Publications & Preprints

Last updated: 2026-01-30

Preprints

[42] M. Mackaay, V. Miemietz, P. Vaz,
Almost finitary birepresentation theory and applications to affine Soergel bimodules
(2026) arXiv
[41] T. Kelomäki, A. Lacabanne, D. Tubbenhauer, P. Vaz, V. L. Zhang,
On detection probabilities of link invariants
(2025) arXiv
[40] G. Janssens, A. Lacabanne, L. Schelstraete, P. Vaz,
A basis and Schur–Weyl duality for the loop Hecke algebra
(2025) arXiv
[39] L. Schelstraete and P. Vaz,
Odd Khovanov homology and higher representation theory
(2023) arXiv
[38] P. Vaz,
KLR algebras and the branching rule II: The categorical Gelfand–Tsetlin bases for the classical Lie algebras
(2014) arXiv
[37] P. Vaz,
KLR algebras and the branching rule I: The categorical Gelfand–Tsetlin basis in type A_n
(2013) arXiv
[36] M. Mackaay, P. Vaz,
The reduced HOMFLY–PT homology for the Conway and the Kinoshita–Terasaka knots (to be rewritten)
(2008) arXiv

2026

[35] M. Mackaay, V. Miemietz, P. Vaz,
Induction for extended affine type A Soergel bimodules: first steps
J. Inst. Math. Jussieu (to appear) (2026). paper · arXiv
[34] A. Lacabanne, D. Tubbenhauer, P. Vaz,
On Hecke and asymptotic categories for a family of complex reflection groups
Port. Math. 83:(1/2), 35-105 (2026). paper · arXiv
[33] A. Lacabanne, D. Tubbenhauer, P. Vaz,
Big data approach to Kazhdan–Lusztig polynomials
Journal of Experimental Mathematics, (2026) 2(1), 21-62. paper · arXiv
[32] M. Mackaay, J. Macpherson, P. Vaz,
Evaluation 2–functors for Kac–Moody 2–categories of type A₂
Pac. J. Math. 341 (2026) No. 1, 103-145. paper · arXiv

2025

[31] A. Lacabanne, D. Tubbenhauer, P. Vaz,
Asymptotics in infinite monoidal categories
Higher Structures 9(2): 168–197 (2025). paper · arXiv
[30] A. Lacabanne, D. Tubbenhauer, P. Vaz,
Verma Howe duality and LKB representations
New York J. Math. 31 (2025), 1507–1542. paper · arXiv
[29] A. Lacabanne, P. Vaz, A. Wilbert, Two-row Delta Springer varieties. Algebr. Comb. 8 (2025) no. 4, 925–953. paper · arXiv
[28] E. Rizzo and P. Vaz, Enhanced nilHecke algebras and baby Verma modules. Tunisian Journal of Mathematics (2025), 91–130. paper · arXiv

2024

[27] A. Lacabanne, D. Tubbenhauer and P. Vaz, A formula to evaluate type A webs and link polynomials. Ark. Math. 62 (2024) 83–101. paper · arXiv
[26] M. Khovanov, K. Putyra and P. Vaz, Odd two-variable Soergel bimodules and Rouquier complexes. Contemp. Math. 791 (2024). arXiv
[25] M. Mackaay, V. Miemietz and P. Vaz, Evaluation birepresentations of affine Type A Soergel bimodules. Advances in Math. 436 (2024). paper · arXiv

2023

[24] R. Maksimau and P. Vaz, DG-enhanced Hecke and KLR algebras. SIGMA 19 (2023), 095, 24 pages. paper · arXiv
[23] A. Lacabanne, D. Tubbenhauer and P. Vaz, Asymptotics in finite monoidal categories. Proc. Amer. Math. Soc. Ser. B 10 (2023), 399–412. paper · arXiv
[22] A. Lacabanne, D. Tubbenhauer and P. Vaz, Annular webs and Levi subalgebras. J. Comb. Algebra 7 (2023), no. 3/4, 283–326. paper · arXiv
[21] D. Tubbenhauer and P. Vaz, Handlebody diagram algebras. Rev. Mat. Iberoam. 39 (2023), no. 3, 845–896. paper · arXiv

2021

[20] G. Naisse and P. Vaz, 2-Verma modules. J. Reine Angew. Math. 782 (2021), 43–108. paper · arXiv (2017)
[19] A. Lacabanne and P. Vaz, Schur–Weyl duality, Verma modules, and row quotients of Ariki–Koike algebras. Pac. J. Math. 311-1 (2021), 113–133. paper · arXiv (2020)
[18] A. Lacabanne, G. Naisse and P. Vaz, Tensor product categorifications, Verma modules and the blob 2-category. Q. Topol. 12 (2021), no. 4, 705–812. paper · arXiv (2020)
[17] G. Naisse and P. Vaz, 2-Verma modules and the Khovanov–Rozansky link homologies. Math. Z. (2021) 299: 139–162. paper · arXiv

2020

[16] P. Vaz, Not even Khovanov homology. Pac. J. Math. 308-1 (2020), 223–256. paper · arXiv

2019

[15] P. Vaz, A survey on categorification of Verma modules (survey based on a 4.5h lecture course given at the HIM in Bonn in Nov 2017). J. Interdiscip Math. 22:3 (2019), 265–315. paper

2018

[14] G. Naisse and P. Vaz, An approach to categorification of Verma modules. Proc. Lond. Math. Soc. (3) 117 (2018), no. 6, 1181–1241. paper · arXiv
[13] G. Naisse and P. Vaz, On 2-Verma modules for quantum sl(2). Selecta Math. (2018) 24: 3763–3821. paper · arXiv
[12] G. Naisse and P. Vaz, Odd Khovanov's arc algebra. Fundamenta Mathematicae 241 (2018), 143–178. paper · arXiv

2017

[11] D. Tubbenhauer, P. Vaz, P. Wedrich, Super q-Howe duality and web categories. Algebr. Geom. Topol. 17 (2017) 3703–3749. paper

2014

[10] P. Vaz, E. Wagner, A remark on BMW algebra, q-Schur algebras and categorification. Canad. J. Math. 66 (2014) no. 2, 453–480. paper · arXiv

2013

[9] M. Mackaay, M. Stosic, P. Vaz, A diagrammatic categorification of the q-Schur algebra. Quantum Topology 4 (2013), 1–75. paper

2012

[8] P. Vaz, On Jaeger's HOMFLY-PT expansions, branching rules and link homology: a progress report. Boletim Soc. Port. Matem., n. especial (2012), 91–94. paper · arXiv

2011

[5] M. Mackaay, M. Stosic, P. Vaz, The 1,2-coloured HOMFLY-PT link homology. Trans. Amer. Math. Soc. 363 (2011) 2091–2124. paper

2010

[7] M. Mackaay, P. Vaz, The diagrammatic Soergel category and sl(N)-foams for N ≥ 4. International Journal of Mathematics and Mathematical Sciences (2010). paper
[6] P. Vaz, The diagrammatic Soergel category and sl(2) and sl(3) foams. International Journal of Mathematics and Mathematical Sciences (2010). paper

2009

[4] M. Mackaay, M. Stosic, P. Vaz, sl(N)-link homology (N ≥ 4) using foams and the Kapustin–Li formula. Geometry & Topology 13 (2009), 1075–1128. paper

2008

[3] M. Mackaay, P. Vaz, The foam and the matrix factorization sl3 link homologies are equivalent. Algebr. Geom. Topol. 8 (2008), 309–342. paper

2007

[2] M. Mackaay, P. Vaz, The universal sl3-link homology. Algebr. Geom. Topol. 7 (2007), 1135–1169. paper
[1] M. Mackaay, P. Turner, P. Vaz, A remark on Rasmussen’s invariant of knots. J. Knot Theory Ramifications 16(3) (2007): 333–344. paper

P. Vaz — Three lectures on categorification of Verma modules (2017). Notes for a 4.5 hour lecture course at the HIM-Bonn. PDF
P. Vaz — The Kapustin–Li formula and the evaluation of closed foams (2010). Notes not intended for publication. PDF
P. Vaz — A categorification of the quantum sl(N)-link polynomials using foams PhD Thesis (2008), Universidade do Algarve – Portugal. arXiv
P. Vaz — Induced representations and the geometric quantization of the coadjoint orbits of SU(2) and SL(2,C) (2004). In Portuguese. Undergrad. Thesis. Not intended for publication. PDF
P. Vaz — Geometric Quantization (2003). In Portuguese. Notes not intended for publication. PDF
P. Vaz — Symplectic Geometry (2003). In Portuguese. Notes not intended for publication. PDF