometry and its interactions, principally between noncommutative and homological algebra, resolutions of singularities, and the minimal model program. In the process of doing this, I have research interests in all related structures, including: deformation theory, derived categories, stability conditions, associated commutative and homological structures and their representation theory, curve invariants, McKay correspondence, Cohen--Macaulay modules, finite dimensional algebras and cluster-tilting theory. My papers can be found on my webpage, arXiv, or Google Scholar. | |

Michael Whittaker | |

My primary research interest is the connection between topological dynamical systems and operator algebras. One can associate a C*-algebra to a dynamical system that can be used to ascertain dynamical invariants in a noncommutative framework. Some of my specific interests in this area include hyperbolic dynamical systems called Smale spaces, self-similar group actions, graph and k-graph algebras, and aperiodic substitution tilings. Using the noncommutative geometry program, developed by Alain Connes, these algebras are used to construct K-theoretic invariants including Poincaré duality classes, KMS equilibrium states, and spectral triples. | |

Andrew Wilson | |

My research interests lie in Algebraic Geometry and applications, specifically Birational Geometry and problems surrounding the Minimal Model Program. I also have a keen interest in the Learning & Teaching of Mathematics. Please see my personal webpages or UofG webpage for more information. | |

Runlian Xia | |

My research interests lie in the interactions between operator algebras and harmonic analysis, and their connections to geometric group theory and non-commutative geometry. Most recently I have been particularly interested in Calderón–Zygmund operators/Fourier multipliers on non-commutative Lp spaces associated with von Neumann algebras (non-commutative counter parts of measure spaces). | |

Joachim Zacharias | |

My research interests are in C*-algebras and their applications. C*-algebras and their measure theoretical counterpart, von Neumann algebras, are algebras of operators on a Hilbert space. I am particularly interested in classification of simple nuclear C*-algebras, non commutative dimension concepts, dynamical systems, special examples of C*-algebras, in particular the very rich class of Cuntz algebras and various generalisations (graph, Pimsner, higher rank, continuous etc.), K-theory for those C*-algebras, approximation properties of C*- and von Neumann algebras, dynamical systems and their applications to C*-algebras, noncommutative geometry (spectral triples). |

#### Other faculty in Glasgow with related interests

Chris Athorne | |

Broadly speaking my interests arise from issues in "integrability" of differential systems. This has included study of monopoles in Yang-Mills-Higgs theories and solitons both from a hamiltonian and algebraic point of view. Most recently I've been working on invariants of linear partial differential operators which are connected with Toda field theories and with generalised Weierstrass P-functions for Riemann surfaces of genus greater than one. | |

Misha Feigin | |

The area of my research is theory of integrable systems in relations with algebra, geometry and mathematical physics. More specifically, I am interested in quantum integrable systems of Calogero-Moser and Ruijsenaars-Macdonald types, Coxeter and other hyperplane arrangements, rings of quasi-invariants, representations of Cherednik algebras, Frobenius manifolds, as well as in the relations between all these areas. Various PhD projects in these areas are available. Please see some more details at the link and please feel free to get in touch. | |

Christian Korff | |

I am interested in areas where algebra and representation theory meet problems arising in physical systems. My research focusses on quantum integrable models connected with solutions of the Yang-Baxter equation. The latter include exactly solvable lattice models in statistical mechanics, quantum many body systems and lower dimensional quantum field theories. My papers can be found on my webpage and arXiv. | |

Kitty Meeks | |

My interests lie at the interface of pure maths and theoretical computer science, including (but not limited to!) graph theory, combinatorial algorithms, parameterised complexity and real-world networks. I am particularly interested in using mathematical insights to make the study of computational complexity more relevant to practical computational problems: much of my recent research focuses on trying to understand how mathematical structure in datasets can be exploited to develop more efficient algorithms. My papers can be found on my webpage. | |

Ian Strachan | |

My research interests are in integrable systems and mathematical physics. In particular I am interested in Frobenius manifolds and their applications. Such objects lie at the intersection of many areas of mathematics, from Topological Quantum Field Theories (TQFT's), to quantum cohomology, singularity theory and mathematical physics. Specific areas of interest are: symmetries of Frobenius manifolds and related structures; bi-Hamiltonian geometry and the deformation of dispersionless integrable systems. An informal introduction to the theory may be found here: What is a Frobenius Manifold?. My papers may be found on arXiv and on ResearchGate. Other interests are in the connections between integrable systems, Donaldson-Thomas invariants and complex hyperKahler geometry. |

#### Emeritus

Andrew Baker | |

I retired in 2018 to devote time to research and writing. My main research interests are in Algebraic Topology, especially stable homotopy theory, operations in periodic cohomology theories, structured ring spectra including Galois theory and other applications of algebra, number theory and algebraic geometry. For further information see the above web page and my personal home page. | |

Kenneth Brown | |

My main research interests are in noncommutative algebra, more specifically the structure of noncommutative rings and algebras and of their representations. At present my focus is primarily on Hopf algebras, on quantum groups and on homological questions, but in the past I have worked on symplectic reflection algebras, on enveloping algebras, on rings of differential operators, on group rings, and on invariant rings, as well as on "abstract" noetherian ring theory, and I maintain an active interest in all these topics. I have recently retired and so am no longer supervising PhD students, but I am happy to give informal advice on any of the above subjects. |

#### Fellowships, Postdocs and Temporary Lecturers

Rebecca Bellovin | |

I am a number theorist working as a Rankin–Sneddon Fellow. | |

Christian Bonicke | |

My research focuses on the structure and K-theory of C*-algebras. I am particularly interested in C*-algebras associated to various sorts of (generalized) topological dynmical systems. Starting with such a system (e.g. a discrete group acting on a topological space by homeomorphisms) one constructs a C*-algebra and studies its properties and how they relate back to properties of the underlying system. Using the language of groupoids as a unifying framework, I try to uncover the principles underlying the behaviour of seemingly very different classes of examples. | |

Timothy De Deyn | |

I am a research associate working in (noncommutative) algebraic geometry. My mentor is Michael Wemyss. Broadly my interests are in algebraic geometry and categorical incarnations of this. My current research focusses on the interactions between commutative and noncommutative algebraic geometry, more precisely on noncommutative resolutions of various kinds with applications to noncommutative motives in mind. Lately, I have also been thinking about Brauer groups and have been delving into the realm of tensor triangular geometry. | |

Maxime Fairon | |

I am interested in the relations that exist between algebraic and geometric structures in the context of integrable systems. In particular, I study the non-commutative versions of Poisson geometry defined on associative algebras in order to find new classes of integrable systems on the representation spaces associated to these algebras. | |

Jacek Krajczok | |

I am a research associate interested in the theory of topological quantum groups (their approximation properties, properties related to (non)unimodularity and type I quantum groups), as well as operator algebras and operator spaces. | |

Emma Lepri | |

I am a research associate, working in algebraic geometry. My mentor is Michael Wemyss. My research interests revolve around deformation theory, differential graded Lie algebras and L-infinity structures. Recently, I have also become interested in noncommutative deformations. | |

Adam Morgan | |

I am a number theorist working as a postdoc. | |

Matthew Pressland | |

I'm an EPSRC postdoctoral fellow working on the interplay between representation theory (primarily of associative algebras), cluster algebras and algebraic geometry. At the moment I am especially interested in how structures in all of the above areas may arise from dimer models, certain graphs on surfaces appearing in mathematical physics. A theme of my work is "categorification": finding conceptual explanations for combinatorial phenomena using homological algebra. | |

Franco Rota | |

I'm a Research Associate, I work in algebraic geometry with Michael Wemyss. My interests are complex and algebraic geometry. In particular, I'm interested in derived categories, moduli spaces of sheaves, Bridgeland stability conditions, the stability manifold and its relation with mirror symmetric questions. |

#### Graduate Students

Robin Ammon | |

I am a PhD student in number theory, working with Alex Bartel. I am interested in algebraic number theory and arithmetic statistics. | |

Aitor Azemar | |

I am mostly interested in the interplay between geometry and probability. In particular, the behaviour of random walks on geometric spaces, and the ways we might extract geometric properties from that. I am also interested in applying random walks to real life problems. Lately I have been looking into using random walks to measure the polarization of social subnetworks. I am doing a PhD under the supervision of Vaibhav Gadre and Maxime Fortier-Bourque. | |

Philipp Bader | |

I am a second year PhD student, supervised by Vaibhav Gadre and Tara Brendle. My research interests lie in low dimensional topology, in particular mapping class groups of surfaces. I am currently working on questions related to pseudo Anosov theory, as well as moduli spaces of translation surfaces. | |

Charlotte Bartram | |

I am a second year PhD student, working with Michael Wemyss. | |

Giulia Carfora | |

I am a third year PhD student, working with Brendan Owens. I am interested in low dimensional topology and knot theory. I am currently working on smooth embeddings of the real projective plane in 4-space. | |

Simone Castellan | |

I am a second year PhD student, working with Gwyn Bellamy and Daniele Valeri. I am broadly interested in algebra and representation theory, in particular I like topics that have connections to mathematical physics. I'm currently working on some problems related to deformation quantization of Poisson and Poisson vertex algebras. | |

Ujan Chakraborty | |

I am a second year PhD student supervised by Joachim Zacharias and Runlian Xia. I am interested in several aspects of noncommutative functional analysis centred around C* Algebra theory. Currently I am studying some problems in classification and dynamics. | |

Gabriel Corrigan | |

Hi! I am a first-year PhD student, supervised by Rachael Boyd and Tara Brendle. I live somewhere at the intersection of algebra and topology - in particular, in low-dimensional topology and geometric group theory. I have recently been studying automorphisms of right-angled Artin groups, and their connections to other areas of interest, such as certain embedding spaces. I am happiest when I have the opportunity to study algebraic structures from a geometric or topological viewpoint. | |

Rhys Davies | |

I'm a second year PhD student supervised by Gwyn Bellamy. I'm broadly interested in algebra, geometry and topology, with a particular interest in geometric representation theory. I'm currently working with rational Cherednik algebras. | |

Lewis Dean | |

Second year PhD student, supervised by Christian Korff. I'm part of the Glasgow integrable systems & mathematical physics group, with an interest in topological quantum field theory. | |

Gabriel Frey | |

I am a first year PhD student from Switzerland, under supervision of Ruadhaí Dervan. My interests lie in the realm of complex algebraic geometry, including Kähler geometry, K-stability and moduli theory. | |

Daniel Galvin | |

I am a third year PhD student supervised by Mark Powell. I work primarily on 4-manifolds, both smooth and topological. | |

Marina Godinho | |

My interests centre around algebraic geometry, non-commutative and homological algebra, as well as category theory. Currently, I'm a second year PhD student supervised by Michael Wemyss. | |

Isambard Goodbody | |

I'm a PhD student supervised by Greg Stevenson. Here are some things I'm interested in: homological algebra, representation theory, homotopy theory, triangulated categories and their enhancements. | |

Luke Hamblin | |

I'm interested in classification of C*-algebras, and in particular the application of different ideas of dimension to the classification program. My focus at present is widening the application of the so-called Rokhlin dimension, and on the classification of C*-algebras associated to tilings. | |

Sam Lewis | |

I am a third year PhD student, supervised by Gwyn Bellamy and Michael Wemyss. I am interested in preprojective algebras, derived categories and stability conditions, with a particular interest in the wild case. I am currently thinking about real variations of stability conditions for hyperbolic quivers, such as the n-Kronecker for n>=3. | |

Lisa Lokteva | |

I am a PhD student under the supervision of Ana Lecuona. I am interested in topology, algebraic geometry, model theory, and their interactions. | |

Mohammad | |

First year PhD - supervised by Christian V and Xin. Love C*-algebras, low-dimensional topology, category theory, and logic. | |

Ross Paterson | |

I am a number theorist in my last year of PhD supervised by Alex Bartel. | |

Francesco Pagliuca | |

I am a first year PhD student supervised by Christian Voigt. I am mainly interested in Noncommutative Algebra, Noncommutative Geometry and Groupoids. | |

Mark Pencovitch | |

I am a PhD student supervised by Mark Powell and I'm interested in 4-manifolds and knotted surfaces. | |

Jessica Ryan | |

I am a third year PhD student supervised by Kitty Meeks. My research interests include graph theory, graph algorithms and parameterised complexity. | |

Tanushree Shah | |

I am a final year PhD student under the supervision of Ana Lecuona, Brendan Owens and Andy Wand. I am interested in low dimensional topology and geometric group theory. | |

Parth Shimpi | |

I started my PhD in 2022, under the supervision of Michael Wemyss. My interests include commutative and homological algebra, algebraic geometry, and derived categories. | |

Cameron Wilson | |

I am a number theorist currently in my first year of PhD supervised by Efthymios Sofos. My interests lie in analytic number theory and arithmetic geometry. I am funded by a PhD scholarship from the Carnegie Trust. | |

Weizhe Niu | |

I am a fourth-year PhD student working with Brendan Owens. I am interested in low-dimensional topology, especially the mapping class group of 3- and 4-manifolds. | |

Hao Zhang | |

I am a third year PhD student working with Michael Wemyss on contraction algebras. |