View source for Hugo Duminil-Copin

{{short description|French mathematician}}
{{Use dmy dates|date=July 2022}}
{{Infobox scientist
| name             = Hugo Duminil-Copin
| image            = Hugo_Duminil-Copin_in_Oberwolfach.jpg
| caption          = Duminil-Copin in 2014
| birth_date       = {{birth date and age|1985|08|26|df=y}}
| birth_place      = [[Châtenay-Malabry]], [[Île-de-France]], France
| fields           = Mathematics
| workplaces       = {{ubl|[[University of Geneva]]|[[Institut des Hautes Études Scientifiques]]}}
| alma_mater       = {{ubl|[[Lycée Louis-le-Grand]]|[[École normale supérieure (Paris)|École normale supérieure]]|[[University of Paris-Sud]]}}
| doctoral_advisor = [[Stanislav Smirnov]]
| thesis_title = Phase transition in random-cluster and O(n)-models
| thesis_year = 2011
| thesis_url = https://archive-ouverte.unige.ch/unige:18929
| awards           = {{ubl|[[Rollo Davidson Prize]] (2012) | [[Oberwolfach Prize]] (2013) |[[EMS Prize]] (2016)|[[New Horizons in Mathematics Prize]] (2017)|[[Fields Medal]] (2022)}}
}}

'''Hugo Duminil-Copin''' (born 26 August 1985) is a French mathematician specializing in [[probability theory]]. He was awarded the [[Fields Medal]] in 2022.

==Biography==
The son of a middle school sports teacher and a former female dancer who became a primary school teacher, Duminil-Copin grew up in the outer suburbs of Paris, where he played a lot of sports as a child, and initially considered attending a sports-oriented high school to pursue his interest in handball.<ref name=qf>{{cite web | first=Jordana | last=Cepelewicz | title=Hugo Duminil-Copin Wins the Fields Medal | website=Quanta Magazine | date=5 July 2022 | url=https://www.quantamagazine.org/hugo-duminil-copin-wins-the-fields-medal-20220705/ | access-date=5 July 2022 | archive-date=5 July 2022 | archive-url=https://web.archive.org/web/20220705073201/https://www.quantamagazine.org/hugo-duminil-copin-wins-the-fields-medal-20220705/ | url-status=live }}</ref> He decided to attend a school focused on mathematics and science,<ref name=qf/> and enrolled at the [[Lycée Louis-le-Grand]] in Paris, then at the [[École normale supérieure (Paris)]] and the [[Paris-Sud University|University Paris-Sud]]. He decided to focus on math instead of physics, because he found the rigour of mathematical proof more satisfying, but developed an interest in [[percolation theory]], which is used in [[mathematical physics]] to address issues in [[statistical mechanics]].<ref name=qf/> In 2008, he moved to the [[University of Geneva]] to write a PhD thesis under [[Stanislav Smirnov]]. Duminil-Copin and Smirnov used percolation theory and the vertices and edges connecting them in a lattice to model fluid flow and with it [[phase transition]]s. The pair investigated the number of [[self-avoiding walk]]s that were possible in [[hexagonal lattice]]s, connecting [[combinatorics]] to percolation theory. This was published in the ''[[Annals of Mathematics]]'' in 2012, the same year in which Duminil-Copil was awarded his PhD at the age of 27.<ref name=qf/>

In 2013, after his postdoctorate, Duminil-Copin was appointed assistant professor, then full professor in 2014 at the University of Geneva.<ref name=":0">{{Cite web |title=Hugo Duminil-Copin, a French mathematician and a permanent professor at IHES, has been awarded the Fields Medal |url=https://www.cnrs.fr/en/hugo-duminil-copin-french-mathematician-and-permanent-professor-ihes-has-been-awarded-fields-medal |access-date=6 July 2022 |website=CNRS |date=5 July 2022 |language=en |archive-date=5 July 2022 |archive-url=https://web.archive.org/web/20220705100814/https://www.cnrs.fr/en/hugo-duminil-copin-french-mathematician-and-permanent-professor-ihes-has-been-awarded-fields-medal |url-status=live }}</ref> In 2016, he became permanent professor at the [[Institut des Hautes Études Scientifiques]].<ref>{{Cite web|url=https://www.ihes.fr/~duminil/CV.html|title=Webpage of Hugo Duminil-Copin|website=www.ihes.fr|access-date=15 August 2020|archive-date=22 October 2020|archive-url=https://web.archive.org/web/20201022114443/https://www.ihes.fr/~duminil/CV.html|url-status=live}}</ref> Since 2019, he has been member of the [[Academia Europaea]].<ref name="Hasani Hoffmann">{{cite web | last1=Hasani | first1=Ilire | last2=Hoffmann | first2=Robert | title=Academy of Europe: Duminil-Copin Hugo | website=Academy of Europe | url=https://www.ae-info.org/ae/Member/Duminil-Copin_Hugo | access-date=5 July 2022 | archive-date=11 April 2021 | archive-url=https://web.archive.org/web/20210411153807/https://www.ae-info.org/ae/Member/Duminil-Copin_Hugo | url-status=live }}</ref>

Since 2017, Duminil-Copin has been the principal investigator of the [[European Research Council]] – Starting Grant “Critical behavior of lattice models (CriBLam)”. He is a member of the Laboratory Alexander Grothendieck, a [[French National Centre for Scientific Research|CNRS]] joint research unit with IHES.<ref name=":0" />

Duminil-Copin's work focuses on the mathematical area of statistical physics. Duminil-Copin uses ideas from probability theory to study the critical behavior of various models on networks.<ref name=":0" /> His work focuses on identifying the critical point at which phase transitions occur, what happens at the critical point, and the behaviour of the system just above and below the critical point.<ref name=qf/> He has been working on dependent percolation models whereby the state of an edge in one part of a lattice will affect the state of edges elsewhere, to shed light of [[Ising model]]s, which are used to study phase transitions in [[ferromagnetic]] materials. In collaboration with Vincent Beffara in 2011, he was able to produce a formula for a determining the critical point for many two-dimensional dependent percolation models.<ref name=qf/> In 2019, along with Vincent Tassion and Aran Raoufi, he published research on the size of connected components in the lattice when the system is just below and above the critical point. They showed that below the critical point, the probability of having two vertices in the same connected component of the lattice would decay exponentially with separation distance, and that a similar result applies above the critical point, and that there is an infinite connected component above the critical point. Duminil-Copin and his associates proved this characteristic, which they called "sharpness", using [[mathematical analysis]] and [[computer science]].<ref name=qf/> He has also shed more light on the nature of the phase transition at the critical point itself, and whether the transition will be continuous or discontinuous, under various circumstances, with a focus on [[Potts model]]s.<ref name=qf/>

Duminil-Copin is researching [[conformal invariance]] in dependent percolation models in two dimensions. He said that by proving the existence of these symmetries, a great deal of information about the models would be extracted.<ref name=qf/> In 2020, he and his collaborators proved that [[rotational invariance]] exists at the boundary between phases in many physical systems.<ref>{{Cite magazine|title=Mathematicians Prove Symmetry of Phase Transitions|language=en-US|magazine=Wired|url=https://www.wired.com/story/mathematicians-prove-symmetry-of-phase-transitions/|access-date=14 July 2021|issn=1059-1028|archive-date=14 July 2021|archive-url=https://web.archive.org/web/20210714020405/https://www.wired.com/story/mathematicians-prove-symmetry-of-phase-transitions/|url-status=live}}</ref><ref>{{cite arXiv|last1=Duminil-Copin|first1=Hugo|last2=Kozlowski|first2=Karol Kajetan|last3=Krachun|first3=Dmitry|last4=Manolescu|first4=Ioan|last5=Oulamara|first5=Mendes|date=21 December 2020|title=Rotational invariance in critical planar lattice models|class=math.PR|eprint=2012.11672}}</ref>

Duminil-Copin was awarded the 2017 [[New Horizons in Mathematics Prize]] for his work on [[Ising model|Ising type model]]s.<ref name="Breakthrough Prize "/>

Duminil-Copin was awarded the [[Fields Medal]] in 2022 for "solving longstanding problems in the probabilistic theory of [[phase transitions]] in statistical physics, especially in dimensions three and four".<ref>{{Cite web |url=https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2022/IMU_Fields22_Duminil-Copin_citation.pdf |title=Fields Medal 2022: Short citation |access-date=5 July 2022 |archive-date=5 July 2022 |archive-url=https://web.archive.org/web/20220705101407/https://www.mathunion.org/fileadmin/IMU/Prizes/Fields/2022/IMU_Fields22_Duminil-Copin_citation.pdf |url-status=live }}</ref><ref name="Hoyer 2022">{{cite web | last=Hoyer | first=Lukas von | title=Der "Nobelpreis der Mathematik" geht an Schweizerin und Schweizer | website=[[Augsburger Allgemeine]] | date=5 July 2022 | url=https://www.augsburger-allgemeine.de/panorama/fields-medaille-2022-nobelpreis-der-mathematik-an-2-forscher-aus-der-schweiz-id63197656.html | language=de | access-date=5 July 2022 | archive-date=5 July 2022 | archive-url=https://web.archive.org/web/20220705091535/https://www.augsburger-allgemeine.de/panorama/fields-medaille-2022-nobelpreis-der-mathematik-an-2-forscher-aus-der-schweiz-id63197656.html | url-status=live }}</ref> [[Wendelin Werner]] credited Duminil-Copin with generalising the field of percolation theory, saying that "Everything is easier, streamlined. The results are stronger. … The whole understanding of these physical phenomena has been transformed."<ref name=qf/> Werner said that Duminil-Copin has solved "Basically half of the main open questions" in percolation theory.<ref name=qf/>

Duminil-Copin's hobbies include sports, which he has stated helps him find inspiration when working.<ref name=qf/> He is married and has a daughter.<ref>{{cite web | last=Celerier | first=Pierre | title=Duminil-Copin, Fields-winning mathematician with 'aesthetic vision' | website=Phys.org | date=5 July 2022 | url=https://phys.org/news/2022-07-duminil-copin-fields-winning-mathematician-aesthetic-vision.html | access-date=5 July 2022 | archive-date=5 July 2022 | archive-url=https://web.archive.org/web/20220705100104/https://phys.org/news/2022-07-duminil-copin-fields-winning-mathematician-aesthetic-vision.html | url-status=live }}</ref>

== Awards ==

* 2022 [[Fields Medal]]<ref name="International Mathematical Union (IMU) 1958">{{cite web | title=Fields Medals 2022 | website=International Mathematical Union (IMU) | date=6 June 1958 | url=https://www.mathunion.org/imu-awards/fields-medal/fields-medals-2022 | access-date=5 July 2022 | archive-date=5 July 2022 | archive-url=https://web.archive.org/web/20220705072608/https://www.mathunion.org/imu-awards/fields-medal/fields-medals-2022 | url-status=live }}</ref><ref name="Larousserie 2022">{{cite web | last=Larousserie | first=David | title=La médaille Fields pour Hugo Duminil-Copin, mathématicien probabiliste de 36 ans et " percolateur " universel | website=Le Monde.fr | date=5 July 2022 | url=https://www.lemonde.fr/sciences/article/2022/07/05/la-medaille-fields-pour-hugo-duminil-copin-percolateur-universel_6133388_1650684.html | language=fr | access-date=5 July 2022 | archive-date=5 July 2022 | archive-url=https://web.archive.org/web/20220705072301/https://www.lemonde.fr/sciences/article/2022/07/05/la-medaille-fields-pour-hugo-duminil-copin-percolateur-universel_6133388_1650684.html | url-status=live }}</ref><ref name="CNRS 2022">{{cite web | title=Hugo Duminil-Copin, mathématicien français et professeur permanent à l'IHES, est lauréat de la médaille Fields | website=CNRS | date=5 July 2022 | url=https://www.cnrs.fr/fr/hugo-duminil-copin-mathematicien-francais-et-professeur-permanent-lihes-est-laureat-de-la-medaille | language=fr | access-date=5 July 2022 | archive-date=5 July 2022 | archive-url=https://web.archive.org/web/20220705081144/https://www.cnrs.fr/fr/hugo-duminil-copin-mathematicien-francais-et-professeur-permanent-lihes-est-laureat-de-la-medaille | url-status=live }}</ref>
* 2019 Dobrushin Prize<ref name=":0" />
* 2018 Invited speaker (session Probability and session Mathematical Physics) at the [[International Congress of Mathematicians]] of [[Rio de Janeiro]]<ref name="National Meeting of the SPM 2021 – Encontro Nacional da Sociedade Portuguesa de Matemática 2021 1940">{{cite web | title=Hugo Duminil-Copin – National Meeting of the SPM 2021 | website=National Meeting of the SPM 2021 – Encontro Nacional da Sociedade Portuguesa de Matemática 2021 | date=12 December 1940 | url=https://enspm2021.spm.pt/hugo-dominil-coupin/ | access-date=5 July 2022 | archive-date=7 July 2022 | archive-url=https://web.archive.org/web/20220707010940/https://enspm2021.spm.pt/hugo-dominil-coupin/ | url-status=live }}</ref>
* 2017 [[Loève Prize]]<ref name="IHES 2017">{{cite web | title=Hugo Duminil-Copin awarded the Loève Prize and the Grand Prix Jacques Herbrand | website=IHES | date=8 August 2017 | url=https://www.ihes.fr/en/hugo-duminil-copin-awarded-the-loeve-prize-and-the-grand-prix-jacques-herbrand/ | access-date=5 July 2022 | archive-date=7 July 2022 | archive-url=https://web.archive.org/web/20220707010939/https://www.ihes.fr/en/hugo-duminil-copin-awarded-the-loeve-prize-and-the-grand-prix-jacques-herbrand/ | url-status=live }}</ref>
* 2017 [[Jacques Herbrand Prize]]<ref name="Home 2017">{{cite web | title=Hugo Duminil-Copin receives the Prix Jacques Herbrand 2017 | website=SwissMAP | date=21 November 2017 | url=https://www.nccr-swissmap.ch/news-and-events/news/hugo-duminil-copin-receives-prix-jacques-herbrand-2017 | access-date=5 July 2022 | archive-date=7 July 2022 | archive-url=https://web.archive.org/web/20220707010947/https://www.nccr-swissmap.ch/news-and-events/news/hugo-duminil-copin-receives-prix-jacques-herbrand-2017 | url-status=live }}</ref>
* 2017 [[New Horizons in Mathematics Prize]]<ref name="Breakthrough Prize ">{{cite web | title=Breakthrough Prize – Mathematics Breakthrough Prize Laureates – Hugo Duminil-Copin | website=Breakthrough Prize | url=https://breakthroughprize.org/Laureates/3/L3806 | ref={{sfnref | Breakthrough Prize }} | access-date=5 July 2022 | archive-date=4 June 2022 | archive-url=https://web.archive.org/web/20220604184316/https://breakthroughprize.org/Laureates/3/L3806 | url-status=live }}</ref> 
* 2016 Prize of the [[European Mathematical Society]]<ref name="IHES 2016">{{cite web | title=Hugo Duminil-Copin is awarded the European Mathematical Society Prize | website=IHES | date=30 June 2016 | url=https://www.ihes.fr/en/hugo-duminl-copain-is-awarded-the-european-mathematical-society-prize/ | access-date=5 July 2022 | archive-date=7 July 2022 | archive-url=https://web.archive.org/web/20220707010943/https://www.ihes.fr/en/hugo-duminl-copain-is-awarded-the-european-mathematical-society-prize/ | url-status=live }}</ref>
* 2015 Early Career Award of the [[International Association of Mathematical Physics]]<ref name="IAMP 2018">{{cite web | title=International Association of Mathematical Physics | website=IAMP | date=31 January 2018 | url=http://www.iamp.org/page.php?page=page_award | access-date=5 July 2022 | archive-date=31 December 2021 | archive-url=https://web.archive.org/web/20211231092049/http://iamp.org/page.php?page=page_award | url-status=live }}</ref>
* 2015 [[Peccot Lectures]] at the [[Collège de France]]<ref>{{Cite web |title=Hugo Duminil-Copin |url=https://www.college-de-france.fr/site/en-cours-peccot/guestlecturer-2014-2015__1.htm |access-date=6 July 2022 |website=Collège de France |archive-date=7 July 2022 |archive-url=https://web.archive.org/web/20220707010943/https://www.college-de-france.fr/site/en-cours-peccot/guestlecturer-2014-2015__1.htm |url-status=live }}</ref>
* 2013 [[Oberwolfach Prize]]<ref name="Home 2014">{{cite web | title=Hugo Duminil-Copin receives the Oberwolfach Prize | website=SwissMAP | date=5 June 2014 | url=https://www.nccr-swissmap.ch/news-and-events/news/hugo-duminil-copin-receives-oberwolfach-prize | access-date=5 July 2022 | archive-date=7 July 2022 | archive-url=https://web.archive.org/web/20220707010951/https://www.nccr-swissmap.ch/news-and-events/news/hugo-duminil-copin-receives-oberwolfach-prize | url-status=live }}</ref>
* 2012 [[Rollo Davidson Prize]] (with {{ill|Vincent Beffara|de||fr}})<ref name="CNRS 2022" />
* 2012 Vacheron-Constantin Prize<ref>{{Cite web|url=http://pages.rts.ch/la-1ere/programmes/cqfd/4740869-cqfd-du-29032013.html|title=Rencontre avec Hugo Duminil-Copin, CQFD du 29.03.2013|date=29 March 2013|website=rts.ch|access-date=5 July 2022|archive-date=7 July 2022|archive-url=https://web.archive.org/web/20220707010951/https://pages.rts.ch/la-1ere/programmes/cqfd/29-03-2013|url-status=live}}</ref>

==  Selected publications ==
* {{cite book | last=Duminil-Copin | first=Hugo | title=Graphical representations of lattice spin models : cours Peccot, Collège de France : janvier-février 2015 | year=2016 | publisher=Spartacus IDH | isbn=978-2-36693-022-1 | oclc=987302673}}
* {{cite journal |last1=Duminil-Copin |first1=Hugo |last2=Smirnov |first2=Stanislav |author-link2=Stanislav Smirnov |title=The connective constant of the honeycomb lattice equals <math>\sqrt{2+\sqrt 2}</math> |journal=Annals of Mathematics |volume=175 |issue=3 |date=1 May 2012 |issn=0003-486X |doi=10.4007/annals.2012.175.3.14 |arxiv=1007.0575 |pages=1653–1665 |s2cid=59164280}}
* {{cite journal | last1=Beffara | first1=Vincent | last2=Duminil-Copin | first2=Hugo | title=The self-dual point of the two-dimensional random-cluster model is critical for <math>q \geq 1</math> | journal=Probability Theory and Related Fields | publisher=Springer Science and Business Media LLC | volume=153 | issue=3–4 | date=18 March 2011 | issn=0178-8051 | arxiv=1006.5073 | doi=10.1007/s00440-011-0353-8 | pages=511–542| s2cid=55391558 | url=https://hal-ens-lyon.archives-ouvertes.fr/ensl-00495872/file/BD%3Afkcriticalpoint.pdf }}
* {{cite journal | last1=Duminil-Copin | first1=Hugo | last2=Hammond | first2=Alan | title=Self-Avoiding Walk is Sub-Ballistic | journal=Communications in Mathematical Physics | publisher=Springer Science and Business Media LLC | volume=324 | issue=2 | date=13 October 2013 | issn=0010-3616 | doi=10.1007/s00220-013-1811-1 | pages=401–423| arxiv=1205.0401 | bibcode=2013CMaPh.324..401D | s2cid=10829154 }}
* {{cite journal |last1=Bauerschmidt |first1=Roland |last2=Duminil-Copin |first2=Hugo |last3=Goodman |first3=Jesse |last4=Slade |first4=Gordon |author-link4=Gordon Douglas Slade |journal=MathProblems |title=Lectures on Self-Avoiding Walks |year=2012 |doi= |arxiv=1206.2092 }}

==  References  ==
{{reflist}}

==Further reading==
* {{cite web |first=Kenneth |last=Chang | title=Fields Medals in Mathematics Won by Four Under Age 40 | website=[[The New York Times]] | date=5 July 2022 | url=https://www.nytimes.com/live/2022/07/05/science/fields-medal-math | ref={{sfnref | The New York Times | 2022}} | access-date=5 July 2022}}
* {{cite web | title=Le Français Hugo Duminil-Copin remporte la médaille Fields, avec trois autres mathématiciens | website=[[leparisien.fr]] | date=5 July 2022 | url=https://www.leparisien.fr/sciences/le-francais-hugo-duminil-copin-remporte-la-medaille-fields-avec-trois-autres-mathematiciens-05-07-2022-TP4PTEJ3XRB7BKWPHGY6ECQBSY.php | language=fr | access-date=5 July 2022}}
* {{cite web | last=Bischoff | first=Manon | title=Fields-Medaille: Mathematik-Preis für 24-dimensionale Kugeln | website=Spektrum der Wissenschaft | date=5 July 2022 | url=https://www.spektrum.de/news/fields-medaille-2022-vier-gewinner-darunter-eine-frau/2037034 | language=de | access-date=5 July 2022}}

== External links ==
* [https://arxiv.org/search/math-ph?searchtype=author&query=Duminil-Copin,+H Hugo Duminil-Copin's papers on arxiv]
* {{Cite web|url=https://www.youtube.com/watch?v=oqMLxYHe5lg|title=Chemins auto-évitants sur le réseau en nid d'abeille, Lecture at the Institut Henri Poincaré, 19/11/2016|website=YouTube |date=23 November 2016 }}
* {{Cite web|url=https://www.ihes.fr/professeur/hugo-duminil-copin/|title=Page on IHES website}}
* {{MathGenealogy}}

{{Fields medalists}}

{{Authority control}}

{{DEFAULTSORT:Duminil-Copin, Hugo}}
[[Category:1985 births]]
[[Category:Living people]]
[[Category:French mathematicians]]
[[Category:Lycée Louis-le-Grand alumni]]
[[Category:École Normale Supérieure alumni]]
[[Category:University of Geneva alumni]]
[[Category:Academic staff of the University of Geneva]]
[[Category:People from Châtenay-Malabry]]
[[Category:Fields Medalists]]