Daniel Ruberman
Degrees
University of California, Berkeley, Ph.D.Wesleyan University, M.A.
Wesleyan University, B.A.
Expertise
Geometric topology and gauge theory.Profile
Please visit my new faculty profile page.
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. Webpage
Courses 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." Gauge theory and low-dimensional topology: progress and interaction. Mathematical Sciences Publishers, 2021 (forthcoming)
Ruberman, Daniel, ed. A Levine-Tristram invariant for knotted tori. 2021. (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)
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)
Ratcliffe, John, Ruberman, Daniel, and Tschantz, Steven. "Harmonic spinors on the Davis Manifold." 2019.
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.