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American mathematician
Ian Agol (/ˈeɪˌɡʊl/; born May 13, 1970) is an American mathematician who deals primarily with the topology of three-dimensional manifolds. Agol graduated
Ian_Agol
Name list
Korea, Ian is pronounced as 이안(I-an), and in Japan, Ian is pronounced as 偉杏, 伊庵, 一晏, etc. Ian (rapper) (born 2005), American rapper Ian Agol (born 1970)
Ian
Quanta Magazine. Retrieved 2022-08-17. Agol, Ian (2013). "The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves, and Jason Manning)"
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Mathematics award
2018. "Breakthrough Prize – Mathematics Breakthrough Prize Laureates – Ian Agol". breakthroughprize.org. "Breakthrough Prize – Breakthrough Prize Marks
Breakthrough Prize in Mathematics
Breakthrough_Prize_in_Mathematics
American mathematician and billionaire (1938–2024)
Zoltán Szabó 2010 Tobias Colding and William Minicozzi; Paul Seidel 2013 Ian Agol and Daniel Wise 2016 Fernando Codá Marques and André Neves 2019 Xiuxiong
Jim_Simons
Unique knot with a crossing number of four
original (PDF) on 2020-07-27, retrieved 2020-10-19 "4_1", The Knot Atlas. Ian Agol, Bounds on exceptional Dehn filling, Geometry & Topology 4 (2000), 431–449
Figure-eight knot (mathematics)
Figure-eight_knot_(mathematics)
American astronomer and astrophysicist
Eric Agol (/ˈeɪˌɡʊl/; born May 13, 1970, in Hollywood, California) is an American astronomer and astrophysicist who was awarded a Guggenheim Fellowship
Eric_Agol
Network of Q&A sites based in New York City
Stack Overflow) Ravi Vakil (co-founder of MathOverflow) Scott Aaronson Ian Agol John Baez Carlo Beenakker Andreas Blass Robert Bryant Cleo Noam Elkies
Stack_Exchange
Weiping Zhang Xiangyu Zhou Günter M. Ziegler Maciej Zworski Oleg N. Ageev Ian Agol Manindra Agrawal Valery Alexeev Michèle Artigue Franck Barthe Alexander
List of International Congresses of Mathematicians Plenary and Invited Speakers
List_of_International_Congresses_of_Mathematicians_Plenary_and_Invited_Speakers
List of notable twins
Württemberg (1876–1936) and Duchess Olga of Württemberg (1876–1932) Eric and Ian Agol (1970–) Alex and Michael Bronstein (1980–) Brian and Keith Conrad (1970–)
List_of_twins
Mathematics award
products of modular curves" 2010 not awarded 2009 Jean-Loup Waldspurger Ian Agol, Danny Calegari and David Gabai "For his work in p-adic harmonic analysis
Clay_Research_Award
Every compact, irreducible 3-manifold with infinite fundamental group is virtually Haken
problem list. A proof of the conjecture was announced on March 12, 2012 by Ian Agol in a seminar lecture he gave at the Institut Henri Poincaré. The proof
Virtually_Haken_conjecture
Mathematics concept
infinite fundamental group is virtually Haken. This conjecture was proven by Ian Agol. Haken manifolds were introduced by Wolfgang Haken (1961). Haken (1962)
Haken_manifold
American foundation
an annual prize – the Clay Research Award. Its recipients to date are Ian Agol, Manindra Agrawal, Yves Benoist, Manjul Bhargava, Bhargav Bhatt, Tristan
Clay_Mathematics_Institute
Branch of mathematics
Society. Retrieved 5 May 2025. Agol, Ian (2013). "The virtual Haken Conjecture". Doc. Math. 18. With an appendix by Ian Agol, Daniel Groves, and Jason Manning:
Geometry
Mathematical theorem
compact 3-manifolds). This latter conjecture was proved, independently, by Ian Agol and by Danny Calegari and David Gabai. Canary also showed that in the case
Ahlfors_measure_conjecture
24 mathematical problems stated in 1982
Solved by Ian Agol. 2012 17th Having 3-manifold that is aspherical, does it have finite cover with positive first Betti number? Solved by Ian Agol. 2013 18th
Thurston's_24_questions
Award of the American Mathematical Society
Math. 172 (2008), no. 1, 1–27. (with Kenji Fukaya and Ivan Smith) 2013 Ian Agol for: Lower bounds on volumes of hyperbolic Haken 3-manifolds. With an appendix
Oswald Veblen Prize in Geometry
Oswald_Veblen_Prize_in_Geometry
American mathematician (born 1951)
Institute for Advanced Study UC Berkeley Thesis Codimension-Two Surgery (1973) Doctoral advisor William Browder Doctoral students Ian Agol Zhenghan Wang
Michael_Freedman
Conjecture pertaining to finite covers of 3-manifold subfields
quasiconvex hierarchy (PDF). Agol, Ian (2013). "The virtual Haken conjecture". Documenta Mathematica. 18. With an appendix by Ian Agol, Daniel Groves and Jason
Virtually_fibered_conjecture
Gromov, Richard Schoen, Shing-Tung Yau, Fernando Codá Marques, André Neves, Ian Agol, among others.[excessive citations] The theory allows the construction
Almgren–Pitts_min-max_theory
MR 1869847. S2CID 123298695. Agol, Ian (2013). "The virtual Haken conjecture". Documenta Mathematica. 18. With an appendix by Ian Agol, Daniel Groves, and Jason
Arithmetic hyperbolic 3-manifold
Arithmetic_hyperbolic_3-manifold
Colombian mathematician
obtained his PhD at the University of California at Berkeley in 2014 with Ian Agol as advisor (thesis: Homomorphisms between groups of diffeomorphisms). He
Sebastián_Hurtado-Salazar
Shestakov Nagata's conjecture on automorphisms polynomial rings 2004 Ian Agol; and independently by Danny Calegari–David Gabai tameness conjecture geometric
List_of_conjectures
Mathematical space
In March 2012, during a conference at Institut Henri Poincaré in Paris, Ian Agol announced he could prove the virtually Haken conjecture for closed hyperbolic
3-manifold
NTEyYWFiMjczZmIz/edit?pli=1 Agol, Ian (2013). "The virtual Haken Conjecture". Doc. Math. 18. With an appendix by Ian Agol, Daniel Groves, and Jason Manning:
Cubical_complex
Agricultural and Resource Economics Department at UC Berkeley (1979–present) Ian Agol – professor of mathematics at UC Berkeley; mathematician of the topology
List of University of California, Berkeley faculty
List_of_University_of_California,_Berkeley_faculty
Orientable surface whose boundary is a knot or link
place upper bounds on the genus. The knot genus is NP-complete by work of Ian Agol, Joel Hass and William Thurston. It has been shown that there are Seifert
Seifert_surface
Frank Adams Jeffrey D. Adams Alejandro Adem Roy Adler Vaneet Aggarwal Ian Agol Manindra Agrawal Yakir Aharonov Lars Ahlfors Alfred Aho Michael Aizenman
List of people by Erdős number
List_of_people_by_Erdős_number
Sciences Christopher Voigt, PhD 2002 Sam Wang, BS 1986 Ned Wingreen, BS 1984 Ian Agol, BS 1992; Breakthrough Prize laureate William Arveson, BS 1960 Michael
List of California Institute of Technology people
List_of_California_Institute_of_Technology_people
Award
Boris Zilber 2006 Miles Reid 2008 Kevin Buzzard 2010 Dusa McDuff 2012 Ian Agol 2014 Daniel Freed, Michael Hopkins & Constantin Teleman 2016 Keisuke Hara [de]
Berwick_Prize
Caltech student residence system
Mathematics) Mathematician, known for introducing the essential dimension Ian Agol (1992, Mathematics) Mathematician known for work in topology, professor
House system at the California Institute of Technology
House_system_at_the_California_Institute_of_Technology
Manifold of dimension 3 equipped with a hyperbolic metric
of 3-dimensional topology. Recent breakthroughs of Kahn–Markovic, Wise, Agol and others have answered most long-standing open questions on the topic but
Hyperbolic_3-manifold
Institution Year elected J. Frank Adams (died 1989) University of Cambridge 1985 Ian Agol University of California, Berkeley 2016 Manindra Agrawal Indian Institute
List of members of the National Academy of Sciences (mathematics)
List_of_members_of_the_National_Academy_of_Sciences_(mathematics)
American physicist (born 1963)
Maxim Kontsevich, Jacob Lurie, Terence Tao and Richard Taylor (2015) Ian Agol (2016) Jean Bourgain (2017) Christopher Hacon, James McKernan (2018) Vincent
Charles_L._Kane
Gives sufficient condition for Dehn filling to result in a negatively curved 3-manifold
complete hyperbolic metric. An argument of Agol's shows that there are at most 12 exceptional slopes. Agol, Ian (2000), "Bounds on exceptional Dehn filling"
2π_theorem
needed] The conjecture was proved in 2004 by Ian Agol, and independently, by Danny Calegari and David Gabai. Agol's proof relies on the use of manifolds of
Tameness_theorem
Brazilian mathematician
Willmore conjecture (Willmore, 1965) In May 2012, in cooperation with Ian Agol and André Neves, Marques provided the solution to the Freedman–He–Wang
Fernando_Codá_Marques
American mathematician
needed to transform a diagram of the unknot into a standard circle. With Ian Agol and William Thurston, he proved that knot genus in 3-manifolds is NP-complete
Joel_Hass
American mathematician (born 1971)
subgroup separability for a wide class of groups, Daniel Wise together with Ian Agol was awarded in 2013 the Oswald Veblen Prize in Geometry. In 2019, he was
Daniel_Wise_(mathematician)
actress David A. R. White, actor and producer May 13 Eric Agol, astronomer and astrophysicist Ian Agol, mathematician Mark Beaufait, ice hockey player Mindy
1970_in_the_United_States
French mathematician (1975–2024)
3-Dimensional Compact Ashperical Variety is Virtually Haken") (following Ian Agol, Daniel Wise) Bergeron edited a few articles for the site Images des mathématiques
Nicolas_Bergeron
Fellowship". University of Illinois. 2005-04-15. Retrieved 2022-11-07. "Ian Agol". John Simon Guggenheim Memorial Foundation. Retrieved 2022-11-07. "Stalking
List of Guggenheim Fellowships awarded in 2005
List_of_Guggenheim_Fellowships_awarded_in_2005
Portuguese mathematician (born 1975)
Willmore conjecture (Thomas Willmore, 1965). In the same year, jointly with Ian Agol and Fernando Codá Marques, he solved the Freedman–He–Wang conjecture (Freedman–He–Wang
André_Neves
American annual mathematics conference
Perelman's Ricci flow Claude LeBrun (Stony Brook): Mass in Kähler Geometry Ian Agol (UC Berkeley and IAS): Pseudo-Anosov stretch factors and homology of mapping
Geometry_Festival
Conference held at Pusan, Korea, August 18–25, 1994. de Gruyter. p. 234. Ian Agol, Bounds on exceptional Dehn filling II, Geom. Topol. 14 (2010) 1921-1940
Hyperbolic_Dehn_surgery
American mathematician
formulated in 1974 the tameness conjecture, which was proved in 2004 by Ian Agol and independently by a collaborative effort of Danny Calegari and David
Albert_Marden
American astronomer
Technology (B.S. 1992), where he lived in Blacker Hovse (sharing a room with Ian Agol) and was awarded the George Green Prize for Creative Scholarship. His graduate
Niel_Brandt
Particular knot energy
stereographic projection of the standard Hopf link. This was proved in 2012 by Ian Agol, Fernando C. Marques and André Neves, by using Almgren–Pitts min-max theory
Möbius_energy
Red dwarf star in the constellation Aquarius
b and c". arXiv:2509.02128 [astro-ph.EP]. Ducrot, Gillon & Agol 2022. Kipping 2018. Agol et al. 2021. Ducrot et al. 2020, p. 8. Greene et al. 2023. Radica
TRAPPIST-1
(link) Wong, Ian; Knutson, Heather A.; Kataria, Tiffany; Lewis, Nikole K.; Burrows, Adam; Fortney, Jonathan J.; Schwartz, Joel; Shporer, Avi; Agol, Eric; Cowan
List_of_hottest_exoplanets
3847/1538-3881/ab3e63. ISSN 0004-6256. Ducrot, Elsa; Gillon, M.; Delrez, L.; Agol, E.; Rimmer, P.; Turbet, M.; Günther, M. N.; Demory, B.-O.; Triaud, A. H
List_of_coldest_exoplanets
Album by Frank Zappa
Don "Sugarcane" Harris – organ (7) Producer: Frank Zappa Engineers: Stan Agol, Roy Baker, Dick Kunc, Bruce Margolis Production assistant: Dick Barber Arranger:
Chunga's_Revenge
Earth-size exoplanet orbiting TRAPPIST-1
Bibcode:2017Natur.542..456G. doi:10.1038/nature21360. PMC 5330437. PMID 28230125. Agol, Eric; Dorn, Caroline; Grimm, Simon L.; Turbet, Martin; et al. (1 February
TRAPPIST-1e
Small rocky exoplanet orbiting TRAPPIST-1
221G. doi:10.1038/nature17448. ISSN 1476-4687. PMC 5321506. PMID 27135924. Agol, Eric; Dorn, Caroline; Grimm, Simon L.; Turbet, Martin; et al. (1 February
TRAPPIST-1d
List of systems with multiple planets
Marcy, Geoffrey W; Bryson, Stephen T; Rowe, Jason F; Jontof-Hutter, Daniel; Agol, Eric; Borucki, William J; Carter, Joshua A; Ford, Eric B; Gilliland, Ronald
List of multiplanetary systems
List_of_multiplanetary_systems
Hot Jupiter exoplanet in the constellation Vulpecula
Bibcode:2007Natur.447..183K. doi:10.1038/nature05782. PMID 17495920. Majeau, Carl; Agol, Eric; Cowan, Nicolas B. (March 2012). "A Two-dimensional Infrared Map of
HD_189733_b
Orbits where planets may have liquid surface water
temperatures over their surfaces despite tidal locking. Astronomy professor Eric Agol argues that even white dwarfs may support a relatively brief habitable zone
Habitable_zone
Soviet mathematician (1913–2009)
Gelfand and his seminar — a presence) ru:Гельфанд, Израиль Моисеевич V.I. Agol, Notes about I.M. Gelfand’s Seminar[link removed], Russian Journal Developmental
Israel_Gelfand
Regular and periodic mutual gravitational influence of orbiting bodies
December 2017. Luger, R.; Sestovic, M.; Kruse, E.; Grimm, S. L.; Demory, B.-O.; Agol, E.; Bolmont, E.; Fabrycky, D.; Fernandes, C. S.; Van Grootel, V.; Burgasser
Orbital_resonance
Bibcode:2013PCCP...15..397W. doi:10.1039/C2CP42695A. PMID 23172634. S2CID 12351374. Agol, Ian; Hass, Joel; Thurston, William (19 May 2002). "3-manifold knot genus is
List_of_NP-complete_problems
Two interlinked loops with five structural crossings
Mathematical models (2nd ed.), Oxford: Clarendon Press, p. 59, MR 0124167 Agol, Ian (2010), "The minimal volume orientable hyperbolic 2-cusped 3-manifolds"
Whitehead_link
Tiling of the hyperbolic plane
Combinatorics. 11 (2). Research Paper 7. doi:10.37236/1864. MR 2120102. Agol, Ian (26 January 2018). "Smallest tile to tessellate the hyperbolic plane"
Binary_tiling
Shreyas; Fu, Guangwei; Han, Te; Greklek-McKeon, Michael; Mahadevan, Suvrath; Agol, Eric; Bello-Arufe, Aaron; Berta-Thompson, Zachory; Cañas, Caleb I.; Chachan
List_of_exoplanet_extremes
Terrestrial planet orbiting the star Proxima Centauri
Luger, Rodrigo; Lustig-Yaeger, Jacob; Fleming, David P.; Tilley, Matt A.; Agol, Eric; Meadows, Victoria S.; Deitrick, Russell; Barnes, Rory (3 March 2017)
Proxima_Centauri_b
Global radio telescope array
Astrophysics. 75: 228. Bibcode:1979A&A....75..228L. Falcke, Heino; Melia, Fulvio; Agol, Eric (January 1, 2000). "Viewing the Shadow of the Black Hole at the Galactic
Event_Horizon_Telescope
Normalized hyperbolic volume of the complement of a hyperbolic knot
Mathematicae, 146 (3): 451–478, doi:10.1007/s002220100167, MR 1869847 Agol, Ian (2010), "The minimal volume orientable hyperbolic 2-cusped 3-manifolds"
Hyperbolic_volume
Subfield of mathematical topology
107796, arXiv:1604.00290, doi:10.1016/j.aim.2021.107796, S2CID 119307517 Agol, Ian; Hass, Joel; Thurston, William (2006), "The computational complexity of
Computational_topology
Number, approximately 0.916
des beaux-arts de Belgique (in French). 33. Brussels. hdl:2268/193841. Agol, Ian (2010). "The minimal volume orientable hyperbolic 2-cusped 3-manifolds"
Catalan's_constant
The Authors Guild. 2017-04-14. Retrieved 2022-10-10. Bell, Susan; Geckler, Ian (2017-04-11). "Three USC professors honored as 2017 Guggenheim Fellows".
List of Guggenheim Fellowships awarded in 2017
List_of_Guggenheim_Fellowships_awarded_in_2017
Sebastian; Kreidberg, Laura; Morley, Caroline; Gillon, Michaël; Selsis, Franck; Agol, Eric; Bolmont, Emeline; Ducrot, Elsa; Hu, Renyu; Koll, Daniel D. B.; Lyu
List of terrestrial exoplanet candidates for atmosphere detection
List_of_terrestrial_exoplanet_candidates_for_atmosphere_detection
Theory of gravitation as curved spacetime
galaxy's central black hole horizon are eagerly sought, cf. Falcke, Melia & Agol 2000 Dalal et al. 2006 Barack & Cutler 2004 Einstein 1917; cf. Pais 1982
General_relativity
Planet outside of the Solar System
June 2015. Knutson, H. A.; Charbonneau, D.; Allen, L. E.; Fortney, J. J.; Agol, E.; Cowan, N. B.; Showman, A. P.; Cooper, C. S.; Megeath, S. T. (2007).
Exoplanet
Link formed from a finite number of twisted sections
Boletín de la Sociedad Matemática Mexicana, 2, 18: 1–32, MR 0341467 Agol, Ian (2010), "The minimal volume orientable hyperbolic 2-cusped 3-manifolds"
Pretzel_link
Matrix group
Proposition 9.10. Sury 2003, Section 3.7. Lubotzky & Segal 2003, Theorem 7.2. Agol, Ian (2013). "The Virtual Haken Conjecture". Documenta Mathematica. 18: 1045–1087
Congruence_subgroup
Star
Douglas A.; Ciardi, David R.; Devore, Edna; Cochran, William; Jenkins, Jon; Agol, Eric; Carter, Joshua A.; Geary, John (2014). "Validation Ofkepler's Multiple
Kepler-160
Smallest closed orientable hyperbolic 3-manifold
of Lie Theory. 8 (1). Heldermann Verlag: 51–66. Retrieved 2025-05-28. Agol, Ian; Storm, Peter A.; Thurston, William P. (2007), "Lower bounds on volumes
Weeks_manifold
American astronomer
2004 by astronomers Matthew J. Holman and Norman W. Murray; and by Eric Agol, Jason Steffen, Re’em Sari, and Will Clarkson. Ballard was the principal
Sarah_Ballard
Romanian mathematician, educator, and writer
Mare (2013) - collected short stories Scrisori de la Polul Est, Editura Agol, Bucharest (2015) - essays Republica, Editura Polirom, Iași (2016) - novel
Bogdan_Suceavă
Citizen science project to find exoplanets
exoplanetarchive.ipac.caltech.edu. Retrieved 2020-02-14. Schmitt, Joseph R.; Agol, Eric; Deck, Katherine M.; Rogers, Leslie A.; Gazak, J. Zachary; Fischer
Planet_Hunters
Heather A.; David Charbonneau; Lori E. Allen; Jonathan J. Fortney; Eric Agol; Nicolas B. Cowan; Adam P. Showman; Curtis S. Cooper; S. Thomas Megeath (10
List_of_exoplanet_firsts
Stellar core remnant
false-positives as far as Gaia non-single star processing is concerned. Agol, Eric (2011). "Transit Surveys for Earths in the Habitable Zones of White
White_dwarf
Star in the constellation Delphinus
; Knutson, Heather A.; Zhao, Ming; Fortney, Jonathan J.; Burrows, Adam; Agol, Eric; Deming, Drake; Désert, Jean-Michel; Howard, Andrew W.; Lewis, Nikole
HAT-P-23
Star in the constellation Aquarius
Jessie L.; Ciardi, David R.; Crossfield, Ian J. M.; Dressing, Courtney D.; Livingston, John H.; Volk, Kathryn; Agol, Eric; Barclay, Thomas; Barentsen, Geert;
K2-138
Extrasolar planet
Deming, Drake; Burrows, Adam; Cowan, Nicolas B.; Triaud, Amaury H. M. J.; Agol, Eric; Desert, Jean-Michel; Fulton, Benjamin J.; Howard, Andrew W.; Laughlin
WASP-6b
Bibcode:2025A&A...693A.228C. doi:10.1051/0004-6361/202452527. ISSN 0004-6361. Agol, Eric; Dorn, Caroline; Grimm, Simon L.; Turbet, Martin; Ducrot, Elsa; Delrez
List_of_smallest_known_stars
List of largest planets by size
842..118L. doi:10.3847/1538-4357/aa6fb5. ISSN 0004-637X. S2CID 119249195. Agol, Eric; Dorn, Caroline; Grimm, Simon L.; Turbet, Martin; Ducrot, Elsa; Delrez
List_of_largest_exoplanets
Star in the constellation Aquarius
"K2-58". SIMBAD. Centre de données astronomiques de Strasbourg. Kruse, Ethan; Agol, Eric; Luger, Rodrigo; Foreman-Mackey, Daniel (2019), "Detection of Hundreds
K2-58
Water, sanitation and hygiene services
hosted by GIZ and SuSanA. (Report). Germany: Sustainable Sanitation Alliance. Agol D, Harvey P, Maíllo J (2018-03-01). "Sanitation and water supply in schools
WASH
Area of astronomical research
2013. Deming, D.; Wilkins, A.; McCullough, P.; Burrows, A.; Fortney, J. J.; Agol, E.; Dobbs-Dixon, I.; Madhusudhan, N.; Crouzet, N.; Desert, J. M.; Gilliland
Extraterrestrial_atmosphere
Extrasolar planet in the constellation Camelopardalis
Heather A.; Lewis, Nikole K.; Stassun, Keivan G.; Fortney, Jonathan J.; Agol, Eric; Laughlin, Gregory P.; Burrows, Adam; Collins, Karen A.; Deming, Drake;
XO-3b
Language native to Papua New Guinea
267–308. Majnep, Ian Saem and Ralph Bulmer. 1977. Birds of my Kalam Country. Auckland: Auckland and Oxford University Presses. Majnep, Ian Saem and Ralph
Kalam_language
1093/mnras/stz1334 Hamann, Aaron; Montet, Benjamin T.; Fabrycky, Daniel C.; Agol, Eric; Kruse, Ethan (2019), "K2-146: Discovery of Planet c, Precise Masses
List of exoplanets discovered in 2019
List_of_exoplanets_discovered_in_2019
Douglas A.; Ciardi, David R.; Devore, Edna; Cochran, William; Jenkins, Jon; Agol, Eric; Carter, Joshua A.; Geary, John (2014), "Validation Ofkepler's Multiple
List of exoplanets discovered in 2014
List_of_exoplanets_discovered_in_2014
Xavier Bonfils; Felipe Murgas; Jose-Manuel Almenara; Thierry Forveille; Eric Agol; Sarah Ballard; Zachory K. Berta-Thompson; Franc¸ois Bouchy; Ryan Cloutier;
List of exoplanets discovered in 2018
List_of_exoplanets_discovered_in_2018
IAN AGOL
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