Geometry and Topology Seminars in METU

Spring 2002
Mustafa Kalafat
Stony Brook
May 22 Contact Geometry and the Classification of Legendrian/Transversal Knots (a survey)
Ping Zhang May 15 Some Constructions and Examples in Virtual Knot Theory
Ebru Keyman May 1 Recognizing S^3 (Rubinstein-Thompson algorithm)
Sadettin Erdem Apr 25
Turgut Onder Apr 17 SW-invariants of 4-manifolds with free circle actions, Part II
Ozgur Kisisel Apr 10 Quantum cohomology
Mehmetcik Pamuk Apr 3 Lusternik-Shnirelman category and Massey products (based on papers of Viterbo, et.al.)
Muhiddin Uguz Mar 27 A free Z/p action and the Seiberg-Witten invariants
Mustafa Korkmaz Mar 20 Recent progress in mapping class groups
Ferihe Atalan (Ozan) Mar 13 Enumeration of mapping classes for the torus (based on a paper of Takasawa)
Firat Arikan Mar 6 A branched cover approach to minimal base genus problem
Sergey Finashin Feb 27 A calculus of (complex) Spin structures, Part II
Sergey Finashin Feb 20 A calculus of complex Spin structures and its application in 4-dimensional topology
Yildiray Ozan Feb 13 Circle Actions on Manifolds, Symplectic Manifolds and their Lagrangians

Fall 2001
Ping Zhang Jan 7 The fundamental group and Lusternik-Shnirelman Category of 3-manifolds -- Survey and Remark
Sergey Finashin Dec 24 Membranes' minimal genus problem for surfaces in 4-manifolds
Nermin Salepci Dec 10 Real Algebraic Curves and Quasi-positive Braids (after S.Orevkov)
Ebru Keyman Dec 3 Ordering the Braid Group
Firat Arikan Nov 19 A topological construction of a surface bundle with non-zero signature via a method of subtructing Lefschetz fibrations, Part II
Firat Arikan Nov 12 A topological construction of a surface bundle with non-zero signature via a method of subtructing Lefschetz fibrations
Mustafa Korkmaz Nov 5 Is Poincare Conjecture not true ?
Sergey Finashin Oct 22 Open book decompositions and contact structures on 3-manifolds as an analog of Lefschetz fibrations and symplectic structures on 4-manifolds
Sergey Finashin Oct 15 A survey of the recent progress in Contact Topology (from Eliashberg-Hofer to Giroux)
Nermin Salepci Oct 8 Braids corresponding to Real Algebraic Curves (following the construction of Orevkov)
Sergey Finashin Oct 1 To bury SW-theory in 4-dimensional topology ? (new horizons after the Ozsvath-Szabo theory)
Sergey Finashin Sep 24 Progress in 4-dimensional topology
(a survey report after a conference in Oberwolfach in July 2001)

Spring 2001
Mustafa Korkmaz May 7 The second homology groups of mapping class groups of orientable surfaces
Turgut Onder Apr 30 Smooth group actions on four-manifolds
A survey of results on smooth group actions on some four manifolds like projective spaces CP^2 and their connected sums are given. In this context the results of authors like I. Hambleton-R.Lee, A.Edmunds-J.Ewing, D.Wilcynski are presented, the techniques with emphasis on Equivariant Gauge Theory are outlined.
Yildiray Ozan Apr 16 Real Algebraic Models, Retractions and Massey Products
Ebru Keyman Apr 9 Braided Chord Diagrams
Nermin Salepci Mar 26 Gauss Diagram Algebra for computation of Arnold Invariants of plane curves
Sergey Finashin Mar 19 Patchworking in toric varieties and Maslov dequantization of positive numbers after Viro (Part II)
Yildiray Ozan Mar 12 Viterbo's work on exact lagrange submanifolds, periodic orbits and the cohomology of free loop space, Part II
Yildiray Ozan Feb 26 Viterbo's work on exact lagrange submanifolds, periodic orbits and the cohomology of free loop space
Sergey Finashin Feb 19 Patchworking in toric varieties and Maslov dequantization of positive numbers after Viro

Fall 2000
Yildiray Ozan Jan 10 On (Rational) Homotopy Theory of Real Algebraic Varieties in their Complexifications
In this talk I'll discuss some observations about the homomorphism on (rational) homotopy groups induced by the inclusion map of a real algebraic variety into its complexification. Methods are standard algebraic topology and rational homotopy theory.
Nermin Salepci Dec 19 A St-type invariant of immersed plane curves with a marked point
Mustafa Korkmaz Dec 12 Commutators in the mapping class group and bounded cohomology (Part II)
Semra Kaptanoglu Dec 5 Steenrod Algebra Action and Fixed Point Sets
Sergey Finashin Oct 28 Around minimal genus surfaces in 3-manifolds
Mustafa Korkmaz Oct 21 Commutators in the mapping class group and bounded cohomology
We prove that the stable commutator length of a Dehn twist in the mapping class group is positive. As a result of this, the natural map from the second bounded cohomology of the mapping class group to the ordinary cohomology is not injective and finite index subgroups of mapping class groups are not uniformly perfect. We also prove that the second bounded cohomology of the mapping class group of a surface of genus at most two and of hyperelliptic mapping class groups are infinite dimensional. These results give answers to some problems in Kirby's problem book and some problems of Morita.
Cem Tezer Nov 7 Almost inner automorphisms
Ferit Ozturk Oct 31 Thurston-Bennequin-like invariants of real surface singularities
Ozgur Kisisel Oct 24 Toroidal Pipe Diagrams and String Topology
Toroidal Pipe Diagrams are combinatorial objects that appear naturally in the study of an integrable system; the discrete KP hierarchy. This talk will discuss a conjectural relation of these to "String Topology", recently proposed by Chas and Sullivan, extending previous works of Goldman, Turaev and Wolpert.
Yildiray Ozan Oct 16 On Algebraic K-Theory of Real Algebraic Varieties with Circle Action
Alex Degtyarev
Bilkent
Oct 9 Some Finiteness Results in Algebraic Geometry
Vladimir Golubyatnikov
Novosibirsk, Russia
Oct 4 Cohomotopical Properties of the Thom Spaces

Spring 2000
Rostislav Matveyev
Stony Brook
Jun 6 Convex decomposition of smooth 4-manifolds
Semra Kaptanoglu May 16 Euler Characteristic and Betti numbers of a G-Moore space
Let X be a Moore space with Z2xZ4 action, then the (co) homology groups of X with mod 2 coefficients is a module over F2[Z2xZ4]. There is a tight connection between the multiplicities of modules appearing in the decomposition of M as an F2[C]-module and the fixed point set Xc where C is a cyclic subgroup of Z2xZ4.
Mustafa Korkmaz May 2 On Commutators in Mapping Class Groups
Ilker Yuce Apr 25 Normal all pseudo-Anosov subgroups of mapping class groups (Part III)
Ilker Yuce Apr 18 Normal all pseudo-Anosov subgroups of mapping class groups (Part II)
Semra Kaptanoglu Apr 11 On realizable kG-modules
Yildiray Ozan Apr 4 Solvable Regular Coverings of Real Algebraic Varieties
Mustafa Korkmaz Mar 7 Mapping Class groups of non-orientable surfaces

Fall 1999
Ilker Yuce Jan 4 Normal all pseudo-Anosov subgroups of mapping class groups
Yusuf Ziya
Irvine
Dec 28 Distinguishing knots; dihedral branched covers of 3-sphere
Alexander Klyachko
Bilkent
Dec 21 Kaehler-Einstein Metric on Toric Fano
Mustafa Korkmaz Dec 14 Non-complex smooth 4-manifolds with genus-g Lefschetz fibrations (Part II)
Turgut Onder Dec 7 Topological G-index computations and some applications to Seifert homology 3-spheres
Sergey Finashin Nov 30 Spin mapping class group and Lefschetz fibrations
Nermin Salepci Nov 23 Arnold invariants of immersed plane curves (Part II: Arnold Conjectures, cobordisms, etc.)
Yildiray Ozan Nov 9 On entire rational maps of real algebraic surfaces and realization of smooth manifolds with prescribed algebraic submanifolds (Part II)
Sergey Finashin Nov 2 Khovanov's homology of knots a'la Viro
Khovanov's homology is a generalization of the Jones polinomial of a knot: this polinomial is the Poincare polinomial of the corresponding chain complex. Viro clarified the meaning of a (rather obscure) construction of Khovanov. These results are very recent and unpublished.
Yildiray Ozan Oct 26 On entire rational maps of real algebraic surfaces and realization of smooth manifolds with prescribed algebraic submanifolds
Let X be an R-oriented nonsingular compact real algebraic variety and i : X-->XC a projective nonsingular complexification. It is well-known that ker i* : H*(X,R)-->H*(XC,R) and Im(i* : H*(XC,R)-->H*(X,R)) is independent of XC. We use this invariant to study entire rational maps and also an an obstruction to algebraic realization of smooth pairs of manifolds by algebraic varieties.
Nermin Salepci Oct 19 Arnold invariants of immersed plane curves
The starting point of the classification of immersed plane curves was the paper of Arnold in which he gave the definitions of the invariants St and J+, J-. We discussed some of the properties of the space of immersions using these invariants.
Cem Tezer Oct 12 Rarity of Moebius transformations with invariant connections
The purpose of this talk is to show that a linear fractional transformation (considered as a diffeomorphism of S2) admits an invariant connection only trivially, that is only if it admits an invariant Riemannian metric. This demonstrates that, of the group of linear fractional transformations an open dense subset consists of diffeomorphisms which admit no invariant connection.

Spring 1999
Nermin Salepci Jun 8 Plane curves, their invariants, perestroikas and classifications (after V.I. Arnold)
Sergey Finashin May 21 Branched coverings and quotients as a source of new constructions in Low-dimensional topology (some old ideas and new projects)
Sergey Finashin May 14 Minimal genus in S1xM3 (after P. Kronheimer)
Sergey Finashin May 7 Invariants of 3-dimensional homology spheres: from Rokhlin to Froyshov
Mustafa Korkmaz Apr 30 Non-complex smooth 4-manifolds with Lefschetz fibrations
Sergey Finashin Apr 9 Generic immersions of circle to surfaces and complex topology of real algebraic curves (after V.Arnold and O.Viro)
Sergey Finashin Mar 19 The Rokhlin Conjecture and singular real algebraic surfaces, with smooth quotients by the complex conjugation
Mustafa Korkmaz Mar 12 Minimal number of singular fibers in a Lefschetz fibration
Alexander Klyachko
Bilkent
Mar 5 Quantum cohomology, parabolic bundles and unitary operators
Selahi Durusoy Feb 19 Holomorphic functions in neighborhoods of spheres embedded in CP2 (after S. Nemirovski)

Fall 1998
Mustafa Korkmaz Dec 28 Relations in the Mapping Class Groups
Burak Ozbagci
Irvine
Dec 25 Continuation to: Signatures of Lefschetz fibrations
Burak Ozbagci
Irvine
Dec 21 Signatures of Lefschetz fibrations
Turgut Onder Dec 7 Equivariant Cross Sections of Complex Stiefel Manifolds
Sinan Sertoz
Bilkent
Nov 30 Classification of Algebraic Threefolds; the Mori Program
Sergey Finashin Nov 23 Intersection homologies, Mixed Hodge structures and Topology of real ICIS (elementary use of non-elementary tools)
Hursit Onsiper Nov 16 On uniformization of complex surfaces
Mustafa Korkmaz Nov 2 Endomorphisms of surface mapping class groups
Vladimir Golubyatnikov
(Novosibirsk, Russia)
Oct 26 On reconstruction of shapes of smooth surfaces from the shapes of their apparent contours
Yuri N. Obukhov
Moscow
Oct 19 On quantum anomalies in Riemann-Cartan spacetime
Muhiddin Uguz Oct 12 A short proof of a Donaldson theorem with SW-theory
based on the notes of A. Parker
Ferit Ozturk Oct 5 Introduction to the topology of surface singularities
tentatively: analytic and topological invariants of such singularities and their relationship

[ Geometry / Topology Seminar Group | Mathematics Department ]