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A major part of my research in the past few years has been aimed at giving a better understanding of the behavior of bricks over algebras. Bricks, also known as Schur representations, appear in various domains, including in stability conditions, wall-and-chamber structures, τ-tilting theory, lattice theory of torsion classes, wide subcategories, to mention just a few. Following my earlier work in my PhD studies, in a series of joint work with Charles Paquette, we treat bricks from the algebraic, combinatorial and geometric viewpoints. Our work is primarily centred around an open conjecture which we call the Second brick-Brauer-Thrall conjecture (2nd bBT). First posed in my preprint in 2019, the 2nd bBT conjecture is analogous to the celebrated Second Brauer-Thrall conjecture (now theorem) and establishes novel conceptual connections between some classical and modern aspects of representation theory, such as τ-tilting theory, geometry of the representation varieties, families of stable modules, and also behaviour of infinite dimensional modules, particularly in connection with the notion of generic modules. For further details, please see my recent work here.

Publications and Preprints 

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  • "Geometric interactions between bricks and τ-rigidity", (arXiv:2311.14863), joint with C. Paquette.

  • "Biserial algebras and generic bricks", (arXiv:2209.05696) [Submitted], joint with C. Paquette.

  • "A Continuous Associahedron of Type A", (arXiv:2108.12927) [Submitted], joint with M. Kulkarni, J. Matherne, J. Rock.

  • "ABHY associahedra and Newton polytopes of F-ploynomials for cluster algebras of simply laced finite type.", (arXiv:1808.09986), Journal of the London Mathematical Society (2023), joint with V. Bazier-Matte, N. Chapelier-Laget, G. Douville, H. Thomas, E. Yıldırım.

  • "Minimal (τ-)tilting infinite algebras",  (arXiv:2103.12700), Nagoya Mathematical Journal (2022), joint with C. Paquette.

  • "τ-Tilting finiteness of biserial algebras", (arXiv:1904.11514), Algebras and Representation Theory (2022).

  • "τ-Tilting finiteness of non-distributive algebras and their module varieties", (arXiv:1910.02251), Journal of Algebra (2022).

  • "On combinatorics of gentle algebras", (arXiv:1707.07665), Canadian Journal of Mathematics (2020), joint with T. Brüstle, G, Douville, H. Thomas, E. Yıldırım.

  • "A categorification of biclosed sets of strings", (arXiv:1808.10346), Journal of Algebra (2020), joint with A. Garver and T. McConville.

  • "On Some Properties of Toeplitz Matrices", Cogent Mathematics (2016), joint with D. Kucerovsky and A. Sarraf.

Conferences, Workshops & Schools (co)-organization

​In the future, I am co-organizing the following events:
 

Previously, I have co-organized the following events:
 
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