Vita

Research

• categorification of quantum invariants
• categorification of quantum groups and its applications to low-dimension topology
• knot theory and quantum topology
• everything that has to do with categorification: representation theory, geometry, algebraic K-theory, homological algebra, category theory, etc ...

Publications

M. Mackaay, M. Stosic, P. Vaz
A diagrammatic categorification of the q-Schur algebra
(2010) (to appear in Quantum Topology)    arXiv

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

P. Vaz
The diagrammatic Soergel category and sl(2) and sl(3) foams
International Journal of Mathematics and Mathematical Sciences (2010)    paper

M. Mackaay, P. Vaz
The reduced HOMFLY-PT homology for the Conway and the Kinoshita-Terasaka knots
(2008)    arXiv

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

P. Vaz
A categorification of the quantum sl(N)-link polynomials using foams
PhD Thesis (2008) - Universidade do Algarve - Portugal    arXiv version

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

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

M. Mackaay, P. Vaz
The universal sl3-link homology
Algebr. Geom. Topol. (2007) 7, 1135-1169    paper

M. Mackaay, P. Turner, P. Vaz
A remark on Rasmussen’s invariant of knots
J. Knot Theory Ramifications (2007) 16(3): 333-344    paper

P. Vaz
The Kapustin-Li formula and the evaluation of closed foams
(2010. Notes not intended for publication) PDF  

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