Faculty Guide

Title

Professor of Mathematics

Mathematics

Expertise

Geometric topology and gauge theory.

Profile

Many of the deepest mysteries in topology concern spaces of dimension 3 and 4, which are just at the edge of our ability to visualize. My work uses tools of differential geometry and analysis, some of it inspired by physics, to study these spaces.

Awards and Honors

Chercheur Invité du CNRS; University of Paris 7 (2011)

Slovenian Science Foundation Travel Grant (2010)

Visiting Scholar, Kyoto University (2010)

Slovenian Science Foundation Travel Grant (2006)

Visiting Member, Institut des Hautes Etudes Scientifiques (2001)

Chercheur Invite, University of Paris, Orsay (2000 - 2001)

Grant from Centre National de Recherche Scientifiques (France) (2000 - 2001)

Engineering and Physical Sciences Research Council (Great Britain) (1994 - 1995)

Sloan Foundation Fellowship (1991 - 1992)

National Science Foundation Fellowship (1988 - 1990)

Rice Prize in Mathematics (1977)

Courses Taught

MATH	20a	Techniques of Calculus: Calculus of Several Variables
MATH	22a	Linear Algebra and Intermediate Calculus, Part I
MATH	22b	Linear Algebra and Intermediate Calculus, Part II
MATH	23b	Introduction to Proofs
MATH	32a	Differential Geometry
MATH	40a	Introduction to Real Analysis, Part I
MATH	140a	Geometric Analysis
MATH	221a	Topology III
MATH	221b	Topics in Topology
MATH	224b	Lie Groups

Scholarship

Kronheimer, Peter, Mrowka, Tomasz, and Ruberman, Daniel. "Mutation and instanton knot homology." Michigan Mathematical Journal (2011). (forthcoming)

Cha, Jae Choon and Ruberman, Daniel. "Concordance to links with unknotted components." Algebraic and Geometric Topology 12. no. 2 (2012): 963–977.

Cha, Jae Choon; Kim, Taehee; Ruberman, Daniel; Strle, Saso. "Smooth concordance of links topologically concordant to the Hopf link." Bulletin of the London Mathematical Society 44. no. 3 (2012): 443-450.

Hedden, Matthew; Livingston, Charles; Ruberman, Daniel. "Topologically slice knots with nontrivial Alexander polynomial." Advances in Mathematics 231. no. 2 (2012): 913–939.

Kim, Hee Jung and Ruberman, Daniel. "Double point surgery and configurations of surfaces." Journal of Topology 4. 2011 (2011): 573-590.

Mrowka, Tomasz, Ruberman, Daniel, and Saveliev, Nikolai. "Seiberg-Witten equations, end-periodic Dirac operators, and a lift of Rohlin's invariant." Journal of Differential Geometry 88. no. 2 (2011): 333–377.

Ruberman, Daniel and Saveliev, Nikolai. "The $\bar\mu$--invariant of Seifert fibered homology spheres and the Dirac operator." Geometriae Dedicata 154. (2011): 93–101.

Cha, Jae-Choon, Livingston, Charles, and Ruberman, Daniel. "Algebraic and Heegaard-Floer invariants of knots with slice Bing doubles." Mathematical Proceedings of the Cambridge Philosophical Society 144. 2 (2008): 403-410.

J. Elisenda Grigsby/Ruberman, Daniel /Saso Strle. "Knot concordance and Heegaard Floer homology invariants in branched covers." Geometry and Topology 12. 4 (2008): 2249--2275.

Kim, Hee-Jung/Ruberman, Daniel. "Smooth surfaces with non-simply-connected complements." Algebraic and Geometric Topology 8. (2008): 2263-2287.

Ruberman, Daniel/Kim, Hee Jung. "Topological triviality of smoothly knotted surfaces in 4-manifolds." Transactions of the AMS 360. 11 (2008): 5869--5881.

Ruberman, Daniel and Nikolai Saveliev. "Dirac operators on manifolds with periodic ends." Gokova Geometry and Topology Journal 1. (2007): 33-50.

Ruberman, Daniel, N. Saveliev. Casson--type invariants in dimension four. Proc. of Fields-McMaster Conference on Geometry and Topology of Manifolds. 2005.

Ruberman, Daniel/Saveliev, Nikolai. "Rohlin's invariant and gauge theory III. Homology 4-tori." Geometry and Topology 9. (2005): 2079-2127..

Ruberman, Daniel ed. N. Saveliev. "Rohlin's invariant and gauge theory I. Homology 3-tori." Commentarii Mathematici Helvetici (2004).

Ruberman, Daniel, ed. N. Saveliev. "Rohlin's invariant and gauge theory, II: Mapping tori." Geometry and Topology (2004): 35-76.

Ruberman,Daniel, with J. Morgan & T. Mrowka. The L2 Moduli Space and a Vanishing Theorem for Donaldson Polynomial Invariants. International Press Monographs in Geometry and Topology, 1994.