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Wei Yeung Lam
Holomorphic quadratic differentials on graphs
Located in Academic Departments / Mathematics
Ilke Canakci (Durham) "Infinite rank surface cluster algebras"
Abstract: Cluster algebras were introduced by Fomin and Zelevinsky in the context of Lie theory in 2002, however they received much attention since many applications in diverse areas of mathematics have been discovered including quiver representations, Teichmuller theory, integrable systems and string theory. An important class of cluster algebras, called surface cluster algebras, were introduced by Fomin, Shapiro and Thurston by associating cluster algebra structure to triangulated marked surfaces. I will review the state of the art in research associated to surface cluster algebras and report on joint work with Anna Felikson where we introduce a generalisation of surface cluster algebras to infinite rank by associating cluster algebras to surfaces with finitely many accumulation points of boundary marked points.
Located in Academic Departments / Mathematics
Nathan Broomhead (Plymouth) "Thick subcategories, arc-collections and mutation"
Abstract: I will explain some work, in which I describe the lattices of thick subcategories of discrete derived categories. This is done using certain collections of exceptional and sphere-like objects related to non-crossing configurations of arcs in a geometric model.
Located in Academic Departments / Mathematics
Tom Bridgeland (Sheffield) Title TBA
Abstract: TBA
Located in Academic Departments / Mathematics
"The additivity problem" Muneerah Saad ALNuwairan (King Faisal University)
Abstract: In our talk, we present the well- known problem in the field of quantum information theory known as “The additivity problem”. It concerns transferring classical information using quantum channels. We will build a mathematical model for the problem, and show that the field of Representation theory provides rich source for solutions. We will also introduce EPOSIC channels, a class of SU(2)-covariant quantum channels that form the extreme points of all SU(2)-irreducibly covariant channels. These channels provide us with a potential solution for the problem.
Located in Academic Departments / Mathematics / Research
"The fundamental crossed module of the complement of a knotted surface in the 4-sphere"Joao Faria Martins (Leeds)
After a review on homotopy 2-types and crossed modules, I will show a method to calculate the homotopy 2-type of the complement of a knotted surface in the 4-sphere given a movie presentation of it. We therefore generalise Wirtinger relations for the fundamental group of a knot complement. [1] Faria Martins J.: The Fundamental Crossed Module of the Complement of a Knotted Surface. Transactions of the American Mathematical Society. 361 (2009), 4593-4630. [2] Faria Martins J., Kauffman L.H.: Invariants of Welded Virtual Knots Via Crossed Module Invariants of Knotted Surfaces, Compositio Mathematica. 144:04 (2008) 1046-1080.
Located in Academic Departments / Mathematics / Research
Pure Maths Seminar Series-Webinar
Pure Mathematics Seminars are usually held at 2:00pm on Tuesdays. In this term, our seminar will be online and tea after seminar will be hosted on gather.town. For any questions or comments please contact Yadira Valdivieso (yvd1 at leicester.ac.uk)
Located in Academic Departments / Mathematics / Research
"Minimal surfaces and geometric flows" Melanie Rupflin (Oxford)
Abstract: The classical Plateau problems has been one of the most influential problems in the development of modern analysis. Posed initially by Lagrange, it asks whether a closed curve in Euclidean space always spans a surfaces with minimal possible area, a question that was answered positively by Douglas and Rado around 1930. In this talk I want to consider some aspects of the classical Plateau Problem and its generalisations and discuss furthermore how one can "flow" to such minimal surfaces by following a suitably defined gradient flow of the Dirichlet energy, i.e. of the integral of gradient squared.
Located in Academic Departments / Mathematics / Research
Prof. Fran Burstall (University of Bath)
Located in Academic Departments / Mathematics
"Modulations and potentials for triangulated surfaces" by Jan Geuenich (Bielefeld)
Triangulations of surfaces with marked points and weighted orbifold points encode the mutation combinatorics of "almost all" cluster algebras of finite mutation type. From a representation-theoretic point of view, Jacobian algebras of triangulations play a key role. Daniel Labardini Fragoso defined and investigated these algebras for surfaces without orbifold points. In joint work with him we extend this theory to surfaces that may have weighted orbifold points. The natural set-up for this generalization are modulations for weighted quivers.
Located in Academic Departments / Mathematics / Research

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