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Seminar information archive ～01/14｜Today's seminar 01/15 | Future seminars 01/16～

2011/02/18

Operator Algebra Seminars

10:30-12:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Pedram Hekmati (Univ. Adelaide)
Dirac families and 1-cocycles (ENGLISH)

[ Abstract ]
Families of Dirac type operators, transforming covariantly under the projective action of the loop group $LG$, determine a class in twisted K-theory on compact Lie groups $G$. The loop group is the gauge group of a principal $G$-bundle over the circle and an interesting problem is to try to generalise the circle to a higher dimensional compact manifold. This is far from obvious and some of the difficulties can be modelled in a slightly simpler setting, by replacing $LG$ and gauge connections by objects which have only small differentiability in the Sobolev sense. In this talk, I will provide some background to this problem and explain how 1-cocycles naturally appear in this construction.

Classical Analysis

11:00-15:45 Room #126 (Graduate School of Math. Sci. Bldg.)
T. Morita (Osaka University) 11:00-12:00
Connection problem on the Hahn-Exton $q$-Bessel functions (ENGLISH)
M. Yamaguchi (University of Tokyo) 13:30-14:30
Rigidity index and middle convolution of $q$-difference equations (Joint work with H. Sakai)
(ENGLISH)
L. Di Vizio (Universite Paris 7) 14:45-15:45
Arithmetic theory of $q$-difference equations and applications (Joint work with C. Hardouin)
(ENGLISH)

Classical Analysis

10:15-10:45 Room #126 (Graduate School of Math. Sci. Bldg.)
Y. Ohyama (Osaka University)
Degeneration shceme of basic hypergeometric equations and $q$-Painlev¥'e equations (ENGLISH)

2011/02/17

Applied Analysis

16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Thomas Giletti (University of Paul Cezanne (Marseilles))
Study of propagation phenomena in some reaction-diffusion systems (ENGLISH)

[ Abstract ]
This talk deals with the existence and qualitative properties of traveling wave solutions of a nonlinear reaction-diffusion system with losses inside the domain, which has numerous applications in various fields ranging from chemical and biological contexts to combusion. Under some KPP type hypotheses, the existence of a continuum of admissible speeds for traveling waves can be shown, thus generalizing the single equation case. Lastly, by considering losses concentrated near the edge of the domain, those results can be compared with those of the boundary losses case.

Classical Analysis

11:00-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)
L. Di Vizio (Universite Paris 7) 11:00-12:00
Overview of local theory of $q$-difference equations and summation, 1
(ENGLISH)
Y. Katsushima (University of Tokyo) 13:30-14:30
Bounded operators on Gevrey spaces and additive difference operators (in a view of differential operators of infinite order) (ENGLISH)
K. Matsuya (University of Tokyo) 14:45-15:45
Blow-up of solutions for a nonlinear difference equation (ENGLISH)
L. Di Vizio (Universite Paris 7) 16:00-17:00
Overview of local theory of $q$-difference equations and summation, 2 (ENGLISH)

2011/02/16

Classical Analysis

13:30-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)
H. Sakai (University of Tokyo) 13:30-14:30
Isomonodromic deformation and 4-dimensional Painlev\\'e type equations (ENGLISH)
H. Kawakami (University of Tokyo) 14:45-15:45
Degeneration scheme of 4-dimensional Painlev¥'e type equations
(Joint work with H. Sakai and A. Nakamura)

(ENGLISH)
S. Nishioka (University of Tokyo) 16:00-17:00
Solvability of difference Riccati equations (ENGLISH)

2011/02/14

GCOE Seminars

13:00-14:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Jin Cheng (Fudan University)
Unique continuation on the analytic curve and its application to inverse problems. (ENGLISH)

[ Abstract ]
The unique continuation is one of the important properties for the partial differential equations, which is applied to the study of inverse problems for PDE. In this talk, we will show the unique continuation on the analytic curve for the elliptic equations with analytic coefficients. Some applications to inverse problems are mentioned.

2011/02/10

Operator Algebra Seminars

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Alan Weinstein (UC Berkeley)
Symplectic and quantum categories (ENGLISH)

Applied Analysis

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Jean-Michel Coron (University of Paris 6)
Control and nonlinearity (ENGLISH)

[ Abstract ]
We present methods to study the controllability and the stabilizability of nonlinear control systems. The emphasis is put on specific phenomena due to the nonlinearities. In particular we study cases where the nonlinearities are essential for the controllability or the stabilizability.
We illustrate these methods on control systems modeled by ordinary differential equations or partial differential equations (Euler and Navier-Stokes equations of incompressible fluids, shallow water equations, Korteweg de Vries equations).

Number Theory Seminar

11:00-12:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Joseph Ayoub (University of Zurich)
The motivic Galois group and periods of algebraic varieties (ENGLISH)

[ Abstract ]
We give a construction of the motivic Galois group of $\\Q$ and explain the conjectural link with the ring of periods of algebraic varieties. Then we introduce the ring of formal periods and explain how the conjectural link with the motivic Galois group can be realized for them.