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The mathematician Shmuel Aaron Weinberger (born February 20, 1963) is an American topologist. He completed a PhD in mathematics in 1982 at New York University under the direction of Sylvain Cappell. Weinberger was, from 1994 to 1996, the Thomas A. Scott Professor of Mathematics at the University of Pennsylvania, and he is currently a professor and chair of the Mathematics department at the University of Chicago.
His research interests include geometric topology, differential geometry, geometric group theory, and, in recent years, applications of topology in other disciplines. He has written a book on topologically stratified spaces and a book on the application of mathematical logic to geometry.
He has given the Porter lectures at Rice University (2000), the Jankowski memorial lecture of the Polish Academy of Sciences (2000), the Zabrodsky Memorial lecture at Hebrew University (2001), the Cairns lectures at University of Illinois at Urbana-Champaign (2002), the Marker lectures in Mathematics at Penn State University (2003), the Lewis Lectures at Rutgers University (2004), the Blumenthal Lectures at Tel Aviv University (2005), the Hardy Lectures of the London Mathematical Society (2008), the William Benter Lecture at the City University of Hong Kong (2010), and the Clifford Lectures at Tulane University (2012). In addition he has given invited lectures at the International Congress of Mathematicians in Zürich (1994), a mini-symposium at the European Congress of Mathematics (2008), the American Mathematical Society (1989), the Canadian Mathematical Society (2006), and the Association for Symbolic Logic (2001).
- Weinberger, Shmuel: The topological classification of stratified spaces. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 1994.
- Weinberger, Shmuel: Computers, rigidity, and moduli. The large-scale fractal geometry of Riemannian moduli space. M. B. Porter Lectures. Princeton University Press, Princeton, NJ, 2005.
- Research articles
- Attie, O.; Block, J.; Weinberger, S.: Characteristic classes and distortion of diffeomorphisms. J. Amer. Math. Soc. 5 (1992), no. 4, 919—921.
- Bangert, V; Katz, M.; Shnider, S.; Weinberger, S.: E_7, Wirtinger inequalities, Cayley 4-form, and homotopy. Duke Math. J. 146 ('09), no. 1, 35-70. See arXiv:math.DG/0608006
- Block, J.; Weinberger, S.: Aperiodic tilings, positive scalar curvature and amenability of spaces. J. Amer. Math. Soc. 5 (1992), no. 4, 907—918.
- Bryant, J.; Ferry, S.; Mio, W.; Weinberger, S.: Topology of homology manifolds. Ann. of Math. (2) 143 (1996), no. 3, 435–467.
- Davis, J.F.; Weinberger, S.: Group actions on homology spheres. Invent. Math. 86 (1986), no. 2, 209–231.
- Dranishnikov, A. N.; Ferry, S.C.; Weinberger, S.: Large Riemannian manifolds which are flexible. Ann. of Math. (2) 157 (2003), no. 3, 919–938.
- Farber, M.; Weinberger, S.: On the zero-in-the-spectrum conjecture. Ann. of Math. (2) 154 (2001), no. 1, 139–154.
- Ferry, S.C.; Weinberger, S.: Curvature, tangentiality, and controlled topology. Invent. Math. 105 (1991), no. 2, 401–414.
- Manevitz, Larry M.; Weinberger, Shmuel: Discrete circle actions: a note using non-standard analysis. Israel J. Math. 94 (1996), 147—155.
- Farb, B.; Weinberger, S.: Isometries, rigidity and universal covers, Ann. of Math. 168 ('08) no. 3, p. 915—940.
- Niyogi, P; Smale, S; Weinberger, S.:Finding the homology of submanifolds with high confidence from random samples, Discrete & Computational Geometry 39 (2008) 419-441.
- Niyogi, P; Smale, S; Weinberger, S.:A topological view of unsupervised learning from noisy data, SIAM J. of Computing 20(2011) 646-663.
- Weinberger, S.:The Topological Social Choice Problem, Revisited. Journal of Economic Theory 115 (2005) 377-384.