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. 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. | |

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. | |

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. | |

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. Other interests are in the connections between integrable systems, Donaldson-Thomas invariants and complex hyperKahler geometry. |

#### 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. | |

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. | |

Adam Morgan | |

I am a postdoc working in number theory. | |

Carlo Pagano | |

I am a number theorist, working in the group of Alex Bartel. My main research interests at the moment are in arithmetic statistics and arithmetic dynamics, but I have broad interests within number theory and have recently been thinking also about rational points and sphere packings. In arithmetic statistics I have been thinking about the statistics of solvability of conics over the integers, recently settling jointly with Peter Koymans a conjecture of Nagell in the refined form proposed by Stevenhagen on the solvability of the negative Pell equation. More generally my interests in the area are on a broad set of conjectures known as Cohen--Lenstra: jointly with Alex Bartel and Efthymios Sofos I have been extending them to setting of ray class groups. I have been working also on the statistics of non-vanishing of L-functions at special points and on Malle's conjecture. In dynamics I have been working mostly in trying to prove that typically dynamical Galois groups are as large as possible: in particular I have been working on a conjectural classification of abelian dynamical Galois group. | |

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. | |

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 first year PhD student with an interest in number theory, supervised by Alex Bartel. | |

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. | |

Ujan Chakraborty | |

I am a first 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 variations of the Rokhlin lemma. | |

Rhys Davies | |

I'm a first year PhD student supervised by Gwyn Bellamy. I'm broadly interested in algebra, geometry and topology, with a particular interest in representation 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. | |

Sarah Kelleher | |

I am a fourth 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 third 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. | |

Cameron Wilson | |

I am a first year PhD student with an interest in analytic number theory and arithmetic geometry, supervised by Efthymios Sofos. | |

Isambard Goodbody | |

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

Mohammad | |

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

Marina Godinho | |

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

Lewis Dean | |

First 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. |