{{Short description|German mathematician}} {{Infobox person | name = Thomas Schick | image = Schick thomas 2012.jpg | caption = Schick in [[Oberwolfach]], Germany 2012 | birth_date = {{Birth date and age|1969|05|22}} | birth_place = [[Alzey]], Germany | occupation = {{hlist|Mathematician}} }} '''Thomas Schick''' (born 22 May 1969 in [[Alzey]]) is a German mathematician, specializing in algebraic topology and differential geometry.
==Education and career== Schick studied mathematics and physics at the [[Johannes Gutenberg University Mainz]], where he received in 1994 his [[Diplom]] in mathematics and in 1996 his PhD ([[Promotion (Germany)|Promotion]]) under the supervision of [[Wolfgang Lück]] with thesis ''Analysis on Manifolds of Bounded Geometry, Hodge-deRham Isomorphism and <math>L^2</math>-Index Theorem''.<ref>{{MathGenealogy|id=27755}}</ref> As a [[postdoc]] he was from 1996 to 1998 at the [[University of Münster]] and from 1998 to 2000 an assistant professor at [[Pennsylvania State University]], where he worked with [[Nigel Higson]] and [[John Roe (mathematician)|John Roe]]. Schick received his [[habilitation]] in 2000 from the University of Münster and is since 2001 a professor for pure mathematics at the [[University of Göttingen]].
His research deals with topological invariants, ''e.g.'' <math>L^2</math>-invariants and those invariants which result from the [[K-theory]] of [[operator algebra]]s. Such invariants arise in generalizations of the [[Atiyah-Singer index theorem]].
Schick, with Wolfgang Lück, introduced the strong Atiyah conjecture. Given a discrete group G, the Atiyah conjecture states that the <math>L^2</math>-[[Betti number]]s of a finite [[CW-complex]] that has fundamental group G are integers, provided that G is torsion-free; furthermore, in the general case, the <math>L^2</math>-Betti numbers are rational numbers with denominators determined by the finite subgroups of G. In 2007 Schick, with Peter Linnell, proved a theorem which established conditions under which the Atiyah conjecture for a torsion-free group G implies the Atiyah conjecture for every finite extension of G; furthermore, they proved that the conditions are satisfied for a certain class of groups.<ref>{{cite journal|author=Schick, T.|author2=Linnell, P.|title=Finite group extensions and the Atiyah conjecture|journal=Journal of the American Mathematical Society|volume=20|year=2007|issue=4|pages=1003–1061|url=http://www.uni-math.gwdg.de/schick/publ/extAtiyah.html|arxiv=math/0403229|doi=10.1090/S0894-0347-07-00561-9|bibcode=2007JAMS...20.1003L |s2cid=12160184}}</ref> In 2000 Schick proved the Atiyah conjecture for a large class of special cases.<ref>{{cite journal|author=Schick, T.|title=Integrality of <math>L^2</math> Betti numbers|journal=Mathematische Annalen|volume=317|issue=4|year=2000|pages=727–750|doi=10.1007/PL00004421|arxiv=math/0001101|s2cid=59127019}}</ref> In 2007 he presented a method which proved the Baum-Connes conjecture for the full braid groups, and for other classes of groups which arise as (finite) extensions for which the Baum-Connes conjecture is known to be true.<ref>{{cite journal|author=Schick, T.|title=Finite group extensions and the Baum-Connes conjecture|journal=Geometry and Topology|volume=11|year=2007|issue=3|pages=1767–1775| arxiv=math/0209165 | doi=10.2140/gt.2007.11.1767|doi-access=free}} [https://arxiv.org/abs/math.KT/0209165 arXiv preprint]</ref><ref>{{cite web|title=Thomas Schick: Finite group extensions and the Baum-Connes conjecture|website=Schick's website at the University of Gôttingen (uni-math.gwdg.de)|url=http://www.uni-math.gwdg.de/schick/publ/BC_finite_ext.html}}</ref>
In the 1990s there were proofs of many special cases of the Gromov-Lawson-Rosenberg conjecture concerning criteria for the existence of a metric with positive [[scalar curvature]]; in 1997 Schick published the first counterexample.<ref>{{cite journal|author=Schick, T.|title=A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture|journal=Topology|volume=37|year=1998|issue=6|pages=1165–1168|arxiv=math/0403063| doi=10.1016/s0040-9383(97)00082-7|doi-access=free}} [https://arxiv.org/abs/math/0403063 arXiv preprint]</ref>
He is the coordinator of the Courant Research Center's ''Strukturen höherer Ordnung in der Mathematik'' (Structures of Higher Order in Mathematics) at the [[University of Göttingen]].<ref>{{cite web|website=Göttinger Tageblatt|title=Neuartige Probleme der Mathematik lösen, Göttingen, Courant Forschungszentrum|date=19 May 2009|url=http://www.goettinger-tageblatt.de/Nachrichten/Wissen/Wissen-vor-Ort/Neuartige-Probleme-der-Mathematik-loesen}}</ref> A major goal of the research center is the investigation of mathematical structures that could play a role in modern theoretical physics, especially [[string theory]] and [[quantum gravity]].
He was the managing editor for [[Mathematische Annalen]]. In 2014 he was an invited speaker with talk ''The topology of scalar curvature'' at the [[International Congress of Mathematicians]] in [[Seoul]]. In 2016 he became a full member of the [[Göttingen Academy of Sciences and Humanities]].
==Selected publications== *''[https://arxiv.org/abs/1405.4220 Topology of scalar curvature.]'' Proc. ICM 2014, Seoul. *''[https://arxiv.org/abs/math/0209164 Operator algebras and topology.]'' ICTP Summer School, Triest 2001. * with Ulrich Bunke: ''[https://arxiv.org/abs/1011.6663 Differential K-Theory.]'' * with Ulrich Bunke: ''[https://arxiv.org/abs/0707.0046 Smooth K-Theory.]'' In: ''[[Astérisque]].'' No. 328 (2009), 45–135 (2010). {{ISBN|978-2-85629-289-1}}. * with Bernhard Hanke and Wolfgang Steimle: ''The space of metrics of positive scalar curvature.'' [[Publications Mathématiques de l'IHÉS]] 120 (2014), 335–367. {{doi|10.1007/s10240-014-0062-9}} * with Bernhard Hanke: ''Enlargeability and index theory.'' [[Journal of Differential Geometry]] 74 (2006), no. 2, 293–320. [https://arxiv.org/abs/math/0403257 Arxiv] * with Józef Dodziuk, Peter Linnell, [[Varghese Mathai]], Stuart Yates: ''Approximating L<sup>2</sup>-invariants and the Atiyah conjecture. Dedicated to the memory of [[Jürgen K. Moser]].'' [[Communications on Pure and Applied Mathematics]] 56 (2003), no. 7, 839–873. {{doi|10.1002/cpa.10076}} * with [[Rostislav Grigorchuk]], Peter Linnell, Andrzej Żuk: ''On a question of Atiyah.'' [[Comptes rendus de l'Académie des Sciences]] 331 (2000), no. 9, 663–668. [https://arxiv.org/abs/math/0009175 Arxiv] * with [[Wolfgang Lück]]: ''<math>L^2</math> torsion of hyperbolic manifolds of finite volume.'' In: ''[[Geometric and Functional Analysis]].'' vol. 9, 1999, pp. 518–567, [https://arxiv.org/abs/dg-ga/9707009 Arxiv.] *''Integrality of <math>L^2</math> Betti numbers'', ''[[Mathematische Annalen]]'' vol. 317, 2000, pp. 727–750, [https://arxiv.org/abs/math/0001101 Arxiv.] *''<math>L^2</math>-index theorem for elliptic boundary problems'', ''[[Pacific Journal of Mathematics]]'' vol. 197, 2001, pp. 423–439, [https://arxiv.org/abs/math/9810133 Arxiv.]
==References== <references/>
==External links== *[https://topologie.math.uni-goettingen.de/tschick/ Homepage] *{{cite web|title=Presseinformation: Antrittsvorlesung des Mathematikers Prof. Dr. Thomas Schick|date=15 January 2002|website=Georg-August-Universität Göttingen|url=http://www.uni-goettingen.de/de/3240.html?cid=601}}
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{{DEFAULTSORT:Schick, Thomas}} [[Category:German topologists]] [[Category:Differential geometers]] [[Category:20th-century German mathematicians]] [[Category:21st-century German mathematicians]] [[Category:University of Mainz alumni]] [[Category:Academic staff of the University of Göttingen]] [[Category:Members of the Göttingen Academy of Sciences and Humanities]] [[Category:1969 births]] [[Category:Living people]] [[Category:German academic journal editors]] [[Category:Pennsylvania State University faculty]] [[Category:People from Alzey]]