Ciprian Manolescu

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Ciprian Manolescu (born December 24, 1978 in Alexandria ) is a Romanian mathematician who deals with symplectic geometry, low-dimensional topology and the mathematics of gauge field theories.

Ciprian Manolescu

Manolescu went to school in Piteşti . In 1995, 1996 and 1997 he won a gold medal at the International Mathematical Olympiad, each with a perfect score. He studied at Harvard University , where he received his bachelor's degree in 2001 ( summa cum laude ) and his doctorate in 2004 under Peter Kronheimer ( A spectrum valued Topological Quantum Field Theory from the Seiberg – Witten equations ). In his dissertation he simplified the Seiberg-Witten-Floer homology of Kronheimer and Mrowka. As a student he received the Morgan Prize of the American Mathematical Society in 2001 for his work Finite Dimensional Approximations in Seiberg-Witten Theory , received the 2001 Mumford Prize from Harvard University for the most promising mathematics student (undergraduate) and entered the William Lowell Putnam competition in 1997, 1998 and 2000 to one of the top five places (from 2002 to 2004 he was a Putnam Fellow). In 2004/2005 he was a Veblen Instructor at Princeton University and the Institute for Advanced Study . From 2004 to 2008 he was a Clay Research Fellow. He was Assistant Professor at Columbia University from 2005 and has been Associate Professor since 2008 and Professor at the University of California, Los Angeles since 2012 . Among other things, he was visiting scholar at the University of Paris, MSRI and Cambridge University .

Manolescu made important contributions to Floer homology with application to nodes and the topology of 3- and 4-dimensional manifolds . In 2013 he refuted the triangulation conjecture for higher dimensions ( ) after Michael Freedman constructed a manifold in dimension in 1982 , which Andrew Casson then showed that it is not triangulatable. In contrast, the assumption is true in up to three dimensions. The conjecture said that every compact topological manifold can be triangulated as a locally finite simplicial complex . It was one of the best known topology problems that had been open since the beginning of the 20th century. The triangulation conjecture for higher dimensions (five and more) had been traced back by Ronald Stern , David Galewski and independently Takao Matumoto in the 1970s to a problem in low dimensions, which concerned the question of whether a homology 3 sphere with certain properties existed. Further progress was made with the introduction of two different invariants, one by Andrew Casson and the other by Kim Frøyshov, which did not yet solve the problem. Only a modification of the invariant by Frøyshov ( called the beta invariant by Manolescu ), which Manolescu found with results from his old dissertation on Seiberg-Witten-Floer homology (incorporation of the Pin (2) symmetry of the Seiberg-Witten equations into the invariant ), was able to prove the non-existence of the special homology 3 sphere, since its properties would result in the beta invariant being even and odd at the same time. For this work he received the AMS Moore Research Article Prize in 2019.

With Peter Ozsváth and Sucharit Sankar , he applied Floer's homology to knots and found an algorithm to detect an unknot . Manolescu also deals with applying topology to distributed computing.

In 2012 he received the EMS award . In 2018 he is invited speaker at the ICM (Homology cobordism and triangulations).

Fonts

  • Seiberg-Witten-Floer stable homotopy type of three-manifolds with b 1 = 0. Geom. Topol. 7: 889-932 (2003)
  • with Peter Ozsváth , Zoltán Szabó , Dylan Thurston : On combinatorial link Floer homology. Geom. Topol. 11: 2339-2412 (2007).
  • with Peter Ozsváth, Sucharit Sankar : A combinatorial description of knot Floer homology. Ann. of Math. (2) 169 (2009), no. 2, 633-660.
  • Grid diagrams in Heegard Floer theory , Proc. 6. ECM, Arxiv 2012
  • Pin (2) -equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture , J. Amer. Math. Soc. 29 (2016), no. 1, 147–176. Arxiv preprint from 2013
  • with Kristen Hendricks: Involutive Heegard Floer homology , Duke Math. J., Volume 166, 2017, pp. 1211–1299, Arxiv
  • Floer theory and its topological applications, Takagi Lectures University of Tokyo, Arxiv
  • An introduction to knot Floer homology, in: Physics and mathematics of link homology, Contemp. Math. 680, AMS (2016), 99-135, Arxiv
  • Lectures on the triangulation conjecture, Proceedings of the 22nd Gokova Geometry / Topology Conference, Arxiv
  • Homology cobordism and triangulations, Proc. ICM 2018, Arxiv

Web links

Individual evidence

  1. ↑ Laudation for the EMS Prize
  2. ↑ Arxiv
personal data
SURNAME Manolescu, Ciprian
BRIEF DESCRIPTION Romanian mathematician
DATE OF BIRTH December 24, 1978
PLACE OF BIRTH Alexandria , Romania