Nathan Geer Ph.D.

Publications | Journal Articles

Academic Journal

• Geer, N.C, Ha, ., Patureau-Mirand, B., (2024). Modified symmetrized integral in G-coalgebras. Journal of Knot Theory and Its Ramifications
• Geer, N.C, Lauda, A., Patureau-Mirand, B., Sussan, J., (2022). A Hermitian TQFT from a non-semisimple category of quantum sl(2)-modules. Lett. Math. Phys., 112
• Geer, N.C, Kujawa, J., Patureau-Mirand, B., (2022). M-traces in (non-unimodular) pivotal categories. Algebras and Representation Theory, 25
• Geer, N.C, Ha, ., Patureau-Mirand, B., (2022). Modified graded Hennings invariants from unrolled quantum groups and modified integral. J. Pure Appl. Algebra, 226
• Geer, N.C, Lauda, A., Patureau-Mirand, B., Sussan, J., (2022). Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs. Ann. Physics, 442
• Anghel, C., Geer, N.C, Patureau-Mirand, B., (2021). Relative (pre)-modular categories from special linear Lie superalgebras. Journal of Algebra, 586, 479-525.
• Hu, Y., Geer, N.C, Wu, Y., (2018). Full Dyon Excitation Spectrum in Generalized Levin-Wen Models. Phys. Rev. B, 97:195154
• Geer, N.C, Patureau-Mirand, B., (2018). The trace on projective representations of quantum groups. Letters in Mathematical Physics, 108
• Blanchet, C., Costantino, F., Geer, N.C, Patureau-Mirand, B., (2016). Non semi-simple TQFTs from unrolled quantum sl(2). Proceedings of the Gokova Geometry-Topology Conference 2015, 218--231.
• Blanchet, C., Costantino, F., Geer, N.C, Patureau-Mirand, B., (2016). Non semi-simple TQFTs, Reidemeister torsion and Kashaev’s invariants. Advances in Mathematics, 301, 1-78.
• Costantino, F., Geer, N.C, Patureau-Mirand, B., (2015). Relations between Witten–Reshetikhin–Turaev and nonsemisimple sl (2) 3–manifold invariants. Algebraic & Geometric Topology, 15:3, 1363–1386.
• Costantino, F., Geer, N.C, Patureau-Mirand, B., (2015). Some remarks on the unrolled quantum group of sl (2). Journal of Pure and Applied Algebra, 219:8, 3238–3262.
• Costantino, F., Geer, N.C, Patureau-Mirand, B., (2014). Quantum invariants of 3-manifolds via link surgery presentations and non-semi-simple categories. Journal of Topology, jtu006.
• Geer, N.C, (2014). The Kontsevich integral and re-normalized link invariants arising from Lie superalgebras. Knots in Poland. III. Part 1, 79–84, Banach Center Publ., 100, Polish Acad. Sci. Inst. Math., Warsaw
• Geer, N.C, Kujawa, J., Patureau-Mirand, B., (2013). Ambidextrous objects and trace functions for nonsemisimple categories. Proceedings of the American Mathematical Society, 141:9, 2963–2978.
• Geer, N.C, Patureau-Mirand, B., (2013). G-LINKS INVARIANTS, MARKOV TRACES AND THE SEMI-CYCLIC Uq (2)-MODULES. Journal of Knot Theory and Its Ramifications, 22:11, 1350063.
• Geer, N.C, Patureau-Mirand, B., (2013). Topological invariants from nonrestricted quantum groups. Algebraic & Geometric Topology, 13:6, 3305–3363.
• Geer, N.C, Patureau-Mirand, , Virelizier, , (2013). Traces on ideals in pivotal categories. Quantum Topology, 4:no. 1, 91-124.
• Geer, N.C, Kashaev, R., Turaev, V., (2012). Tetrahedral forms in monoidal categories and 3-manifold invariants. Journal für die reine und angewandte Mathematik (Crelles Journal), 2012:673, 69–123.
• Geer, N.C, Patureau-Mirand, B., Kujawa, J., (2011). Generalized trace and modified dimension functions on ribbon categories. Selecta Mathematica, 17:no. 2, 453-504.
• Geer, N.C, Patureau-Mirand, B., (2011). Polynomial 6j-Symbols and States Sums. Algebraic and Geometric Topology, 11, 1821-1860.
• Geer, N.C, Patureau-Mirand, B., Turaev, V., (2011). Modified 6j-Symbols and 3-Manifold Invariants. Advances in Mathematics, 228:no. 2, 1163--1202.
• Geer, N.C, Patureau-Mirand, B., (2010). Multivariable link invariants arising from Lie superalgebras of type I. Journal Knot Theory Ramifications, 19:1, 93-115.
• Geer, N.C, Enriquez, B., (2009). Compatibility of quantization functors of Lie bialgebras with duality and doubling operations. Selecta Mathematica, 15:1, 1-59.
• Geer, N.C, Patureau-Mirand, B., Turaev, V., (2009). Modified quantum dimensions and re-normailized link invariants. Composiito Mathematica, 145:1, 196-212.
• Geer, N.C, Reshetikhin, N., (2009). On Invariants of Graphs Related to Quantum sl(2) at Roots of Unity. Letters in Mathematical Physics, 88:1-3, 321-331.
• Geer, N.C, Patureau-Mirand, B., (2008). An invariant supertrace for the category of representations of Lie superalgebras of type I. Pacific Journal of Mathematicis, 238:2, 331-348.
• Geer, N.C, Patureau-Mirand, B., (2008). On the colored HOMFLY-PT, multivariable and Kashaev link invariants. Communications in Contemporary Mathematics, 10:1, 993-1011.
• Geer, N.C, Etingof, P., (2007). Monodromy of the trigonometric KZ equations. International Mathematics Research Notices, 24
• Geer, N.C, Patureau-Mirand, B., (2007). Multivariable link invariants arising from sl (2| 1) and the Alexander polynomial. Journal of Pure and Applied Algebra, 210:1, 283–298.
• Geer, N.C, (2007). Some remarks on quantized Lie superalgebras of classical type. Journal of Algebra, 314:2, 565-580.
• Geer, N.C, (2006). Etingof–Kazhdan quantization of Lie superbialgebras. Advances in Mathematics, 207:1, 1–38.
• Geer, N.C, (2005). The Kontsevich integral and quantized Lie superalgebras. Algebr. Geom. Topol., 5:45, 1111-1139.

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.

Publications | Other

An asterisk (*) at the end of a publication indicates that it has not been peer-reviewed.