[Turkmath:7707] [FGE-Duyuru] Differential Geometry,May 27 - 29, 2011, TÜBİTAK - FEZA GÜRSEY INSTITUTE
Kursat Aker
aker at gursey.gov.tr
10 Mayıs 2011 Sal 11:42:07 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
<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
-------------- sonraki bölüm --------------
Bir HTML eklentisi temizlendi...
URL: <http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/private/turkmath/attachments/20110510/9f834dc9/attachment-0001.htm>
-------------- sonraki bölüm --------------
A non-text attachment was scrubbed...
Name: char21.png
Type: image/png
Size: 152 bytes
Desc: kullanılamıyor
URL: <http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/private/turkmath/attachments/20110510/9f834dc9/attachment-0002.png>
-------------- sonraki bölüm --------------
A non-text attachment was scrubbed...
Name: char31.png
Type: image/png
Size: 249 bytes
Desc: kullanılamıyor
URL: <http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/private/turkmath/attachments/20110510/9f834dc9/attachment-0003.png>
-------------- sonraki bölüm --------------
_______________________________________________
FGE-Duyuru mailing list
FGE-Duyuru at roksan.gursey.gov.tr
http://roksan.gursey.gov.tr/cgi-bin/mailman/listinfo/fge-duyuru
Turkmath mesaj listesiyle ilgili
daha fazla bilgi