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Draft:David M. Fisher

From Wikipedia, the free encyclopedia
  • Comment: The named professorship at Rice is enough for notability through WP:PROF#C5. However, everything here must be supported by reliable published sources, preferably by authors and publishers that are independent of Fisher and Rice. Papers by Fisher are not helpful: we need the sources to be about Fisher, not by Fisher. —David Eppstein (talk) 06:39, 20 April 2026 (UTC)



David M. Fisher
Education
Known for
AwardsFellow of the American Mathematical Society (2013)
Scientific career
FieldsMathematics
Workplaces
Thesis On the Arithmetic Structure of Lattice Actions on Compact Manifolds  (1999)
Robert Zimmer

David Fisher is an American mathematician who is the Milton B. Porter Professor of Mathematics at Rice University.[1] His research concerns rigidity in geometry and dynamical systems, discrete subgroups of Lie groups, and geometric group theory.[2] With Aaron Brown [de] and Sebastián Hurtado-Salazar, he proved Zimmer's conjecture for several major classes of lattices.[3] He is a fellow of the American Mathematical Society and was an invited speaker at the 2022 International Congress of Mathematicians.[4][5]

Education and career

[edit]

Fisher received a bachelor's degree in mathematics from Columbia University.[1] He completed his PhD at the University of Chicago in 1999 with the dissertation On the Arithmetic Structure of Lattice Actions on Compact Manifolds, supervised by Robert Zimmer.[6]

After his doctorate, Fisher was a National Science Foundation postdoctoral fellow and Gibbs Assistant Professor at Yale University, and then held faculty positions at Lehman College and the CUNY Graduate Center.[2][7] In 2005 he moved to Indiana University Bloomington, where he was promoted to professor in 2010, named Ruth N. Halls Professor of Mathematics in 2020, and named Distinguished Professor in 2021.[7] He joined the faculty of Rice University in 2022.[2]

Research

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Quasi-isometric rigidity

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Fisher's research in geometric group theory focuses on the classification of finitely generated groups via their large-scale geometry, a program initiated by Mikhail Gromov. He has worked on the quasi-isometric rigidity of solvable groups, which were considered more "flexible", and therefore more difficult to classify, than semisimple groups. With Alex Eskin and Kevin Whyte, Fisher established the quasi-isometric rigidity of various solvable groups, including Sol(m, n) and lamplighter groups.[8][9] For instance, they settled a conjecture by Benson Farb and Lee Mosher, proving that if a finitely generated group is quasi-isometric to Sol(n, n), then the group is virtually a lattice in Sol(n, n). This work introduced the technique of coarse differentiation.

Higher-rank group actions on manifolds

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Fisher has studied smooth actions of higher-rank groups on compact manifolds, specifically addressing two problems in the field: the Zimmer program and the Katok–Spatzier conjecture.

Zimmer program

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The Zimmer program, initiated by Robert Zimmer in the 1980s, seeks to understand the constraints on actions on manifolds by higher-rank lattices (for example, SL(n, Z) with n ≥ 3). With Aaron Brown and Sebastian Hurtado, Fisher proved the main cases of Zimmer's conjecture.[10][11][12] For example, they demonstrated that, for n > 2, any smooth action of SL(n, Z) on a compact manifold of dimension less than n − 1 must be trivial, that is, factor through a finite group action. In their proof, they synthesized diverse tools from smooth ergodic theory, homogeneous dynamics, and group theory. The proof was the subject of a Séminaire Bourbaki talk by Serge Cantat in 2017[13] and was reported in Quanta Magazine.[3]

Prior to this, Fisher worked on the local rigidity of higher-rank lattice actions. In joint works with Gregory Margulis, Fisher showed the local rigidity of algebraic actions by higher-rank lattices and the local rigidity of isometric actions by groups with Kazhdan's Property (T).[14][15]

Katok–Spatzier conjecture

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The Zimmer program is closely related to understanding higher-rank abelian group actions. Anatole Katok and Ralf Spatzier conjectured that sufficiently chaotic (Anosov) actions on a manifold by a higher-rank free abelian group must be algebraic. Fisher, along with Boris Kalinin and Ralf Spatzier, proved cases of the conjecture: any smooth totally non-symplectic (TNS) Anosov action on a nilmanifold is smoothly conjugate to an algebraic action.[16][17] Here, the TNS assumption is a robust way to ensure that the action does not factor through rank 1 groups.

Superrigidity and arithmeticity of discrete subgroups in Lie groups

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In collaboration with Uri Bader, Nicholas Miller, and Matthew Stover, Fisher investigated the geometric conditions that allow hyperbolic manifolds to be arithmetic.[18][19] They proved that if a finite-volume real or complex hyperbolic manifold of dimension at least 3 contains infinitely many maximal totally geodesic submanifolds of dimension at least two, then the manifold is arithmetic, meaning that it is built in a precise number-theoretic way. They showed arithmeticity by showing superrigidity. With Simion Filip and Ben Lowe, Fisher extended similar results to closed negatively curved analytic manifolds.[20]

Honors and awards

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Fisher held a fellowship at the Radcliffe Institute for Advanced Study in 2008–2009 and received a National Science Foundation CAREER award.[21] He has twice been a Simons Fellow in Mathematics.[7][22][23] He was named to the inaugural 2013 class of fellows of the American Mathematical Society.[4][24] His survey with Eskin on quasi-isometric rigidity of solvable groups was an invited lecture at the 2010 International Congress of Mathematicians,[25] and he was an invited speaker at the 2022 Congress, in the sections on dynamics, geometry, and topology.[26][5] In 2023 he, Brown and Hurtado-Salazar received a Frontiers of Science Award from the International Congress of Basic Science for their Annals of Mathematics paper on Zimmer's conjecture.[27]

References

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  1. 1 2 "David Fisher". The People of Rice. Rice University. Retrieved 22 September 2026.
  2. 1 2 3 "New Faculty 2022". Wiess School of Natural Sciences, Rice University. Retrieved 22 September 2026.
  3. 1 2 Hartnett, Kevin (23 October 2018). "A Proof About Where Symmetries Can't Exist". Quanta Magazine. Retrieved 22 September 2026.
  4. 1 2 "List of Fellows of the American Mathematical Society". American Mathematical Society. Retrieved 22 September 2026.
  5. 1 2 Fisher, David. "Rigidity, lattices, and invariant measures beyond homogeneous dynamics". In Beliaev, Dmitry; Smirnov, Stanislav (eds.). International Congress of Mathematicians 2022. EMS Press. pp. 3484–3507.
  6. ↑ David M. Fisher at the Mathematics Genealogy Project
  7. 1 2 3 "David Fisher". Alliance of Distinguished and Titled Professors. Indiana University. Retrieved 2 October 2026.
  8. ↑ A. Eskin, D. M. Fisher and K. M. Whyte, Coarse differentiation of quasi-isometries I: Spaces not quasi-isometric to Cayley graphs, Ann. of Math. (2) 176 (2012), no. 1, 221–260; MR2925383
  9. ↑ A. Eskin, D. M. Fisher and K. M. Whyte, Coarse differentiation of quasi-isometries II: Rigidity for Sol and lamplighter groups, Ann. of Math. (2) 177 (2013), no. 3, 869–910; MR3034290
  10. ↑ A. W. Brown, D. M. Fisher and S. Hurtado-Salazar, Zimmer's conjecture: subexponential growth, measure rigidity, and strong property (T), Ann. of Math. (2) 196 (2022), no. 3, 891–940; MR4502593
  11. ↑ A. W. Brown, D. M. Fisher and S. Hurtado-Salazar, Zimmer's conjecture for actions of SL(m, Z), Invent. Math. 221 (2020), no. 3, 1001–1060; MR4132960
  12. ↑ A. W. Brown, D. M. Fisher and S. Hurtado-Salazar, Zimmer's conjecture for non-uniform lattices: escape of mass and growth of cocycles, 2021; arXiv:2105.14541.
  13. ↑ Cantat, Serge (2019). "Progrès récents concernant le programme de Zimmer, d'après A. Brown, D. Fisher et S. Hurtado". Séminaire Bourbaki, Volume 2017/2018, Exposés 1136–1150. Astérisque (in French). Vol. 414. Société Mathématique de France.
  14. ↑ D. M. Fisher and G. A. Margulis, Local rigidity of affine actions of higher rank groups and lattices, Ann. of Math. (2) 170 (2009), no. 1, 67–122; MR2521112
  15. ↑ D. M. Fisher and G. A. Margulis, Almost isometric actions, property (T), and local rigidity, Invent. Math. 162 (2005), no. 1, 19–80; MR2198325
  16. ↑ D. M. Fisher, B. V. Kalinin and R. J. Spatzier, Global rigidity of higher rank Anosov actions on tori and nilmanifolds, J. Amer. Math. Soc. 26 (2013), no. 1, 167–198; MR2983009
  17. ↑ D. M. Fisher, B. V. Kalinin and R. J. Spatzier, Totally nonsymplectic Anosov actions on tori and nilmanifolds, Geom. Topol. 15 (2011), no. 1, 191–216; MR2776843
  18. ↑ U. Bader, D. M. Fisher, N. Miller and M. Stover, Arithmeticity, superrigidity, and totally geodesic submanifolds, Ann. of Math. (2) 193 (2021), no. 3, 837–861; MR4250391
  19. ↑ U. Bader, D. M. Fisher, N. Miller and M. Stover, Arithmeticity, superrigidity and totally geodesic submanifolds of complex hyperbolic manifolds, Invent. Math. 233 (2023), no. 1, 169–222; MR4601998
  20. ↑ Filip, Simion; Fisher, David; Lowe, Ben (2024). "Finiteness of totally geodesic hypersurfaces". arXiv:2408.03430.{{cite arXiv}}: CS1 maint: missing class (link) A bot will complete this citation soon. Click here to jump the queue
  21. ↑ "David Fisher". Radcliffe Institute for Advanced Study, Harvard University. Retrieved 22 September 2026.
  22. ↑ "David Fisher". Simons Foundation. Retrieved 22 September 2026.
  23. ↑ Pilgrim, Kevin (3 August 2020). "David Fisher awarded Simons Fellowship". Department of Mathematics, Indiana University Bloomington. Retrieved 22 September 2026.
  24. ↑ "American Mathematical Society's first class of fellows includes six from IU Bloomington". Indiana University. Retrieved 2 October 2026.
  25. ↑ "International Congress of Mathematicians 2010 Abstracts" (PDF). International Mathematical Union. Retrieved 22 September 2026.
  26. ↑ "ICM Plenary and Invited Speakers". International Mathematical Union. Retrieved 22 September 2026.
  27. ↑ "Frontiers of Science Awards". International Congress of Basic Science. 2023. Retrieved 2 October 2026.
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