# Daniel Ruberman

Degrees

University of California, Berkeley, Ph.D.Wesleyan University, M.A.

Wesleyan University, B.A.

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. WebpageCourses Taught

MATH | 20a | Multi-variable Calculus |

MATH | 140a | Geometry of Manifolds |

MATH | 140b | Differential Geometry |

MATH | 151a | Topology I |

MATH | 221a | Topology III |

Awards and Honors

Visiting Scholar, Stanford University (2018)

Fellow of the American Mathematical Society (2017)

Visiting Scholar, University of Pisa (2017)

Simons Fellow in Mathematics (2016 - 2018)

Residential Fellow, Institute for Advanced Study, Indiana University (2015)

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

Slovenian Science Foundation Travel Grant (2010 - 2012)

Visiting Scholar, Kyoto University (2010)

Slovenian Science Foundation Travel Grant (2006 - 2008)

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)

Scholarship

Lin, Jianfeng, Ruberman, Daniel, and Saveliev, Nikolai. "On the monopole Lefschetz number of finite order diffeomorphisms." __Geometry and Topology (in the press)__ (2021). (forthcoming)

Ruberman, Daniel and Saveliev, Nikolai. "On the spectral sets of Inoue surfaces." December, 2020. (forthcoming)

Ruberman, Daniel. "A Levine-Tristram invariant for knotted tori." October, 2020. (forthcoming)

Kazaras, Demetre, Ruberman, Daniel, and Saveliev, Nikolai. "On positive scalar curvature cobordisms and the conformal Laplacian on end-periodic manifolds." 2/1/2019. (forthcoming)

Ratcliffe, John, Ruberman, Daniel, and Tschantz, Steven. "Harmonic spinors on the Davis Manifold." 2019. (forthcoming)

Auckly, David, Kim, Hee Jung, Melvin, Paul, and Ruberman, Daniel. "Infinite families of homologous 2-spheres in 4-manifolds." 2018. (forthcoming)

Jianfeng Lin, Daniel Ruberman, and Nikolai Saveliev. "On the Frøyshov invariant and monopole Lefschetz number." 2018. (forthcoming)

Kim, Hee Jung and Ruberman, Daniel. "Topological spines of 4-manifolds." __Algebraic and Geometric Topology__ 20. 7 (2020): 3589--360.

Auckly, David, Kim, Hee Jung, Melvin, Paul, Ruberman, Daniel, and Schwartz, Hannah. "Isotopy of surfaces in 4-manifolds after a single stabilization." __Advances in Mathematics__ 341. (2018): 609--615.

Auckly, David, Kim, Hee Jung, Melvin, Paul, and Ruberman, Daniel. "Equivariant hyperbolization of 3-manifolds via homology cobordisms." 2018.

Lin, Jianfeng, Ruberman, Daniel, and Saveliev, Nikolai. "A splitting theorem for the Seiberg-Witten invariant of a homology S^1 x S^3." __Geometry and Topology__ 22. 5 (2018): 2865--2942.

Levine, Adam, and Ruberman, Daniel. "Heegaard Floer invariants in codimension one." __Transactions of the American Mathematical Society__ 371. 5 (2017): 3049--3081.

Ray, Arunima, and Ruberman, Daniel. "4-dimensional analogues of Dehn's lemma." __Journal of the London Mathematical Society__ 96. no. 1 (2017): 111--132.

Ruberman, Daniel, and Starkston, Laura. "Topological realizations of line arrangements." __International Mathematical Research Letters__ rnx190. electronic publication (2017): 1--37.

Auckly, David, Kim, Hee Jung, Melvin, Paul, and Ruberman, Daniel. "Equivariant corks." __Algebraic and Geometric Topology__ 17. no. 3 (2016): 1771--1783.

Ruberman, Daniel. "On smoothly superslice knots." __New York Journal of Mathematics__ 22. (2016): 711--714.

Auckly, David, Kim, Hee Jung, Melvin, Paul, and Ruberman, Daniel. "Stable isotopy in four dimensions." __Journal of the London Mathematical Society__ 91. 2 (2015): 439-463.

Gessel, Ira, Levine, Adam, Ruberman, Daniel, and Strle, Sašo. "Non-orientable surfaces in homology cobordisms." __Geometry and Topology__ 19. (2015): 439--494.

Mrowka, Tomasz, Ruberman, Daniel, and Saveliev, Nikolai. "Index theory of the de Rham complex on manifolds with periodic ends." __Algebraic & Geometric Topology__ 14. (2015): 3689--3700.

Mrowka, Tomasz, Ruberman, Daniel, and Saveliev, Nikolai. "An index theorem for end-periodic operators." __Compositio Mathematica__ 152. 2 (2015): 399-444.

Levine, Adam, and Ruberman, Daniel. __Generalized Heegaard Floer correction terms__. Proc. of 20th Gökova Geometry and Topology Conference. Gökova, Turkey: International Press, 2014.

Ruberman, Daniel and Saveliev, Nikolai. "Casson-type invariants from the Seiberg-Witten equations." __New Ideas in Low-Dimensional Topology__. Ed. Louis Kauffman and Vassily Manturov. World Scientfic Publishing, 2014. 1--18.

Ruberman, Daniel and Strle, Sašo. "Concordance properties of parallel links." __Indiana Univ. Math. Journal__ 62. 3 (2013): 799-814.

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, Sašo. "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.

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

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

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

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

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.