Lecturers
The school brings together six minicourses, supported by tutorials, collaborative sessions, and mentoring activities. Click on a lecturer's name to view the course abstract.
Course: Representation theory and knots
Course: Cluster structures on flag varieties and applications in particle physics
Course: Representation theory for combinatorial algebras
Course: Functor-category-theoretic methods in representation theory
Course: Infinite-dimensional Lie algebras and their representations: an introduction through examples
Course: Representation Theory of Groups
Course: Homological methods in Representation Theory
Prof. Stéphane Launois
Role: External Co-organizer; coordination of tutorials, jigsaw sessions, mentoring activities, and complementary programme components.
Lara Bossinger
Cluster structures on flag varieties and applications in particle physics
This course introduces cluster algebra structures arising from partial flag varieties and explores their applications in particle physics. Topics include total positivity, foundations of cluster algebras, cluster structures on partial flag varieties, and realizations of configuration spaces in quantum field theory. Applications to scattering amplitudes will also be discussed.
Samuel Lopes
Infinite-dimensional Lie algebras and their representations: an introduction through examples
This course introduces structural aspects of the representation theory of infinite-dimensional Lie algebras through key examples. The focus will be on the Heisenberg Lie algebra, the Virasoro algebra, and Lie algebras of infinite matrices such as gl(∞) and sl(∞). Connections such as Bosonic Fock space and the Boson-Fermion correspondence will be used to illustrate fundamental concepts in infinite-dimensional representation theory.
Andrea Solotar
Homological methods in representation theory
This lecture series introduces homological tools central to modern representation theory. The course discusses Hochschild (co)homology, global dimension, and triangulated and derived categories, with particular emphasis on their role in studying Han's conjecture, which relates infinite global dimension to infinite Hochschild homology. Recent tools such as tau-Hochschild (co)homology will also be introduced.
Roozbeh Hazrat
Representation theory for combinatorial algebras
This course focuses on the representation theory of algebras associated with combinatorial structures, particularly Kumjian-Pask algebras arising from higher-rank graphs. The lectures examine irreducible representations and their connections to invariants in symbolic dynamics, illustrating how graph-theoretic constructions interact with algebraic representation theory.
Véronique Bazier-Matte
Representation theory and knots
This course explores connections between knot theory and cluster algebras via representation theory. To a knot diagram one associates a cluster algebra whose cluster variables specialize to the Alexander polynomial. The lectures describe constructions of indecomposable representations of associated quivers and their relation to mutation sequences arising from Reidemeister moves and diagram reductions. Symmetry properties of the resulting representations are also discussed.
Amit Kuber
Functor-category-theoretic methods in representation theory
This course introduces functor-category methods in representation theory, focusing on concepts such as Serre localisation, Krull-Gabriel dimension, duality, definable categories, and the Ziegler spectrum. The lectures emphasize the role of finitely presented functors and algebraically compact modules in understanding the structure and complexity of module categories, especially for bound quiver algebras.
Pooja Singla
Representation theory of groups
This lecture series develops the representation theory of groups through examples from linear groups over finite and p-adic fields. Topics include group algebras, irreducible representations, character theory, induction and restriction methods, Mackey theory, Clifford theory, and representations of GLn(Fq). The course also discusses smooth admissible representations of p-adic groups and the Bernstein decomposition.
Lecture Hall
Science Cluster Classroom Building
North-Eastern Hill University, Shillong, Meghalaya, India
Umshing Mawkynroh, Shillong, Meghalaya 793022, India
The school will be held at the Mathematics Section of the Science Cluster Classroom Building, NEHU.
The venue has lecture halls and seminar rooms equipped with blackboards, smart-board facilities, campus-wide Wi-Fi, and access to university services and local transport.