The team of algebraic topolgy has expertise and interests in rational homotopy theory, Goodwillie-Weiss manifold calculus, categorification of quantum invariants (Khovanov homology and Khovanov-Rozansky homology), higher representation theory and its applications to low-dimensional topology.
Professors
Emeritus
Post-doc
PhD students
On calculus of functors and the little disk operad:
Lambrechts, Pascal; Volić, Ismar Formality of the little N-disks operad. Mem. Amer. Math. Soc. 230 (2014), no. 1079, viii+116 pp.
Lambrechts, Pascal; Turchin, Victor; Volić, Ismar The rational homology of spaces of long knots in codimension >2. Geom. Topol. 14 (2010), no. 4, 2151–2187.
Lambrechts, Pascal; Turchin, Victor Homotopy graph-complex for configuration and knot spaces. Trans. Amer. Math. Soc. 361 (2009), no. 1, 207–222.
Arone, Gregory; Lambrechts, Pascal; Volić, Ismar Calculus of functors, operad formality, and rational homology of embedding spaces. Acta Mathematica 199 (2007), no. 2, 153–198.
On rational homotopy theory:
Félix, Yves; Halperin, Steve; Thomas, Jean-Claude Rational homotopy theory. II. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2015. xxxvi+412 pp. ISBN: 978-981-4651-42-4
Felix, Yves; Halperin, Steve; Thomas, Jean-Claude Exponential growth and an asymptotic formula for the ranks of homotopy groups of a finite 1-connected complex. Annals of Mathematics (2) 170 (2009), no. 1, 443–464
Félix, Yves; Halperin, Stephen; Thomas, Jean-Claude Rational homotopy theory. Graduate Texts in Mathematics, 205. Springer-Verlag, New York, 2001. xxxiv+535 pp. ISBN: 0-387-95068-0
Hardt, Robert; Lambrechts, Pascal; Turchin, Victor; Volić, Ismar Real homotopy theory of semi-algebraic sets. Algebr. Geom. Topol. 11 (2011), no. 5, 2477–2545.
Lambrechts, Pascal; Stanley, Don Poincaré duality and commutative differential graded algebras. Ann. Sci. Éc. Norm. Supér. (4) 41 (2008), no. 4, 495–509.
On link homology/categorification:
M. Mackaay, Stošić, M. and P. Vaz, sl(N) -link homology (N≥4) using foams and the Kapustin-Li formula. Geom. Topol. 13 (2009), no. 2, 1075–1128.
M. Mackaay and P. Vaz, The universal sl3 -link homology. Algebr. Geom. Topol. 7 (2007), 1135–1169.
D. Tubbenhauer, P. Vaz and P. Wedrich,Super q -Howe duality and web categories. Algebr. Geom. Topol. 17 (2017), no. 6, 3703–3749.
G. Naisse and P. Vaz, An approach to categorification of Verma modules. Proc. Lond. Math. Soc. (3) 117 (2018), no. 6, 1181–1241.
G. Naisse and P. Vaz, 2-Verma modules and the Khovanov-Rozansky link homologies. Math. Z. 299 (2021), no. 1-2, 139–162.