[{"content":"This page is about a french-speaking working group around non-sofic groups. Details are given in the french version of this page.\n","permalink":"https://stalder.pages.math.cnrs.fr/en/recherche/gt-groupes-non-sofiques/","summary":"\u003cp\u003eThis page is about a french-speaking working group around non-sofic groups.\nDetails are given in the french version of this page.\u003c/p\u003e","title":"Working seminar around non-sofic groups"},{"content":"Broadly speaking, my research focuses on group theory. I am particularly interested in combinatorial, geometric, and dynamical properties of countable groups, as well as certain connections with operator algebras and Polish groups.\nIn my recent work, I am particularly interested in (discrete or topological) high transitivity , (dense) embeddings in certain Polish groups, and the properties of the space of subgroups (of a countable group G) and the dynamical system obtained when G acts by conjugation. In the past, I have worked on large-scale geometric properties such as coarse embeddings in Hilbert spaces or weak forms of amenability such as the Haagerup property and inner amenability, as well as on the space of marked finitely generated groups.\nMy favorite groups are those acting on trees, in particular free groupes and Baumslag-Solitar groups, and wreath products.\nI often work with combinatorial objects like graphs, spaces with walls, cubical complexes, etc. I also use analytical tools, among which the Baire category theorem is one of my favorites.\n","permalink":"https://stalder.pages.math.cnrs.fr/en/recherche/presentation/","summary":"\u003cp\u003eBroadly speaking, my research focuses on group theory. I am particularly interested in combinatorial, geometric, and dynamical properties of countable groups, as well as certain connections with operator algebras and Polish groups.\u003c/p\u003e\n\u003cp\u003eIn my recent work, I am particularly interested in (discrete or topological) \u003cem\u003ehigh transitivity\u003c/em\u003e , (dense) embeddings in certain Polish groups, and the properties of the \u003cem\u003espace of subgroups\u003c/em\u003e (of a countable group \u003cem\u003eG\u003c/em\u003e) and the dynamical system obtained when \u003cem\u003eG\u003c/em\u003e acts by conjugation. In the past, I have worked on large-scale geometric properties such as coarse embeddings in Hilbert spaces or weak forms of amenability such as the Haagerup property and inner amenability, as well as on the \u003cem\u003espace of  marked finitely generated groups\u003c/em\u003e.\u003c/p\u003e","title":"My research themes"},{"content":"This page is still under construction.\nEmployment Since 2006 - Maître de conférences at Université Clermont Auvergne (formerly Université Blaise Pascal) 2003-2006 - Ph.D. student funded by Fonds national suisse de la recherche scientifique 2003-2006 - Teaching assistant in mathematics at Université de Neuchâtel (50%) 2001-2003 - Teaching assistant in mathematics at Université de Neuchâtel (100%) 2000-2001 - Uncertified Teaching assistant in mathematics at Université de Neuchâtel (50%) 1998-2004 - Various short-term substitute teaching assignments (outside university) Degrees 2005 - Ph. D. (\u0026ldquo;doctorat ès sciences\u0026rdquo;), Université de Neuchâtel 2001 - Degree in Mathematics (\u0026ldquo;diplôme de mathématicien\u0026rdquo;), Université de Neuchâtel, summa cum laude (\u0026ldquo;mention très bien\u0026rdquo;) 1996 - Science Baccalaureate (\u0026ldquo;Maturité fédérale type C\u0026rdquo;), Gymnase cantonal de La Chaux-de-Fonds, summa cum laude (\u0026ldquo;mention très bien\u0026rdquo;) Key Computer Skills LaTeX, Markdown Spreadsheets Git Python Languages French: native English: intermediate German: beginner ","permalink":"https://stalder.pages.math.cnrs.fr/en/a-propos/cv/","summary":"\u003cp\u003eThis page is still under construction.\u003c/p\u003e\n\u003ch2 id=\"employment\"\u003eEmployment\u003c/h2\u003e\n\u003cul\u003e\n\u003cli\u003eSince 2006 - Maître de conférences at \u003ca href=\"https://www.uca.fr/\"\u003eUniversité Clermont Auvergne\u003c/a\u003e (formerly  Université Blaise Pascal)\u003c/li\u003e\n\u003cli\u003e2003-2006 - Ph.D. student funded by Fonds national suisse de la recherche scientifique\u003c/li\u003e\n\u003cli\u003e2003-2006 - Teaching assistant in mathematics at \u003ca href=\"https://www.unine.ch/\"\u003eUniversité de Neuchâtel\u003c/a\u003e (50%)\u003c/li\u003e\n\u003cli\u003e2001-2003 - Teaching assistant in mathematics at \u003ca href=\"https://www.unine.ch/\"\u003eUniversité de Neuchâtel\u003c/a\u003e (100%)\u003c/li\u003e\n\u003cli\u003e2000-2001 - Uncertified Teaching assistant in mathematics at \u003ca href=\"https://www.unine.ch/\"\u003eUniversité de Neuchâtel\u003c/a\u003e (50%)\u003c/li\u003e\n\u003cli\u003e1998-2004 - Various short-term substitute teaching assignments (outside university)\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch2 id=\"degrees\"\u003eDegrees\u003c/h2\u003e\n\u003cul\u003e\n\u003cli\u003e2005 - Ph. D. (\u0026ldquo;doctorat ès sciences\u0026rdquo;), \u003ca href=\"https://www.unine.ch/\"\u003eUniversité de Neuchâtel\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e2001 - Degree in Mathematics (\u0026ldquo;diplôme de mathématicien\u0026rdquo;), \u003ca href=\"https://www.unine.ch/\"\u003eUniversité de Neuchâtel\u003c/a\u003e, summa cum laude (\u0026ldquo;mention très bien\u0026rdquo;)\u003c/li\u003e\n\u003cli\u003e1996 - Science Baccalaureate (\u0026ldquo;Maturité fédérale type C\u0026rdquo;), Gymnase cantonal de La Chaux-de-Fonds, summa cum laude (\u0026ldquo;mention très bien\u0026rdquo;)\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch2 id=\"key-computer-skills\"\u003eKey Computer Skills\u003c/h2\u003e\n\u003cul\u003e\n\u003cli\u003eLaTeX, Markdown\u003c/li\u003e\n\u003cli\u003eSpreadsheets\u003c/li\u003e\n\u003cli\u003eGit\u003c/li\u003e\n\u003cli\u003ePython\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch2 id=\"languages\"\u003eLanguages\u003c/h2\u003e\n\u003cul\u003e\n\u003cli\u003eFrench: native\u003c/li\u003e\n\u003cli\u003eEnglish: intermediate\u003c/li\u003e\n\u003cli\u003eGerman: beginner\u003c/li\u003e\n\u003c/ul\u003e","title":"Brief CV"},{"content":"My scientific publications, including preprints, are exhaustively referenced in HAL.\nThis is the page I update most often when it comes to revisions. I also post the published versions of my articles there whenever possible.\nYou can also find me on ArXiV, ORCID and ResearchGate, but these sources are less up-to-date than HAL.\n","permalink":"https://stalder.pages.math.cnrs.fr/en/recherche/publications/","summary":"\u003cp\u003eMy scientific publications, including preprints, are exhaustively referenced in \u003ca href=\"https://cv.hal.science/yves-stalder\"\u003eHAL\u003c/a\u003e.\u003c/p\u003e\n\u003cp\u003eThis is the page I update most often when it comes to revisions. I also post the published versions of my articles there whenever possible.\u003c/p\u003e\n\u003cp\u003eYou can also find me on\n\u003ca href=\"https://arxiv.org/a/stalder_y_1.html\"\u003eArXiV\u003c/a\u003e,\n\u003ca href=\"https://orcid.org/0000-0001-5371-3168\"\u003eORCID\u003c/a\u003e\nand \u003ca href=\"https://www.researchgate.net/profile/Yves-Stalder\"\u003eResearchGate\u003c/a\u003e,\nbut these sources are less up-to-date than HAL.\u003c/p\u003e","title":"Publications"},{"content":"E-mail address yves.stalder@uca.fr\nMy office This is office nr 229, on the second floor in the Mathematics building\nLocalization You can also open the map on cartes.app\nPostal address Université Clermont Auvergne - LMBP\nUMR 6620 - CNRS\nCampus des Cézeaux\n3, place Vasarely\nTSA 60026\nCS 60026\n63178 Aubière cedex\nFrance\n","permalink":"https://stalder.pages.math.cnrs.fr/en/a-propos/contact/","summary":"\u003ch2 id=\"e-mail-address\"\u003eE-mail address\u003c/h2\u003e\n\u003cp\u003e\u003ca href=\"mailto:yves.stalder@uca.fr\"\u003eyves.stalder@uca.fr\u003c/a\u003e\u003c/p\u003e\n\u003ch2 id=\"my-office\"\u003eMy office\u003c/h2\u003e\n\u003cp\u003eThis is office \u003cstrong\u003enr 229\u003c/strong\u003e, on the second floor in the Mathematics building\u003c/p\u003e\n\u003ch2 id=\"localization\"\u003eLocalization\u003c/h2\u003e\n\u003ciframe\n    src=\"https://cartes.app/?allez=Laboratoire de Mathématiques Blaise Pascal|w62840258|3.11255|45.76023#16.5/45.760362/3.112113\"\n    style=\"\n    width: 95%;\n    height: 36rem;\n    max-width: 100%;\n    margin: 0 auto;\n    margin-bottom: 5vh;\n    display: block;\n    box-shadow: rgba(0, 0, 0, 0.1) 0px 20px 25px -5px,\n        rgba(0, 0, 0, 0.04) 0px 10px 10px -5px;\n    background: linear-gradient(white, white) padding-box, linear-gradient(to right, #2988e6, #57bff5) border-box;\n    border: 0.2rem solid transparent;\n    border-radius: 0.5rem;\n    \"\n\u003e\u003c/iframe\u003e\n\u003cp\u003eYou can also \u003ca href=\"https://cartes.app/?allez=Laboratoire\u0026#43;de\u0026#43;Math%25C3%25A9matiques\u0026#43;Blaise\u0026#43;Pascal%7Cw62840258%7C3.11253%7C45.76023\"\u003eopen the map on cartes.app\u003c/a\u003e\u003c/p\u003e","title":"Where to find me / how to contact me"},{"content":"Space of marked groups and Baumslag-Solitar groupsEspace des groupes marqués et groupes de Baumslag-Solitar Original title : Espace des groupes marqués et groupes de Baumslag-Solitar Defense : 5 décembre 2005, à l\u0026rsquo;Université de Neuchâtel Comitee : Prof. Alain Valette (advisor, Neuchâtel), Dr. Paul Jolissaint (referee, Neuchâtel), Prof. Goulnara Arjantseva (referee, Genève), Prof. Thomas Delzant (referee, Strasbourg), Prof. Bruno Colbois (Neuchâtel) Direct access : Version pdf DOI : 10.35662/unine-thesis-1845 Keywords Baumslag-Solitar groups, inner amenability, HNN extensions, space of marked groups, groups acting on trees, a-T-menability, presentations. Abstract Baumslag-Solitar groups are very natural groups. As soon as one introduces the concept of an HNN extension, they appear among the simplest examples of such a structure. If $m$ and $n$ are two nonzero integers, the group $BS(m,n)$ is generated by two elements, denoted $a$ and $b$, which satisfy the relation $ab^{m}a^{-1} = b^{n}$.\nGilbert Baumslag and Donald Solitar were interested in these groups because most of them are non-Hopfian. At the time, few non-Hopfian finitely presented groups were known, and these were the first examples of such groups with a single relator. The Baumslag–Solitar groups were classified up to isomorphism by Moldavanskiĭ, while Farb and Mosher, and later Whyte, carried out the classification up to quasi-isometry.\nIt appears that Baumslag-Solitar groups naturally split into two classes: the $BS(±1,n)$ and the $BS(m,n)$ with $|m|, |n| ≥ 2$. The former are metabelian, and thus solvable and amenable, whereas the latter possess neither of these properties. On the other hand, all Baumslag-Solitar groups share weak forms of meanability: for example, they all have the Haagerup property (Gal and Januszkiewicz), and none is uniformly non-ameanable (Arjantseva, Burillo, Lustig, Reeves, Short, and Ventura).\nAnother well-known weak form of amenability is inner-amenability. This property is obvious for groups with a finite (non-trivial) conjugation class. Our results from Chapter 2 on HNN extensions imply, in particular:\nTheorem\nThe group $BS(m,n)$ has infinite conjugacy classes if, and only if, $|m|≠|n|$; The group $BS(m,n)$ is inner-amenable for any non-zero integers $m$ and $n$. The second main concept in this thesis, introduced in Chapter 3, is the space of marked finitely generated groups. Informally, we can say that two marked groups are close if the balls of their Cayley graphs are the same for a large radius.\nThis topology has made it possible to establish several results whose statements do not directly invoke it. For example:\nthe existence of ameanable groups that are not elementary ameanable, proven by Stepin; the existence, for any finitely generated Kazhdan group $G$, of a finitely presented Kazhdan group $H$, such that $G$ is a quotient of $H$, proven by Shalom. It also allows us to characterize Sela\u0026rsquo;s limit groups.\nWe have devoted ourselves to the study of Baumslag–Solitar groups in the space of marked groups, first on our own and then in collaboration with Luc Guyot (see Chapter 4). A new distinction between ameanable and non-ameanable Baumslag–Solitar groups appeared during this work:\nThéorème\nThe marked groups $BS(±1,n)$ converge when $|n| → ∞$; If $m$ is an integer such that $|m|≥2$, the sequence (indexd by $n$) of marked groups $BS(m,n)$ admits uncountably many accumulation points. In the second case, we focus on accumulation points. It turns out that these marked groups are naturally parameterized by $m$-adic integers. A significant part of our work consists of showing that these are extensions of free groups by the wreath product of $\\mathbb{Z}$ with itself, which implies that they are residually solvable and have the Haagerup property. We also provide presentations of them.\n","permalink":"https://stalder.pages.math.cnrs.fr/en/recherche/these_doctorat/","summary":"\u003ch2 id=\"space-of-marked-groups-and-baumslag-solitar-groupsespace-des-groupes-marqués-et-groupes-de-baumslag-solitar\"\u003eSpace of marked groups and Baumslag-Solitar groupsEspace des groupes marqués et groupes de Baumslag-Solitar\u003c/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\u003cstrong\u003eOriginal title :\u003c/strong\u003e Espace des groupes marqués et groupes de Baumslag-Solitar\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eDefense   :\u003c/strong\u003e  5 décembre 2005, à l\u0026rsquo;Université de Neuchâtel\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eComitee   :\u003c/strong\u003e  Prof. Alain Valette (advisor, Neuchâtel), Dr. Paul Jolissaint (referee, Neuchâtel), Prof. Goulnara Arjantseva (referee, Genève), Prof. Thomas Delzant (referee, Strasbourg), Prof. Bruno Colbois (Neuchâtel)\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eDirect access :\u003c/strong\u003e \u003ca href=\"/pdf/These_Stalder.pdf\"\u003eVersion pdf\u003c/a\u003e\u003c/li\u003e\n\u003cli\u003e\u003cstrong\u003eDOI          :\u003c/strong\u003e \u003ca href=\"https://doi.org/10.35662/unine-thesis-1845\"\u003e10.35662/unine-thesis-1845\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch3 id=\"keywords-baumslag-solitar-groups-inner-amenability-hnn-extensions-space-of-marked-groups-groups-acting-on-trees-a-t-menability-presentations\"\u003eKeywords Baumslag-Solitar groups, inner amenability, HNN extensions, space of marked groups, groups acting on trees, a-T-menability, presentations.\u003c/h3\u003e\n\u003ch2 id=\"abstract\"\u003eAbstract\u003c/h2\u003e\n\u003cp\u003eBaumslag-Solitar groups are very natural groups. As soon as one introduces the concept of an HNN extension, they appear among the simplest examples of such a structure. If $m$ and $n$ are two nonzero integers, the group $BS(m,n)$ is generated by two elements, denoted $a$ and $b$, which satisfy the relation $ab^{m}a^{-1} = b^{n}$.\u003c/p\u003e","title":"Ph. D. thesis"}]