Nathan Geer Ph.D.

Mathematics and Statistics

Research Committee Chair | Professor


Nathan Geer

Contact Information

Office Location: Animal Science (ANSC) 306
Phone: (435) 797-0755
Email: nathan.geer@usu.edu

Educational Background

PhD, Mathematics, University of Oregon, 2004
BS, Mathematics, Colorado State University, 1998

Awards

CNRS Directeur de Recherches, 2015

University of Paris Sorbonne

Japan Society for the Promotion of Science (JSPS) Research Fellowship, 2015

Waseda University, Tokyo Japan

Invited Member, 2015

Max-Planck Institute for Mathematics, Bonn, Germany

College of Science Researcher of the Year, 2013

Utah State University

Department of Mathematics and Statistics, Researcher of the Year, 2013

Utah State University

Thank a Teacher Certificate, 2008

Georgia Institute of Technology

Take Your Professor to Lunch, 2005

Georgia Institute of Technology

Harrison Research Award, 2004

University of Oregon

Johnson Research Fellowship, 2003

University of Oregon


Publications | Journal Articles

Academic Journal

  • 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.

Teaching

MATH 1220 - Calculus II, Fall 2020
MATH 1220 - Calculus II, Fall 2019
MATH 5910, 6910 - Directed Reading and Conference, Spring 2019
MATH 1210 - Calculus I, Fall 2018
MATH 1220 - Calculus II, Fall 2017
MATH 1220 - Calculus II, Fall 2016
MATH 1210 - Calculus I, Spring 2015
MATH 4310 - Introduction to Algebraic Structures, Fall 2014
MATH 7810 - Topics in Mathematics (Topic), Fall 2014
MATH 7820 - Topics in Mathematics (Topic), Spring 2014
MATH 2210 - Multivariable Calculus, Fall 2013
MATH 2210 - Multivariable Calculus, Fall 2013
MATH 6810 - Topics in Mathematics (Topic), Fall 2013
MATH 5310 - Introduction to Modern Algebra, Spring 2013
MATH 4310 - Introduction to Algebraic Structures, Fall 2012
MATH 2210 - Multivariable Calculus, Fall 2012
MATH 1220 - Calculus II, Fall 2011
MATH 1220 - Calculus II (Honors), Fall 2011
MATH 5310 - INTRO MODERN ALGEBRA, Spring 2011
MATH 1220 - Calculus II, Fall 2010
MATH 4310 - Introduction to Algebraic Structures, Fall 2010

Graduate Students Mentored

Joseph Keller, Mathematics & Statistics, August 2020