CIMPA 2027
FoRT NEHU
Flavors of Representation Theory (FoRT) is a two-week CIMPA School for master’s students, doctoral students, and early-career researchers. The school builds on preparatory workshops such as IWLPA 2025 and the AESIM School on Flavors of Representation Theory, contributing to the development of a sustained representation theory community in India and neighbouring regions.
The programme consists of six lecture series covering active research directions including cluster theory, infinite-dimensional Lie theory, homological methods, combinatorial structures, knot-theoretic interactions, functor categories, and aspects of group representations.
Alongside lectures, the school emphasises active learning through tutorials, collaborative sessions, Young Researchers’ presentations, mentoring meetings, and guided discussions, fostering mathematical exchange between participants and 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
Role: External Co-organizer; coordination of tutorials, jigsaw sessions, mentoring activities, and complementary programme components.
| Time | Monday | Tuesday | Wednesday | Thursday | Friday |
|---|---|---|---|---|---|
| 9:00 - 9:30 | |||||
| 9:30 - 10:30 | Bossinger (L1) | Kuber (L2) | Lopes (L3) | Solotar (L4) | Kuber (L5) |
| 10:30 - 10:40 | Break | Break | Break | Break | Break |
| 10:40 - 11:40 | Solotar (L1) | Bossinger (L2) | Kuber (L3) | Lopes (L4) | Solotar (L5) |
| 11:40 - 12:00 | Tea Break | Tea Break | Tea Break | Tea Break | Tea Break |
| 12:00 - 1:00 | Lopes (L1) | Solotar (L2) | Solotar (L3) | Bossinger (L4) | Lopes (L5) |
| 1:00 - 2:30 | Lunch | Lunch | Lunch | Lunch | Lunch |
| 2:30 - 3:30 | Kuber (L1) | Lopes (L2) | Bossinger (L3) | Kuber (L4) | Bossinger (L5) |
| 3:30 - 3:40 | Break | Break | Break | Break | Break |
| 3:40 - 4:40 | YRS | Kuber (T) | Lopes (T) | Bossinger (T) | Solotar (T) |
| 4:40 - 5:00 | Tea Break | Tea Break | Tea Break | Tea Break | |
| 5:00 - 6:00 | Opening Social and Snacks | YRS | Jigsaw | Jigsaw | Jigsaw |
| Time | Monday | Tuesday | Wednesday | Thursday | Friday |
|---|---|---|---|---|---|
| 9:30 - 10:30 | Hazrat (L1) | Singla (L2) | Bazier-Matte (L3) | Hazrat (L4) | Singla (L5) |
| 10:30 - 10:40 | Break | Break | Break | Break | Break |
| 10:40 - 11:40 | Bazier-Matte (L1) | Hazrat (L2) | Singla (L3) | Bazier-Matte (L4) | Hazrat (L5) |
| 11:40 - 12:00 | Tea Break | Tea Break | Tea Break | Tea Break | Tea Break |
| 12:00 - 1:00 | Singla (L1) | Bazier-Matte (L2) | Hazrat (L3) | Singla (L4) | Bazier-Matte (L5) |
| 1:00 - 2:30 | Lunch | Lunch | Lunch | Lunch | Lunch |
| 2:30 - 3:30 | Research Talk | YRS | Day Trip | Research Talk | Singla (T) |
| 3:30 - 3:40 | Break | Break | Break | Break | |
| 3:40 - 4:40 | YRS | Hazrat (T) | Bazier-Matte (T) | Jigsaw | |
| 4:40 - 5:00 | Tea Break | Tea Break | Tea Break | Closing and Snacks | |
| 5:00 - 6:00 | Jigsaw | Jigsaw | Jigsaw |
The school is intended for Master's students, PhD students, postdoctoral researchers, and early-career faculty interested in representation theory and related areas.
Coming SoonThe school will be hosted at North-Eastern Hill University, INDIA, Shillong, Meghalaya.
Science Classroom Cluster
North-Eastern Hill University, INDIA
Umshing Mawkynroh, Shillong, Meghalaya 793022, India
The school will be held at the Mathematics Section of the Science Cluster Classroom Building at NEHU. The venue is equipped with lecture halls and seminar rooms with blackboard and smart-board facilities, along with campus-wide Wi-Fi, and access to university services and local transport.
External Coordinator
University of Caen Normandie, FRANCE
Local Coordinator
North-Eastern Hill University, INDIA
North-Eastern Hill University, INDIA
Mindanao State University, PHILIPPINES
North-Eastern Hill University, Shillong, INDIA
North-Eastern Hill University, Shillong, INDIA
North-Eastern Hill University, Shillong, INDIA
North-Eastern Hill University, Shillong, INDIA
North-Eastern Hill University, Shillong, INDIA
North-Eastern Hill University, Shillong, INDIA
North-Eastern Hill University, Shillong, INDIA
North-Eastern Hill University, Shillong, INDIA
North-Eastern Hill University, Shillong, INDIA
North-Eastern Hill University, Shillong, INDIA
Highlights from the beautiful NEHU campus and the state of Meghalaya.
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.
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.
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.
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.
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.
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.
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.