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 Events
National Taiwan University
Thu 5 Aug 2010, 10:30am SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
WMAX 216 (PIMS) "Note the room change"
Revisiting an idea of Brezis and Nirenberg
WMAX 216 (PIMS) "Note the room change"
Thu 5 Aug 2010, 10:30am-11:30am

Abstract

Usually, a nonlinear functional involving the Sobolev exponent does not satisfy the Palais-Smale condition. However, Brezis and Nirenberg showed that under a threshold , the minimax value is in fact a critical value. In this talk, we should extend this idea to the equation involving with the Hardy singular potential.
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University of California, San Diego
Mon 16 Aug 2010, 2:00pm
PIMS Seminars and PDF Colloquiums
WMAX 216
Lie group and homogeneous variational integrators and their applications to geometric optimal control theory
WMAX 216
Mon 16 Aug 2010, 2:00pm-3:00pm

Abstract

The geometric approach to mechanics serves as the theoretical underpinning of innovative control methodologies in geometric control theory.  These techniques allow the attitude of satellites to be controlled using changes in its shape, as opposed to chemical propulsion, and are the basis for understanding the ability of a falling cat to always land on its feet, even when released in an inverted orientation.  We will discuss the application of Lie group variational integrators to the optimal control of mechanical systems.  These methods are based on a discretization of Hamilton's principle that preserves the Lie group structure of the configuration space, and yield minimum-dimensional global representations of the dynamics.  Recent extensions to homogeneous spaces yield intrinsic methods for Hamiltonian flows on the sphere, and have potential applications to the simulation of geometrically exact rods, structures and mechanisms.  Extensions to Hamiltonian PDEs and uncertainty propagation on Lie groups using noncommutative harmonic analysis techniques will also be discussed.  In particular, this allows one to develop attitude state estimation methods for satellite dynamics without assuming that the measurements are frequent, and that the uncertainty distribution is localized.
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Prof. Chih-Wen Shih
Dept of Applied Math, National Chiao Tung University, Hsinchu, Taiwan
Tue 17 Aug 2010, 2:00pm
Mathematical Biology Seminar
WMAX 110
Synchronized Oscillation for Segmentation Clock Gene of Zebrafish
WMAX 110
Tue 17 Aug 2010, 2:00pm-3:00pm

Abstract

Somitogenesis is a process for the development of somites which are transient, segmental structures that lie along the anterior-posterior axis of vertebrate embryos.  The pattern of somites is traced out by the ``segmentation clock genes" which undergo synchronous oscillation over adjacent cells. In this presentation,  we analyze the dynamics for a model on zebrafish segmentation clock-genes which are subject to direct autorepression  by their own products under time delay, and cell-to-cell interaction through Delta-Notch signaling.  For this  system of delayed equations, we present an  ingenious iteration approach to derive the global synchronization and global convergence to the unique synchronous equilibrium. On the other hand, by applying the delay Hopf bifurcation theory and the method of normal form, we derive the criteria for the existence of stable synchronous oscillations.  Our analysis provides the basic range of parameters and delay magnitudes  for stable synchronous, asynchronous oscillation, and oscillation-arrested dynamics.  Based on the derived criteria,  further numerical findings on the dynamics which are linked to the biological phenomena are  explored  for the considered  system.

Note for Attendees

Coffee and cookies will be served at around 1:45 pm.
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University of Athens Panepistimioupolis
Fri 20 Aug 2010, 3:00pm
Topology and related seminars
WMAX 110
Gorenstein dimension and proper actions
WMAX 110
Fri 20 Aug 2010, 3:00pm-4:00am

Abstract

Gedrich and Gruenberg(1987)and Ikenaga(1984)studied the algebraic
invariants silpZG,the supremum of the injective lengths of the projective
ZG-modules,and spli,the supremum of the projective lengths of the
injective ZG-modules,in connection with the existence of complete
cohomological functors for the group G and showed that these are related
to the virtual cohomological dimension of G.  We will show that silpZG and
spliZG are related to the Gorenstein dimension of ZG and to the existence
of a finite dimensional model for E_G, the classifying space for proper
actions
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All Graduate Instructors
Mon 30 Aug 2010, 10:00am SPECIAL
One Time Event
MATH 100 - followed by lunch (Math 125)
Department Graduate Student Orientation
MATH 100 - followed by lunch (Math 125)
Mon 30 Aug 2010, 10:00am-1:00pm

Details

All instructors teaching a graduate course for 2010-11 should attend this "trade show" style graduate orientation and be prepared to talk about their course.
A catered lunch will be provided to faculty and students in Math 125.
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