[Japanese]

The 16th Osaka City University
International Academic Symposium 2008
"Riemann Surfaces, Harmonic Maps and Visualization"



The 16th Osaka City University International Academic Symposium 2008
“ Riemann Surfaces, Harmonic Maps and Visualization ”



  Photo

Sponsor : Osaka City University Advanced Mathematical Institute
The 16th International Academic Symposium Organizing Committee
(Graduate School of Sciences, Osaka City University)


Date: December 15 (Mon)- December 20 (Sat), 2008
Place : Osaka City University Media Center, Main Hall



 Co-Sponsors
  Kyushu University
  Kobe University
  Tokyo Metropolitan University
  Nagoya University
 Support
  Yuko-Kai
  Osaka City University Shinko-Kai
 Organizing Committee
  Yoshihiro Ohnita (head organizer, Osaka City University)
  Yoichi Imayoshi (Osaka City Univ.)
  Akio Kawauchi (Osaka City Univ.)
  Mikiya Masuda (Osaka City Univ.)
  Yohei Komori (Osaka City Univ.)
  Martin Guest (Tokyo Metropolitan University)
  Reiko Miyaoka(Tohoku Univ.)
  Wayne Rossman(Kobe Univ.)
  Ryoichi Kobayashi(Nagoya Univ.)
  Kotaro Yamada(Kyushu Univ.)
 International Scientific Organiziners
  Richard Palais(Univ. of California, Irvine, USA)
  Chuu-lian Terng(Univ. of California, Irvine, USA)
  Ulrich Pinkall (TU Berlin)
  Motohico Mulase(Univ. of California, Davis, USA)
  Iskandar Taimanov(Inst. Math., Novosibirsk, Russia)
  Fran Burstall(Univ. of Bath, UK)


 Confirmed Speakers


  Josef Dorfmeister (TU Muenchen)
  Mark Haskins (Imperial College London)
  John C. Wood (Univ. of Leeds, UK)
  John Bolton (Univ. of Durham, UK)
  Fran Burstall (Univ. Bath, UK)
  Bertrand Eynard (SPT, Saclay, France)
  Kefeng Liu (UCLA, USA)
  Hiraku Nakajima (Kyoto University, Japan)
  Craig A. Tracy (UC Davis, USA)
  Hao Xu (Zhejiang University, China)
  Ulrich Pinkall (TU Berlin)
  Franz Pedit (Univ. Tuebingen & Univ. of Massachusetts)
  Masaaki Umehara (Osaka University)
  Iskandar Taimanov (Novosibirsk)
  Andrey Mironov (Sobolev Inst. of Math.)
  Udo Hertrich-Jeromin (Univ. Bath, UK)
  Tim Hoffmann (Kyushu Univ., Japan)
  Martin Kilian (Univ. College Cork, Ireland)
  Martin Ulrich Schmidt(Univ. of Mannheim,Germany)
  Katrin Leschke (Univ. of Leicester, UK)
  Emma Carberry (Univ. of Sydney, Australia)
  Bennett Palmer(Idaho State Univ.,USA)
  Ryoichi Kobayashi (Nagoya University, Japan)
  Armen Sergeev (Steklov)
  Andery Domrin (Moscow University)
  Sumio Yamada (Tohoku University)
  Yasuyuki Nagatomo (Kyushu University)
  Katsuhiro Moriya (Tsukuba University)
  Shoichi Fujimori (Fukuoka Univ. of Education)
  Yu Kawakami (Nagoya University&OCAMI)
  Toshihiro Nogi(Osaka City University)
  Hironori Sakai (Tokyo Metropolitan University)
  etc.


Symposium Schedule (for print) PDF.

Warming Up Lectures (for graduate students etc.)

Dec.15(Mon)
15:00-16:15 Motohico Mulase (Univ. of California, Davis, USA)
" Again Riemann surfaces ? Still Riemann surfaces ? Yes, Riemann surfaces forever ! "
Abstract: This talk is aimed at graduate students who are curious about the topics to be discussed at the Symposium. The modern Riemann surface theory began with the 1857 paper of Riemann, "Theorie der Abel'schen Functionen." We are startled by his far reaching vision immersed in this paper on birational geometry, theory of Jacobian and Abelian varieties, use of ample line bundles, and moduli theory, among others. So many times we thought we understood Riemann surface theory, and felt we must move on to its generalization. Of course many such generalizations are flourishing now. But Riemann surfaces themselves are again, still, and forever appearing in numerous exciting frontiers of modern mathematics. In this talk some of such appearances will be examined. They include random matrix theory, algebraic geometry, and symplectic geometry.
File of Talk
Dec.15(Mon)
16:45-18:00 Wayne Rossman (Kobe University)
"Discrete surfaces and architecture"
Abstract: Like Prof. Mulase's talk, this talk will also be aimed at graduate students who are curious about the topics covered by this symposium. Discrete differential geometry, and in particular discrete curve and surface theory, has recently developed into a self-sustaining field with a promising future. We look at some basic concepts in discrete surface theory, and make some comments about connections with architecture. One goal will be to explain the definition of discrete "isothermic" surfaces, and to understand why that definition is natural.
File of Talk


Opening

Dec.16(Tue)
9:10-9:15 Opening Remarks (by chairmann of the organizing committee Yoshihiro Ohnita)
Dec.16(Tue)
9:15-9:25 Opening Speech by President of Osaka City University
President Satoru Kaneko PDF

Program of Talks

Dec.16(Tue)
9:30-10:30 Ulrich Pinkall (TU Berlin)
"Conformal equivalence of triangulated surfaces"
Abstract: We present a new algorithm for conformal mesh parameterization. It is based on a precise notion of discrete conformal equivalence for triangle meshes which mimics the notion of conformal equivalence for smooth surfaces. The problem of finding a flat mesh that is discretely conformally equivalent to a given mesh can be solved efficiently by minimizing a convex energy function, whose Hessian turns out to be the well known cot-Laplace operator. Surprisingly, it turns out that the theory is closely related to the geometry of polyhedra in hyperbolic space.
Dec.16(Tue)
10:45-11:45 Masaaki Umehara (Osaka University)
" Surfaces with singularities and Osserman-type Ineqalities "
Abstract: PDF
File of Talk
Dec.16(Tue)
12:00-13:00 Josef Dorfmeister (TU M\"unchen)
"Loop Groups and Surfaces with Symmetries"
Abstract: In this talk we will present applications of the loop group method to the construction of surfaces with symmetries. Starting from the well known procedure in the case of CMC surfaces in R^3, we will discuss the case of CMC surfaces in H^3 with mean curvature H satisfying 0 <= H < 1, the case of pseudospherical surfaces and, time permitting, a surface associated with the quantum cohomology of CP^1.
Dec.16(Tue)
14:30-15:30 Bertrand Eynard (SPT, Saclay, France)
" Random matrix methods in enumerative geometry "
Abstract: We will introduce some newly discovered invariants of spectral curves. Given a plane curve S={y(x)} in C^2, called the "spectral curve", we can associate to it a sequence of invariants F_g(S). The F_g's are invariants under symplectic transformations of the spectral curve. We will give the definitions, and main properties of those F_g's, and present some applications in enumerative geometry, such as Witten-Kontsevich theory, volumes of moduli spaces, and Gromov Witten theory.
File of Talk
Dec.16(Tue)
15:45-16:45 Kefeng Liu (UCLA, USA)
" Recent results on the geometry and topology of moduli spaces "
Abstract: I will present several recent results on the geometry and topology of moduli spaces of Riemann surfaces, including the proof of the Faber intersection number conjecture, the goodness of the Weil-Petersson metric, the Ricci, the perturbed Ricci and the Kahler-Einstein metric, the Nakano negativity of the Weil-Petersson metric and various corollaries such as the Gauss-Bonnet type theorems, vanishing theorems of cohomology groups, rigidity theorems and Chern number inequalities and the Mumford stability of the logarithmic cotangent bundles of the moduli spaces. Finally I will discuss the properties of the period map from the Teichmuller space of polarized Calabi-Yau n-folds to the classifying space of variation of Hodge structures as well as the local and global geometry of the Teichm\"uller and moduli spaces of polarized Calabi-Yau manifolds.
File of Talk
Dec.16(Tue)
17:00-18:00 Hiraku Nakajima (Kyoto Univ., Japan)
" Instanton counting (survey) "
Abstract: Nekrasov defined the instanton partition function by an equivariant integration of $1$ over moduli spaces of instantons on $\mathbf R^4$. I will survey its relations to various subjects:
1) Its leading part is the Seiberg-Witten prepotential defined via a period integral of hyperelliptic curves.
2) (Geometric engineering) The full partition function, setting one of variables 0, is the generating function of Gromov-Witten invariants of a certain local Calabi-Yau 3-fold so that the leading part corresponds to the genus 0 part.
3) The partition function has a natural deformation integrating Chern classes of natural vector bundles over moduli spaces. They are conjecturally related to Poincare polynomials of link homology groups a la Khovanov.
File of Talk
Dec.16(Tue)
18:15-20:15 Banquet(OCU Media Center 10th floor)
Dec.17(Wed)
9:00 - 10:00Yasuyuki Nagatomo(Kyushu Univ.)
" Harmonic maps into Grassmannian manifolds "
Abstract: PDF
Dec.17 (Wed)
10:15-11:15 John C. Wood (Univ. of Leeds, UK)
"A completely explicit formula for harmonic spheres in the unitary group"
Abstract: We report on joint work with B.A. Simoes and M.J. Ferreira (Lisbon) which gives a completely explicit formula for all harmonic maps of finite uniton number from a Riemann surface to a unitary group, and so all harmonic maps from the two-sphere, in terms of freely chosen meromorphic functions on the surface and their derivatives, using only combinations of projections and avoiding the usual dbar-problems or loop group factorizations. The formula is obtained using only techniques in the theory of harmonic maps.
We interpret our construction in terms of Segal's Grassmannian model and an explicit factorization of the algebraic loop group, and show how it specializes to give all harmonic maps into a Grassmannian.
We then describe joint work with M. Svensson (Odense) which extends this interpretation to give explicit formulae for any factorization, in particular, getting formulae for all harmonic two-spheres into the symplectic and orthogonal groups.
Dec.17(Wed)
11:30-12:30Sumio Yamada(Tohoku Univ.)
" Weil-Petersson geometry of Teichm\"uller-Coxeter Complex "
Abstract: Teichmuller space is a moduli space of conformal structures on a topological surface of higher genus. Recently there has been much progress in understanding the geometry of the space via the L^2 (Weil-Petersson) deformation theory of hyperbolic metrics defined on the surface. In this talk, we will introduce a new construction of a WP-geodesically complete simplicial complex where the simplex is a copy of Teichmuller space. This construction suggests a further analogy between the theory of non-compact symmetric space (and Tits buildings) and that of Teichmuller space.
Dec.17(Wed)
14:00-14:45 Tim Hoffmann (TU M\"unchen \& Kyushu Univ.)
"The Steiner formula, curvature and discrete surfaces"
Abstract: The aim of discrete differential geometry is to find "structure preserving" discretizations of classical objects and notions form differential geometry. By preserving the rich structure the smooth diffenrential geometry provides, these discretizations often can be derived in many different ways since they resemble their smooth counterparts in many different aspects.
In case of surfaces of constant mean curvature, one of the many ways is through Steiner's formula. The Steiner formula gives the area of a parallel surface in terms of the distance and the original surface's area and curvatures. For quadrilateral meshes with planar faces, which serve as discretizations of conjugate nets, Schief defined curvatures for these polyhedral surfaces by looking at the area of parallel meshes which in turn leads to discretizations of surfaces with constant curvature. However, it depends on a choice for the Gauss map of the discrete conjugate net. This was carried on by Bobenko, Pottmann, Schief et al and dualizability and curvature formulas for discrete surfaces were found in terms of mixed area. The well known discretizations of surfaces of constant mean curvature can be derived from this approach.
Dec.17(Wed)
14:55-15:40 Shoichi Fujimori (Fukuoka University of Education)
" Triply periodic minimal surfaces bounded by vertical symmetry planes "
Abstract: We give a uniform and elementary treatment of many classical and new triply periodic minimal surfaces in Euclidean three-space, based on a Schwarz-Christoffel formula for periodic polygons in the plane. Our surfaces share the property that vertical symmetry planes cut them into simply connected pieces. This is joint work with Matthias Weber.
File of Talk
Dec.17(Wed)
15:50-16:35 Katrin Leschke(Univ. of Leicester, UK)
"Hamiltonian stationary Lagrangian tori in C^2 revisited"
Abstract: Helein and Romon gave a complete description of HSL tori in C^2 in terms of Fourier polynomials. In recent work with Romon we showed that this description is due to the fact that the spectral curve of the associated harmonic map into the the 2-sphere (the left normal of the HSL torus) has spectral genus zero. To explain this link I will discuss the relation between this spectral curve and the multiplier spectral curve of the HSL torus.
Dec.17(Wed)
16:45-17:30 Bennet Palmer (Idaho State Univ., USA)
" Anisotropic surface energies "
Abstract: An anisotropic surface energy assigns an energy to a surface which depends on the direction of the surface at each point. Such an energy is used to model the shape of an interfaces of anisotropic media.
We will discuss a capillary (free boundary) problem involving anisotropic surface energies which includes wetting and line tension.
File of Talk
Dec.17(Wed)
17:40-18:25 John Bolton (Univ. of Durham, UK)
"Minimal 2-spheres with various symmetry properties in the round 4-sphere"
Abstract: Each minimal 2-sphere in the round 4-sphere has a holomorphic horizontal lift to the total space of the twistor bundle, which is the projection from complex projective 3-space to the 4-sphere. Symmetry properties of the minimal 2-sphere are reflected in corresponding properties of the lift, and this is used to construct, and, in some cases, classify, minimal 2-spheres in the 4-sphere. This is joint work with Prof. L. Fernandez (CUNY).
Dec.18(Thu)
9:00-10:00 Ryoichi Kobayashi(Nagoya University, Japan)
"An Interpretation of the Period Condition of Algebraic Minimal Surfaces from the View Point of Lemma on Logarithmic Derivative"
Abstract: Nevanlinna's Lemma on Logarithmic Derivative is the source of almost all results in the value distribution theory of entire holomorphic curves into projective varieties. On the other hand, the period condition of algebraic minimal surfaces is extremely difficult to realize in the attempt of their construction. The goal of my talk is to give an interpretation of the period condition of algebraic minimal surfaces from the view point of Lemma on Logarithmic Derivative applied to the Gauss map of algebraic minimal surfaces lifted on the universal cover.
File of Talk
Dec.18(Thu)
10:15-11:15 Mark Haskins (Imperial College London)
"A panoply of Special Lagrangian singularities"
Abstract: (joint work with Nikolaos Kapouleas) Special Lagrangian submanifolds are a special type of higher-dimensional minimal submanifold that occur naturally in Calabi-Yau manifolds. They have been the focus of much attention from both mathematicians and string theorists because of their role in Mirror Symmetry. Singularities of special Lagrangians play a very important part in this story but as yet are poorly understood. Special Lagrangian cones with an isolated singularity form the local models for the simplest kinds of singular special Lagrangians. In this talk we will discuss recent progress in the construction of special Lagrangian cones in dimensions three and higher.
Three-dimensional special Lagrangian cones with cross-section a 2-torus all arise from algebraically completely integrable systems constructions. Using spectral curve methods Carberry-McIntosh proved the surprising result that special Lagrangian 2-torus cones can come in continuous families of arbitrarily large dimension. We will show that starting in dimension 6 there are infinitely many topological types of special Lagrangian cone which can come in continuous families of arbitrarily large dimension.
The three main ingredients needed to prove this result are
a. the integrable systems techniques for special Lagrangian 2-torus cones
b. gluing constructions of infinitely many topological types of special Lagrangian cones in dimensions 3 and higher
c. a 'twisted product' construction to produce new special Lagrangian cones from a pair of lower dimensional special Lagrangian cones.
File of Talk
Dec.18(Thu)
11:30-12:30 Hironori Sakai (Tokyo Metropolitan University)
"Normalization of differential equations associated to orbifold quantum cohomology"
Abstract: Starting from the differential equations associated to quantum cohomology, the original quantum cohomology can be recovered by taking a normalized trivialization of the D-module. We will discuss this phenomenon for the orbifold quantum cohomology of a hypersurface in weighted projective space.
File of Talk
Dec.18(Thu)
14:00-15:00 Armen Sergeev(Steklov Mathematical Institute, Moscow)
"Quantization of the Universal Teichm\"uller Space"
Abstract: PDF
File of Talk
Dec.18(Thu)
15:15-16:15 Andery Domrin(Moscow University)
" Meromorphic extension of solutions of soliton equations "
Abstract: We show that every local (in $x$ and $t$) holomorphic solution $u(x,t)$ of any soliton equation belonging to a large class (including Kroteweg--de Vries equation, nonlinear Schroedinger equation, their modifications and hierarchies) admits analytic continuation to a globally meromorphic function of $x$ (on the whole complex plane) for every fixed $t$. The proof uses a local version (independent of any boundary conditions) of the inverse scattering method. In particular, we give a simple criterion of solubility of the local holomorphic Cauchy problem for equations under study in terms of the scattering data of the initial condition.
Dec.18(Thu)
16:25-17:10 Toshihiro Nogi (Osaka City Univ.)
"On holomorphic sections of a holomorphic family of Riemann surfaces of genus two"
Abstract: We study a holomorphic family of Riemann surfaces of genus two constructed by Gonzalo Riera. The main goal of this talk is to estimate the number of holomorphic sections of this family.
File of Talk
Dec.18(Thu)
17:20-18:05 Yu Kawakami(Kyushu Univ.& OCAMI)
"Recent progress in the value distribution of the hyperbolic Gauss map"
Abstract: In this talk, I will explain my recent work on the value distribution of the hyperbolic Gauss map. In particular, I will define ``algebraic'' class of constant mean curvature one (CMC-1) surfaces in the hyperbolic three-space and give the ramification estimate for the hyperbolic Gauss map of them.
File of Talk
Dec.19(Fri)
9:00-10:00 Craig A. Tracy (UC Davis, USA)
"The Asymmetric Simple Exclusion Process : Integrable Structure and Limit Theorems"
Abstract: We consider the asymmetric simple exclusion process (ASEP) on the integer lattice in the case of step initial condition. Using ideas from Bethe Ansatz we show that the probability distribution for the position of an individual particle is given by an integral whose integrand involves a Fredholm determinant. We use this formula to derive a limit theorem for ASEP which extends Kurt Johansson's result for TASEP to ASEP. This is joint work with Harold Widom.
File of Talk
Ref. Japanese Longevity
Dec.19(Fri)
10:15-11:15 Hao Xu (Zhejiang Univ., P.R.China)
"Intersection numbers on the moduli spaces of stable curves"
Abstract: In the first part, we give a survey of algorthms for computing $\psi$ class intersection numbers, Witten's r-spin intersection numbers and higher Weil-Petersson volumes of moduli spaces of curves. In particular, our work on effective recursion formulae of higher Weil-Petersson volumes is motivated by the work of Prof. Mulase and Safnuk.
In the second part, we present our proof of the Faber intersection number conjecture on moduli spaces of curves as well as some vanishing identities of Gromov-Witten invariants. The latter has been proved recently by X. Liu and Pandharipande.
File of Talk
Dec.19(Fri)
11:30-12:30 Motohico Mulase(University of California, Davis, USA)
"An integrable system approach to the newly discovered topological recursion"
Abstract: A recent discovery in topological string theory predicts that Gromov-Witten invariants of toric Calabi-Yau threefolds are miraculously calculated by an effective recursion formula that uses only classical Riemann surface theory.
We found that some of such examples can be explained through a deformation theory of KP tau-functions. In this talk our new theory, based on a joint work with Brad Safnuk, will be reported.
Dec.19(Fri)
14:00-15:00 Iskandar Taimanov (Novosibirsk)
" The Moutard transformation and blowing up solutions of the Novikov-Veselov equation "
Abstract: The Moutard transformation is a generalization of the Darboux transformation he case of two-dimensional Schrodinger operators. Although the Darboux transformation was widely used for constructing differential operators with interesting properties the Moutard transformation until recently was not used in the spectral theory. In our joint papers with S.P. Tsarev we constructed the first known examples of two-dimensional Schrodinger operators on the plane with bounded and fast decaying potentials which have nontrivial (and even multi-dimensional kernel). Moreover we contsruct examples of solutions of the Novikov-Veselov equation (one of two-dimensional generalizations of the Korteweg-de Vries equation) which blow up in finite time and have smooth fast decaying Cauchy data.
File of Talk
Dec.19(Fri)
15:15-16:15 Andrey Mironov (Sobolev Inst. of Math.)
"Spectral data for Hamiltonian-minimal Lagrangian tori in ${\bold C}P^2$"
Abstract: We find spectral data that allow to find in explicit form Hamiltonian-minimal Lagrangian tori in ${\bold C}P^2$ in terms of theta functions of spectral curves.
File of Talk
Dec.19(Fri)
16:30-17:15 Katsuhiro Moriya (Univ. Tsukuba)
"Super-conformal surfaces in the Euclidean four space in terms of null complex holomorphic curves"
Abstract: A super-conformal surface in the Euclidean four space is a surface whose curvature ellipse is a circle. It is the stereographic projection of a surface with vanishing Willmore energy in the conformal four sphere. A surface with vanishing Willmore energy in the conformal four sphere is a twister projection of a complex holomorphic curve in the three dimensional complex projective space. In this talk, a super-conformal surface in the Euclidean four space is constructed by a null complex holomorphic curve in the four dimensional complex Euclidean space. The use of quaternionic analysis makes our proof shorter than Dajczer and Tojeiro's.
File of Talk
Dec.19(Fri)
17:30-18:15 Tetsuya Taniguchi (Kitasato Univ)
"Fourier-Mukai transforms and spectral data of harmonic tori into compact symmetric spaces"
Abstract: PDF
File of Talk
Dec.20(Sat)
9:00-10:00 Franz Pedit (Univ. Tuebingen & Univ. Massachusetts)
"Global Aspects of Integrable Surface Geometry"
Abstract: We will discuss the relevance of the spectral curve construction for conformally immersed tori to global problems in surface geometry and indicate how to extend these ideas to conformally immersed surfaces of arbitrary genus.
File of Talk
Dec.20(Sat)
10:15-11:15 Martin Kilian (Univ. College Cork, Ireland)
"On the Lawson Conjecture"
Abstract: While there are no compact minimal surfaces in Euclidean 3-space, Lawson showed in 1970 that the curvature of the 3-sphere allows for embedded compact minimal surfaces of arbitrary genus. In particular, in collaboration with Hsiang he investigated minimal tori in the 3-sphere, and conjectured that the only embedded minimal torus in the 3-sphere is a torus which possesses a 2-parameter family of isometries, the so-called Clifford torus. In recent work with M. U. Schmidt, we prove that Lawson's conjecture indeed holds, and in this talk I will give an outline of the proof, which uses modern methods from the theory of integrable systems.
Dec.20(Sat)
11:30-12:30 Martin Ulrich Schmidt(Univ. Mannheim,Germany)
"On the Moduli of Alexandrov embedded cmc cylinders in S^3"
Abstract: PDF
Dec.20(Sat)
14:00-14:45 Emma Carberry (Univ. of Sydney, Australia)
"Almost-complex tori in the 6-sphere"
Abstract: Octonionic multiplication defines a natural almost-complex structure on $S^6\subset{Im}\O$ and almost-complex curves $M^2\rightarrow S^6$ are rather pleasant examples of minimal surfaces. In particular, the cone over such a curve is associative and hence absolutely volume minimising. These almost-complex curves come in two types: they are either {\it isotropic} (in which case Bryant has shown they can be algebraically constructed from holomorphic maps) or they are {\it superconformal}. I shall describe a spectral curve approach to superconformal almost-complex tori; the main point of which is to also obtain an algebraic characterisation of these surfaces and hence study their moduli. An interesting feature is that the relevant abelian variety in this case is the intersection of two Prymians.
Dec.20(Sat)
15:00-16:00 Francis Burstall (Univ. Bath, UK)
"Conserved quantities in geometric integrable systems"
Abstract: Many geometric integrable systems admit integrable specialisations: examples include constant mean curvature surfaces in 3-dimensional space forms (specialising both isothermic surfaces and constrained Willmore surfaces); submanifolds of space-forms with constant sectional curvatures and flat normal bundle (specialising conformally flat submanifolds with flat normal bundle and, in two dimensions, Guichard surfaces) and the special isothermic surfaces studied by Bianchi and Darboux. I shall describe joint work with Calderbank and Santos which provides an enlightening characterisation of such specialisations in terms of the associated loop of flat connections and parallel sections thereof depending polynomially in the loop parameter. I shall also describe (if times permits) an application with Hertrich-Jeromin, Rossman and Santos to discrete constant mean curvature surfaces.


Public Lectures "Mathematics and Computer"

Dec.20(Sat)
16:30-17:20 Tim Hoffmann (TU M\"unchen & Kyushu Univ.) , Kotaro Yamada (Kyushu University)
"Mathematics Behind Computer Graphics"
Abstract: When a computer generates an image of a 3 dimensional scene a lot of different mathematics is involved. How do we project a 3 dimensional scene into a plane? How can we tessellate a smooth surface with triangles so that they can be drawn by a computer? What is the best way to map an image onto a surface? In this talk I will show some of the mathematics involved in this. The projective geometry needed for understanding the perspective projection will be discussed as well as different rendering techniques and the problems associated with them like non orderability of triangles in space, and binary space partitioning trees as a way around this problem or the problem of how to draw a chart of a surface not isometric to the plane and its discrete versions.
Dec.20(Sat)
17:30-18:20 Takashi Sakai (OCAMI), Yoshihiro Ohnita (OCU), Martin Guest (TMU), Ulrich Pinkall (TU Berlin)
"Invitation to 3D-XplorMath - Mathematical World Visualized by Computer -"
Abstract: In general Geometry is a mathematical field to treat "Figures (Zukei, in Japanese)". When the figures are complicated, it becomes difficult for us to draw and imagine them. Throught recent developments of the computer, at present it became able to express geometric aspects of such complicated figures by computer graphics. Actually the computer graphics expression enables us to observe properties of figures which are unimaginable only from numerical data. In this lecture we shall invite you to a research on Geometry and Visualization by using a software called "3D-XplorMath" which our internatinal group is researching and developing. Let's explore the misterious world of mathematics by 3D-XplorMath !


Suggestion to Speakers: Unfortunetely there is no blackbord at the lecture rooms of the media center. However there are enough whiteboards, the computer projector and the visualizer. Please prepare your talk using them.

Contribution and Proceedings

The proceedings of the 16th Osaka City University International Academic Symposium 2008 “ Riemann Surfaces, Harmonic Maps and Visualization ” will be published as a volume in OCAMI (Osaka City University Advanced Mathematical Institute) Studies from OMUP (Osaka Municipal Universities Press).

All the speakers of the symposium are encouraged to submit articles based on their talks to the local organizing committee.

Every manuscript should be presented within 15 pages, and should be prepared in a Latex2e format by using the following sample file:
   TeX File    (Figure,    PDF file)

Each contributor is kindly asked to send the source file (and additional figures or so if any) and its pdf file to the address below by e-mail:
   Yoshihiro Ohnita
   Department of Mathematics
   Osaka City University
   3-3-138, Sugimoto, Sumiyoshi-ku
   Osaka, 558-8585 Japan
   E-mail: ohnita@sci.osaka-cu.ac.jp
Deadline of submission: June 30, 2009

N.B. Please prepare a manuscript in a standard LaTeX2e format (without non-standard macros). In case we cannot process the file, the author will be asked to supply additional files (if necessary) or to revise it.

All the papers submitted to the proceedings will be refereed. Only accepted papers will be included in the proceedings.


Poster:
Accommodation: Access: Satelite Conference:

Link


Supported by :
Osaka City University
Grants-in-Aid for Scientific Research (A), JSPS, JAPAN
(Yoshihiro Ohnita)
(Martin Guest)
(Reiko Miyaoka)
Grants-in-Aid for Scientific Research (B), JSPS, JAPAN
(Wayne Rossman)

Contact
Yoshihiro OHNITA ohnita (at) sci.osaka-cu.ac.jp


constructed by T. Noda (OCAMI)Last updated on 11/March/2009.