Faculty

Andrew Baker | |

I have recently retired 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. | |

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. | |

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. | |

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. | |

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. | |

Maxime Fortier Bourque | |

I am mainly interested in the geometry (conformal, hyperbolic, and spectral) of Riemann surfaces. In particular, I study extremal problems asking which surfaces or maps maximize or minimize a given geometric invariant. More generally, I am interested in moduli spaces of geometric structures on manifolds, which themselves often admit natural metrics. For instance, there are many fruitful analogies between the space of flat tori of dimension n, the space of hyperbolic surfaces of genus g, and the space of metric graphs with first Betti number b. | |

Vaibhav Gadre | |

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

Sira Gratz | |

My research focuses on applying combinatorial methods to solve questions arising in representation theory; in suitable frameworks, abstract concepts from representation theory can be made tangible using combinatorics and, quite simply, pictures. More specifically I am interested in cluster algebras and cluster categories of infinite rank, in classification problems in triangulated categories, and in the relations between cluster algebras and representation theory. | |

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. | |

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. | |

Ef Sofos | |

I am a number theorist. | |

Greg Stevenson | |

My research concerns various aspects of the interplay between representation theory, algebraic geometry, commutative algebra, and homotopy theory. I think about things like: derived and singularity categories, tensor triangular geometry, lattices of subcategories, Maximal Cohen-Macaulay modules, tilting objects and exceptional collections, cluster-tilting theory, strong generators and generation times in triangulated categories, Hochschild (co)homology, Koszul duality, brave new algebra, and the representation theory of various gadgets such as groups, posets, and other small categories. | |

Daniele Valeri | |

My research interests lie in the interplay between representation theory and mathematical physics. In particular, I like to use algebraic techniques, coming from Lie theory and vertex algebra theory, to approach problems arising in mathematical physics, such as applications to (quantum and classical) integrable systems, Conformal Field Theory and invariant measures for dynamical systems. | |

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. | |

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, Baker-Akhiezer functions and Hadamard’s problem in the theory of Huygens’ Principle, as well as in the relations between all these areas. | |

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. |

#### Fellowships, Postdocs and Temporary Lecturers

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. | |

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. | |

Carlo Pagano | |

I am a number theorist, working with Alex Bartel. | |

Arthur Soulie | |

My research lies at an interface between algebraic topology, representation theory and category theory. Namely, my research focuses on the study of the representations of braid groups, mapping class groups of surfaces and 3-manifolds, and on the computation of the associated stable twisted homology of these groups. | |

Wahei Hara | |

I'm a Research Associate, working in algebraic geometry. My mentor is Michael Wemyss. I am currently interested in the derived category of algebraic varieties. Especially I have an interest for the notion of noncommutative crepant resolutions. I am also interested in birational geometry of higher dimensional varieties, vector bundles and representation theory. |

#### Graduate Students

Georgios Antoniou | |

I am a third year student under the supervision of Misha Feigin and Ian Strachan. I am working in the area of Integrable systems/Mathematical physics and so far I have been focused on the study of Frobenius manifolds related to finite Coxeter groups. | |

Vitalijs Brejevs | |

I am a second year PhD student with an interest in low-dimensional geometry and topology, jointly supervised by Brendan Owens and Andy Wand. | |

Okke van Garderen | |

I have a background in mathematical physics, and I am mainly interested in non-commutative geometry and Donaldson-Thomas invriants. At the moment I am studying invariants of flops under the supervision of Michael Wemyss and Ben Davison. | |

Dimitris Gerontogiannis | |

I am interested in the index theory of discrete hyperbolic dynamical systems, in particular Smale spaces. These are spaces that locally can be decomposed into expanding and contracting sets (under the dynamics). Under some mild recurrence conditions on the system, a Smale space can been seen as some sort of "foliation", however the leaves might be highly non-smooth. Some examples are hyperbolic toral automorphisms, subshifts of finite type, tiling spaces, solenoids etc. One can recover interesting topological invariants for the dynamical system by following this non-commutative geometrically flavoured circle: dyn.systems -> groupoids ->C*-algebras -> KK-theory and Index theory. | |

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. | |

Naill Hird | |

I am a final year PhD student working in representation theory, with Gwyn Bellamy. | |

Sarah Kelleher | |

I am a third year PhD student, supervised by Michael Wemyss and Gwyn Bellamy. I am interested in algebraic geometry and homological algebra, through weighted projective planes. | |

Jessica Ryan | |

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

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 have just started my PhD under the supervision of Vaibhav Gadre and Maxime Fortier-Bourque. | |

Lisa Lokteva | |

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

Tanushree Shah | |

I am PhD student under the supervision of Ana Lecuona, Brendan Owens and Andy Wand. I am interested in Low dimensional topology. |