[Turkmath:7704] Differential Geometry, May 27 - 29, 2011, TÜBİTAK - FEZA GÜRSEY INSTITUTE
Kursat Aker
aker at gursey.gov.tr
10 Mayıs 2011 Sal 11:46:02 EEST
Differential Geometry May 27 - 29, 2011
TÜBİTAK - FEZA GÜRSEY INSTITUTE
*Speakers:*
- Mustafa Kalafat, Middle East Technical University
- Barış Coşkunüzer, Koc University
- Tekin Dereli, Koc University
- Cenap Özel, Abant İzzet Baysal University
- İbrahim Ünal, Middle East Technical University North Cyprus Campus
- F. Muazzez Şimşir, Middle East Technical University
- Kadri Arslan, Uludag University
- Bayram Tekin, Middle East Technical University
*Lectures:*
- *Reidemeister torsion of Product Manifolds and Quantum Entanglement of
Pure States with Schmidt Rank* *by* Cenap Özel
Using symplectic chain complex, a formula for the Reidemeis- ter torsion
of product of oriented closed connected even dimensional mani- folds is
presented. In applications, the formula is applied to Riemann sur-
faces,Grassmannians, Projective spaces and manifolds of pure bipartite
states with Schmidt ranks.
*References:*
1. M. F. Atiyah and R. Bott, The Yang-Mills Equations over Riemann
Surfaces, Phil. Trans. R. Soc. London Series A, 308 No. 1505 (1983),
523-615.
2. J.M. Bismut, H. Gillet, and C. Soule, Analytic torsion and
holomorphic determinant bundles I. Bott-Chern forms and analytic torsion,
Comm. Math. Phys. 115 No 1 (1988), 49-78.
3. J.M. Bismut and F. Labourie, Symplectic geometry and the Verlinde
formulas, in: S.T. Yau (Ed.), Surveys in di®erential geometry. Vol. V.
Di®erential geometry inspired by string theory. Boston, MA: International
Press. Surv. Di®er. Geom., Suppl. J. Di®er. Geom. 5 (1999), 97-311.
4. T.A. Chapman, Hilbert cube manifolds and the invariance of
Whitehead torsion, Bull. Amer. Math. Soc. 79(1973), 52-56.
5. T.A. Chapman, Topological invariance of Whitehead torsion, Amer. J.
Math. 96(1974), 488-497.
6. G. de Rham, Reidemeister's torsion invariant and rotation of Sn;
in: Di®erential Analysis, Tata Institute and Oxford Univ. Press, 1964,
27-36.
7. W. Franz, Uber die Torsion einer Uberdeckung, J. Reine Angew. Math.
173(1935), 245-254.
8. J. Grabowski, G. Marmo, and M. Kus, , Geometry of quantum systems:
density states and entanglemen, J.Phys. A 38(2005), 10217-10244.
9. J. Grabowski, M. Kus, and G. Marmo, Symmetries, group actions, and
entanglement, Open Sys. and Information Dyn. 13(2006), 343-362.
10. P. Griffiths and J. Harris, Principles of Algebraic Geometry, John
Willey Library Edition, 1994.
11. A. Hatcher, Algebraic Topology, Cambridge University Press, 2002.
12. R.C. Kirby and L.C. Siebenmann, On triangulation of manifolds and
Haupvermutung, Bull. Amer. Math. Soc. 75(1969), 742-749.
13. V.I. Man'ko, G. Marmo, E.C.G. Sudarshan, and F. Zaccaria,
Di®erential geometry of density states and entanglement, Rep. Math. Phys.
55(2005), 405-422.
14. J.P. May, A Concise Course in Algebraic Topology, The University
of Chicago Press, 1999.
15. J. Milnor, A duality theorem for Reidemeister Torsion, Ann. Math.
(1962), 137-147.
16. J. Milnor, Whitehead torsion, Bull. Amer. Math. Soc. 72(1966),
358-426.
17. J. Milnor, Infinite cyclic covers, in: Topology of Manifolds in
Michigan, 1967, 115-133.
18. J. Porti, Torsion de Reidemeister pour les Varieties
Hyperboliques, Mem. Amer. Math. Soc., 1997.
19. K. Reidemeister, Homotopieringe und LinsenrÄaume, Abh. Math. Sem.
Univ. Hamburg 11(1935), 102-109.
20. Y. Sozen, On Reidemeister torsion of a symplectic complex, Osaka
J. Math. 45(2008), 1-39.
21. Y. Sozen, On Fubini-Study form and Reidemeister torsion, Topology
and its Applications, 156 (2009), 951-955.
22. Y. Sozen, A note on Reidemeister torsion and period matrix of
Riemann surfaces, Math. Slovaca, 61 No. 1 (2011), 29-38.
23. Y. Sozen, Symplectic Chain Complex, Reidemeister torsion, compact
manifolds, submitted.
24. E. Witten, On quantum gauge theories in two dimensions, Comm.
Math. Phys. 141(1991), 153-209.
25. Z. Yu, X. Jost-Li, Q. Li, J. Lv., and S. Fei, Differential
Geometry of bipartiate quantum states, Rep. Math. Phys. 60 No. 1 (2007),
125-133.
- *Non-Abelian Magnetic Monopoles and Electric-Magnetic Duality*
*by*Tekin Dereli
I will first present the U(1) gauge theory structure of Maxwell equations
and discuss the definition of conserved charges. After a few comments on the
Dirac monopoles I will give SU(2) Yang-Mills-Higgs theory and discuss the 't
Hooft-Polyakov monopole and dyon solutions. Finally I will introduce the
Montonen-Olive conjecture (1978) and the corresponding electric-magnetic
duality that led in 1994 to the Seiberg-Witten construction of topological
invariants.
*References:*
1. G. 't Hooft, Nucl.Phys.B79 (1974)276
2. E.B.Bogomol'nyi, Sov.J.Nucl.Phys. 24(1976)449
3. C.Montonen, D.Olive, Phys.Lett. B72(1977) 117
4. N.Seiberg,E.Witten, Nucl.Phys.B426 (1994)19; ibid, B430(1994)485
- *Foliations of Hyperbolic Space by Constant Mean Curvature
Hypersurfaces* *by* Barış Coşkunüzer
In this talk, we will start with a survey of asymptotic Plateau problem.
Then, we will show that the constant mean curvature surfaces in the
hyperbolic 3-space spanning a star-shaped curve in the asymptotic sphere
give a foliation of the hyperbolic 3-space. Then, we will talk about
generalizations of these results in more general settings.
*References:*
1. M. Anderson, Complete minimal hypersurfaces in hyperbolic
n-manifolds, Comment. Math. Helv. 58 (1983) 264-290.
2. B. Coskunuzer, Foliations of Hyperbolic Space by Constant Mean
Curvature Hypersurfaces, IMRN (2010) 1417-1431.
3. B. Guan, and J. Spruck, Hypersurfaces of constant mean curvature in
hyperbolic space with prescribed asymptotic boundary at
infinity, Amer. J.
Math. 122 (2000) 1039-1060.
4. R. Hardt and F.H. Lin, Regularity at infinity for absolutely area
minimizing hypersurfaces in hyperbolic space, Invent. Math. 88 (1987)
217-224.
5. Y. Tonegawa, Existence and regularity of constant mean curvature
hypersurfaces in hyperbolic space, Math. Z. 221 (1996) 591--615.
- *Algebraic Surfaces and their applications to Differential Geometry 1
& 2* *by* Mustafa Kalafat
We will talk about complex algebraic surfaces, Kodaira-Enriques
Classification, and their applications to 4-dimensional Riemannian geometry.
In particular we will talk about the Kodaira Dimension and its relationship
with the Yamabe Invariant.
- *Calibrated Geometries* *by* Ibrahim Unal
Calibrated Geometries are introduced by Harvey and Lawson in the
foundational paper [1]. These are the geometries of minimal submanifolds
which are determined by a form φ on a Riemannian manifold called
calibration. I will talk about the well-known examples of calibrated
submanifolds, especially coming from special holonomy, and their deformation
spaces, time permitting.
- *An Introduction to Potential Theory on Calibrated Manifolds*
*by*İbrahim Ünal
Recently, the notion of plurisubharmonic functions in calibrated
geometries are introduced by Harvey and Lawson [2].These functions
generalize the classical plurisubharmonic functions from complex geometry to
calibrated manifolds. In this talk, I will give some information about these
functions and their properties where the calibration is parallel.
*References:*
1. F. R. Harvey and H. B. Lawson, Jr, Calibrated geometries, Acta
Mathematica 148 (1982), 47-157.
2. F. R. Harvey and H. B. Lawson, Jr., An introduction to potential
theory in calibrated geometry, Amer. J. Math. 131 no. 4 (2009), 893-944.
ArXiv:math.0710.3920.
3. D. D. Joyce, Compact Manifolds with Special Holonomy, Oxford
University Press, Oxford, 2000.
4. I. Unal, Topology of Phi-Convex Domains in Calibrated Manifolds" (
to appear in"*Bull*. *Braz*. Math. Soc".)
- *Non-divergence harmonic maps* *by* F. Muazzez Şimşir
We describe work on solutions of certain non-divergence type and
therefore non-variational elliptic and parabolic systems on manifolds. These
systems include Hermitian and affine harmonics which should become useful
tools for studying Hermitian and affine manifolds, resp. A key point is that
in addition to the standard condition of nonpositive image curvature that is
well known and understood in the theory of ordinary harmonic maps (which
arise from a variational problem), here we also need in addition a global
topological condition to guarantee the existence of solutions.
*References:*
1. S.I. Al'ber, Spaces of mappings into a manifold with negative
curvature, Sov. Math. Dokl. 9 (1967), 6--9.
2. S.Y. Cheng and S.T. Yau, The real Monge-Amp\`ere equation and
affine flat structures, Differential Geometry and Differential Equations,
Proc. Beijing Symp. 1980, 339--370, 1982.
3. H.-Ch. Grunau and M.Kuhnel, On the existence of Hermitian-harmonic
maps from complete Hermitian to complete Riemannian manifolds,
Math. Zeit.
249 (2005), 297--325.
4. J. Jost, Harmonic mappings between Riemannian manifolds, Canberra
Univ. Press, 1984.
5. J. Jost, Nonpositive curvature: Geometric and analytic aspects,
Birkhauser, 1997.
6. J. Jost, Riemannian geometry and geometric analysis, 5th ed.,
Springer, 2008.
7. J. Jost, Harmonic mappings, L.Z. Ji et al. (editors), Handbook of
Geometric Analysis, International Press, 2008, 147--194.
8. J. Jost and S.T. Yau, A nonlinear elliptic system for maps from
Hermitian to Riemannian manifolds and rigidity theorems in Hermitian
geometry, Acta Math. 170 (1993), 221--254.
9. J. Jost and F.M. Simsir, Affine harmonic maps, Analysis 29 (2009),
185--197.
10. A. Milgram and P. Rosenbloom, Harmonic forms and heat conduction,
I: Closed Riemannian manifolds, Proc. Nat. Acad. Sci. 37 (1951),
180--184.
11. J. Milnor, On fundamental groups of complete affinely flat
manifolds, Adv. Math. 25 (1977), 178--187.
12. L. Ni, Hermitian harmonic maps from complete Hermitian to complete
Riemannian manifolds, Math. Zeit. 232 (1999), 331--355.
13. W. von Wahl, Klassische Losbarkeit im Grosen fur nichtlineare
parabolische Systeme und das Verhalten der Losungen fur t, Nachr.
Akad. Wiss. Gottingen, II. Math. - Phys. Kl., 131--177, 1981.
14. W. von Wahl, The continuity or stability method for nonlinear
elliptic and parabolic equations and systems, Rend. Sem. Mat.
Fis. Milano 62
(1992), 157--183.
- *On translation-like covering transformations* *by* F. Muazzez Şimşir
The concept of "translation-like elements" of the group of covering
transformations of a covering projection onto a compact space is defined. It
is shown that the group of covering transformations of the universal
covering projection of a compact Riemannian manifold with negative sectional
curvatures admits no non-trivial translation-like elements.
*References:*
1. W. P. Byers, On a theorem of Preissmann , Proc. of the Amer. Math.
Soc. 24 (1970), 50--51.
2. P. Eberlein, Lattices in spaces of non-positive curvature, Annals
of Math. 111 (1980), 435--476.
3. M. Gromov, Almost flat manifolds, J. of Diff. Geo. 13 (1978),
231--241.
4. M. Gromov, Groups of polynomial growth and expanding maps, I. H. E.
S. Publications mathematiques 53 (1981), 53--71.
5. J. Tits, Appendix to M. Gromov, Groups of polynomial growth and
expanding maps, I. H. E. S. Publications mathematiques 53
(1981), 53--71.,
I. H. E. S. Publications mathematiques 53 (1981) 74--78.
6. A. Preissmann, Quelques propietes globales des espaces de Riemann,
Comment. Math. Helvet. 15 (1943) 175--216.
- *3D Shape modelling with superquadrics* *by* Kadri Arslan
The problem of recovering the shape of objects from unstructured 3D data
is important in many areas of computer graphics and computer vision,
including robotics, medical images and the automatic construction of virtual
environments. In last 30 years, much work has done focussed of finding
suitable models for the recovery of objects from 3D data. This work has
largely proposed the use of some form of parametric model, most commonly
spherical product of two 2D curves. Quadrics are the simple type of
spherical products. Superquadrics are solid models that can fairly simple
parametrization of spherical product of two 2D curves. They represent a
large variety of standard geometric solids, as well as smooth shapes in
between. The superquadrics can be deformed by stretching, bending, tapering
or twisting, to built complex objects.
*References:*
1. Arslan, K. Bulca B, Bayram B, et al., On Spherical Product Surfaces
in E-3 International Conference on Cyberworlds (CW 2009), SEP 07-11, 2009
Bradford, ENGLAND.
2. T. Bhabhrawala, Shape Recovery from Medical Image Data Using
Extended Superquadrics. MSc Thesis, State University of New York
at Buffalo,
December,2004.
3. J. Gielis, J Beirinchx, and Bastianens, Superquadrics with rational
and irrational symmetry, Symposium on solid modelling and Applications,
2003.
4. A. Gupta, and R. Bajcsy, Surface and volumetric segmentation of
range images using biquadrics and superquadrics. In Int'l Conf. Pattern
Recognition, 1(1992). 158--162.
5. A. Jaclic, A. Leonardis, and F. Solina, Segmentation and Recovery
of Superquadrics. Kluwer Academic Publishers, Vol. 20, 2000.
- *Covariant Symplectic Structure and Conserved Charges of Topologically
Massive Gravity* *by* Bayram Tekin
I will talk about the covariant symplectic structure of the Topologically
Massive Gauge theory and Gravity. I will also present a compact expression
for the conserved charges of generic spacetimes with Killing symmetries.
This talk is based on : arXiv:1104.3404 [hep-th] by C. Nazaroglu, Y.
Nutku and B. Tekin.
------------------------------
*Accommodation* (including breakfast, lunch) will be provided by Feza Gürsey
Institute *Student Hostel* for participants from outside İstanbul if
desired.
*Travel funds* are *not* available for participants.
*Program* is also featured on the Istanbul Mathematical Agenda:
http://www.google.com/calendar/embed?src=jdf754c331751cbt6q9vc281es%40group.calendar.google.com&ctz=Europe/Istanbul
All participants are encouraged to fill in the following *application form*.
Filling in the form is essential for the TÜBİTAK - FEZA GÜRSEY INSTITUTE to
provide the best service for all participants.
*Number of participants is limited to 30 people.*
*Deadline:* May 22, 2011
*To Apply:* http://www.gursey.gov.tr/apps/app-frm-gen.php?id=diffgeo11
*Web site:* http://www.gursey.gov.tr/new/diffgeo11/
*Organizer:*
F. Muazzez Simsir
------------------------------
Differential Geometry
_______________________________________________
FGE-Duyuru mailing list
FGE-Duyuru at roksan.gursey.gov.tr
http://roksan.gursey.gov.tr/cgi-bin/mailman/listinfo/fge-duyuru
-------------- sonraki bölüm --------------
Bir HTML eklentisi temizlendi...
URL: <http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/private/turkmath/attachments/20110510/bb005dc1/attachment-0001.htm>
-------------- sonraki bölüm --------------
A non-text attachment was scrubbed...
Name: kullanılamıyor
Type: image/png
Size: 249 bytes
Desc: kullanılamıyor
URL: <http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/private/turkmath/attachments/20110510/bb005dc1/attachment-0002.png>
-------------- sonraki bölüm --------------
A non-text attachment was scrubbed...
Name: kullanılamıyor
Type: image/png
Size: 152 bytes
Desc: kullanılamıyor
URL: <http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/private/turkmath/attachments/20110510/bb005dc1/attachment-0003.png>
Turkmath mesaj listesiyle ilgili
daha fazla bilgi