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 - September 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:
Past
visitors:
- Frédéric
Rochon (Université du Québec à Montréal), July 2-5,
2013
- Colin
Guillarmou (Ecole Normale Superieure, Paris),
November 4-9, 2013
- Michel
Pocchiola (Institut de Mathématiques de Jussieu,
Paris), November 18-22, 2013
- Gwénaël
Massuyeau (Université 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 & Université de
Versailles-St. Quentin), April 12-20, 2015
- Jean-Stephane
Dhersin (Université 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
Maïda (Université Lille 1),
October 29 - November 2, 2015
- Conference talk: "Inégalités transport-entropie en
probabilités
libres",
- Fri, Oct. 30, 2015
at 15.00, amfiteatrul "Miron
Nicolescu"
- Jin-ichi
Itoh (Kumamoto University), November
26-30, 2015
- Andrei
Moroianu (CNRS & Université de
Versailles-St. Quentin), November 25 -
December 6, 2015
- Andrei
Moroianu (CNRS & Université 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:
- Cristina
Anghel, Second
Erlangen Fall School on Quantum Geometry,
Friedrich-Alexander
Universität Erlangen-Nürnberg (Germany,
October 6-12, 2013)
- Cristina Anghel,
Forth
Workshop for Young Researchers in
Mathematics, Ovidius University Constanța
(Romania, May 21-23, 2014)
- Cristina Anghel,
Young
Topologists' Meeting, University of Copenhagen
(Denmark, June 29 - July 4, 2014)
- Gabriel Bădițoiu,
Clay
Mathematics
Institute Summer
School 2014 "Periods and Motives:
Feynman amplitudes
in the 21st
century",
ICMAT,
Madrid (Spain, June 29
- July 26, 2014)
- Clement
Radu Popescu, Braids
and Arithmetic,
CIRM,
Marseille (France,
October 12-17, 2014)
- Clement
Radu Popescu, Workshop
for Young
Researchers in
Mathematics, Ovidius University Constanța
(Romania, May 20-24, 2015)
- Clement Radu Popescu,
The Eighth Congress of Romanian
Mathematicians, Iași (Romania, June 26
- July 1, 2015)
- Cristina Anghel and Clement Radu
Popescu, Summer
School "Mapping Class Groups, 3- and 4-
manifolds", Cluj-Napoca
(Romania, July 26 - August 1, 2015)
- Sergiu Moroianu, "MITRE
2015" Conference
(Chișinău, Moldova, July 1-5, 2015)
- Cristina Anghel,
Young
Topologists' Meeting, Lausanne (Switzerland, July
4-11, 2015)
- Radu Popescu, Sergiu
Moroianu, and
Dorin Cheptea, Sixth
Workshop for Young Researchers in
Mathematics, Ovidius University Constanța
(Romania, May 21-23, 2014), including
organizing a special
session
- Sergiu Moroianu,
research visit and invited talk ("Renormalized volume in
hyperbolic geometry", May 10, 2016) in the Colloquium
of the University of Fribourg (Switzerland, May 8-13, 2016)
- Sergiu Moroianu, "Geometry and PDEs"
Workshop, Universitatea de Vest,
Timișoara (Romania, June 10-11, 2016)
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:
- Andrei Moroianu, Sergiu Moroianu, "Ricci
surfaces", Annali
della Scuola Normale Superiore di Pisa,
Classe di Scienze, 14, no. 4
(2015), 1093-1118, DOI Number:
10.2422/2036-2145.201206_007
- Daniela Anca Măcinic, Ștefan Papadima, Clement
Radu Popescu, Alexander I. Suciu, "Flat
connections and resonance varieties: from
rank one to higher ranks", to
appear in Transactions
of the American Mathematical Society
- Colin Guillarmou, Sergiu Moroianu,
Frédéric
Rochon, "Renormalized volume on the
Teichmuller space of punctured surfaces",
Annali
della Scuola Normale Superiore di Pisa,
Classe di Scienze, DOI Number:
10.2422/2036-2145.201506_002
- Sergiu Moroianu, "The
Cotton tensor and Chern-Simons invariants
in dimension 3: and introduction",
Buletinul
Academiei de Științe a Republicii Moldova.
Matematica 78, no. 2 (2015),
3-20
- Daniela Anca Măcinic, Ștefan Papadima, Clement
Radu Popescu, "Modular equalities for
complex reflection arrangements", arXiv:1406.7137,
submitted
- Barbu Berceanu, Daniela Anca Măcinic, Ștefan
Papadima, Clement Radu Popescu,"On
the geometry and topology of partial
configuration spaces of Riemann surfaces",
arXiv:1504.04733, to appear in Algebraic and
Geometric Topology
- Sergiu Moroianu, "Boundaries of
locally conformally flat manifolds in
dimensions 4k", arXiv:1506.05968, to
appear in Indiana
University Mathematics Journal
- Sergiu Moroianu, "Convexity of the
renormalized volume of hyperbolic
3-manifolds", arXiv:1503:07981,
submitted
- Gabriel Bădițoiu,
"Integrable
systems and
Connes-Kreimer
renormalization",
submitted
- Dorin Cheptea, "Jacobi diagrams on
surfaces and quantum invariants",
submitted
- Andrei Moroianu, Sergiu Moroianu, "On
pluricanonical locally conformally Kähler
manifolds", to appear in International
Mathematics Research Notices, DOI
Number: 10.1093/imrn/rnw151 (2016)
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.
Last updated: September 2016
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