Financing agency:
Romanian National Authority for Scientific Research (CNCS-UEFISCDI)

Grant number:
PN-II-RU-TE-2012-3-0492

Contract number: 39 from April 30th, 2013

Project title:
Investigation of quantum and finite type invariants, applications in geometry and topology


Host institution: Institute of Mathematics of the Romanian Academy (IMAR), Bucharest, Romania

Time period:
May 1st, 2013 - Sept
ember 30th, 2016

Project manager:
Dorin Cheptea


Team members: Sergiu Moroianu, Gabriel Bădițoiu, Radu Popescu, Cristina Anghel

Summary: The subfield of geometry and topology that uses ideas, concepts, and methods originally inspired from theoretical physics is known informally as quantum topology. Within it lie the theories of quantum and finite type invariants of knots/links, 3-dimensional manifolds, and (2+1)-cobordisms. The relationship between the two theories is well-understood for knots/links. A comprehensive relation between quantum and finite-type invariants of cobordisms would allow to "translate" methods from one theory to solve problems difficult in the other. Of particular importance to establishing such a correspondence in a proper manner is to look not only at quantum topological problems, but also at related geometric questions. Our investigation focuses on a set of open problems that aim to bridge the gap.



Open positions:  Currently there are no openings.


To develop this work qualitatively we seek to enhance the international collaboration of the Geometry and Topology group at IMAR. In particular, this grant finances short research visits to Bucharest of international research collaborators.

Upcoming visitors:

  • the grant has ended
Past visitors:
  • Frdric Rochon (Universit du Qubec Montral), July 2-5, 2013
  • Colin Guillarmou (Ecole Normale Superieure, Paris), November 4-9, 2013
  • Michel Pocchiola (Institut de Mathmatiques de Jussieu, Paris), November 18-22, 2013
  • Gwnal Massuyeau (Universit de Starsbourg & CNRS), November 19-23, 2013
  • Florin Damian (Universitatea de Stat din Moldova, Chișinău & Institutul de Matematică și Informatică al Academiei de Științe din Moldova), Novermber 25-27, 2013
  • Dan Burghelea (Ohio State University, Columbus, OH), September 6-14, 2014
    • Conference talk: "On the Spectral Geometry of closed Riemannian manifolds in the presence of a smooth function"
    • Wed., Sept. 10, 2014 at 9.00, sala Spiru Haret, Faculty of Mathematics and Computer Science, University of Bucharest
  • Andrei Moroianu (CNRS & Universit de Versailles-St. Quentin), April 12-20, 2015
  • Jean-Stephane Dhersin (Universit Paris 13), October 24 - November 2, 2015
    • Conference talk: "Length of branches of some Lambda-Coalescents"
    • Sat, Oct. 31, 2015 at 11.20, amfiteatrul "Miron Nicolescu"
  • Mylene Mada (Universit Lille 1), October 29 - November 2, 2015
    • Conference talk: "Ingalits transport-entropie en probabilits libres",
    • Fri, Oct. 30, 2015 at 15.00, amfiteatrul "Miron Nicolescu"
  • Jin-ichi Itoh (Kumamoto University), November 26-30, 2015
  • Andrei Moroianu (CNRS & Universit de Versailles-St. Quentin), November 25 - December 6, 2015
  • Andrei Moroianu (CNRS & Universit de Versailles-St. Quentin), March 23 - 31, 2015
    • Geometry seminar talk: "S-reprezentari si algebra Lie exceptionala E8"
    • Tue, March 29, 2016 at 10.00, sala 306-307
  • Colin Guillarmou (Ecole Normale Superieure, Paris), April 17-22, 2016
    • Geometry seminar talk: "Ruelle and quantum resonances for non-compact Riemann surfaces"
    • Tue, April 19, 2016 at 10.00, sala 306-307


Visits of team members fully or partly financed by the grant:

Note: The results obtained within the project are also disseminated through various talks not financed from the project budget; see the webpages of individual team members for more details.


Other activities:
  • A workgroup (seminar) on "Two- and three-dimensional manifolds" (Oct. 23, 2013 - present) was initiated.
  • Talks on the research topics and results covered in this grant were also delivered by team members at the Topology and the Geometry seminars of IMAR.
  • Cristina Anghel has defended a Master thesis "Volume conjecture for knots and links" (co-supervised by Victor Vuletescu (University of Bucharest) and Dorin Cheptea (IMAR)) at the University of Bucharest. One of her on-going research interests is a spin-off from her work for that thesis.

 Links:

 Papers:

 Book:

  • Jean-Pierre Bourguignon, Oussama Hijazi, Jean-Louis Milhorat, Andrei Moroianu, Sergiu Moroianu, "A spinorial approach to Riemannian and conformal geometry", EMS Monographs in Mathematics (2015), ISBN: 978-3-03719-136-1 

 Note: Information on this page will be updated passed September 30, 2016 until all publications appear in print form.

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Last updated: September 2016