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講演者：Franz Pedit (UMass Amherst)
日程：3月11日（土）11:00--15:00
場所：首都大学東京 南大沢キャンパス8号館6階610室

11:00--12:00  1st lecture
Title: Towards a constrained Willmore conjecture
Abstract: The constrained Willmore problem investigates the minimizers, and more generally the critical points, of the Willmore functional (bending energy) on immersions of surfaces under variations preserving the conformal type of the surface.  We give a brief introduction/overview of the topic and discuss a number of conjectures, together with  supporting evidence,  which have emerged over the past years. Ramifications of those conjectures would greatly enhance our understanding of the Willmore functional on the space of conformal immersions of compact Riemann surfaces.

12:00--14:00  lunch and discussion

14:00--15:00  2nd lecture
Title: Energy quantization for harmonic 2-spheres in non-compact symmetric spaces
Abstract: It is well known from results by Uhlenbeck, Chern-Wolfson and Burstall-Rawnsley that harmonic 2-spheres in compact symmetric spaces have quantized energies. Using the reformulation of the harmonic map equation as a family of flat connections, we construct an energy preserving  duality between harmonic maps from non-compact symmetric spaces into their compact duals. Applying this construction to the conformal Gauss maps of Willmore  2-spheres in the n-sphere provides a generalization and unifying approach to existing quantization results in special cases: Bryant for n=3; Montiel for n=4; and Ejiri for Willmore 2-spheres admitting a dual Willmore surface.

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首都大学東京理工学研究科
数理情報科学専攻
酒井 高司