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8月演講

Geometry Seminar, 香港科技大學數學系 張懷良教授
Wednesday, August 2, 13:00—14:00 數學系3F會議室
Title: Recovery of Zinger Formula by MSP Moduli
Abstract: The moduli space of Mixed Spin P field (MSP) is designed to study Gromov Witten invariant of Calabi Yau hypersurfaces in projective spaces. For quintic threefold we use localization of MSP moduli to obtain generating series of g=1 GW invariants, and recover A. Zinger's result.

Algebraic Geometry Seminar, 香港科技大學數學系 張懷良教授
Wednesday, August 16, 10:10—13:00 數學系3F會議室
Title: Zhang-Yun's Work on Taylor Expansions of L Functions
Abstract:Zhang Wei and Yun Zhiwei use intersections of Drinfeld cycles in moduli of shtukas to obtain higher order derivative of L functions, generalizing Gross Zagier formula. We will introduce geometric part of their work in this series.

Algebraic Geometry Seminar, 香港科技大學數學系 張懷良教授
Thursday, August 17, 10:10—13:00 數學系3177
Title: Mumford's Paper on Commutative Rings of Differential Operators
Abstract:We will introduce Mumford's paper and shtukas. We will sketch the constructions and some framework.

Differential Equations Seminar, 清華大學數學系 江金城教授
Thursday, August 17, 11:10—12:00 數學系3F會議室
Title: Weighted Fractional Chain Rule and its Application
Abstract:One Day Workshop on Differential Equations For the structure of the thin electrical double layer (EDL), we analyze boundary layer solutions of a nonlocal electrostatic model with small Debye screening length. The model is an elliptic type with nonlocal dependence on its unknown variable, and it is known that the limiting profiles of solutions asymptotically blow up near the boundary. In this work, a series of fine estimates that combine the Pohozaev's identity, the inverse H\"{o}lder type estimates and some technical comparison arguments is developed for establishing boundary asymptotics for solutions in arbitrary bounded domains. The concept of inverse H\"{o}lder type estimates seems novel, and rarely appears in previous related literatures. Moreover, to gain a clear picture on the curvature effect of the thin boundary layer, we concentrate on the physical domain being a ball with the simplest geometry. The current study involves three contributions. The first one is about the boundary concentration phenomena. We show that the net charge density behaves exactly as Dirac delta measures concentrated at boundary points, which presents that the extra charges are accumulated near the boundary (charged surface), and the ionic distribution approaches electroneutrality in the bulk. For the second one, the boundary asymptotic blow-up behavior is completely illustrated. An interesting outcome shows that the significant curvature effect merely occurs in the part of the boundary layer sufficiently close to the boundary, and this part is quite thinner than the whole boundary layer. The third contribution is a connection to physical applications. Using such pointwise descriptions, we calculate the corresponding EDL capacitance and provides a theoretical way to support that the EDL has higher capacitance in a quite thin region near the charged surface, not in the whole EDL.

Differential Equations Seminar, 台灣大學數學系 陳逸昆教授
Thursday, August 17, 13:00—14:00 數學系3F會議室
Title: Regularity for Diffuse Reflection Boundary Problem to the Stationary Linearized Boltzmann Equation in a Convex Domain
Abstract: One Day Workshop on Differential Equations We consider the diffuse reflection boundary problem for linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or Maxwellian molecular gases in a C^2 strictly convex bounded domain. We obtain a pointwise estimate for the derivative of the solution provided the boundary temperature is bounded differentiable and the solution is bounded. This talk is based on the joint work with Chun-Hsiung Hsia and Daisuke Kawagoe.

Differential Equations Seminar, 清華大學計算與建模科學所 李俊璋教授
Thursday, August 17, 14:20—15:20 數學系3F會議室
Title: On Boundary Layers of an Electrostatic Model: Pointwise Description for Concentration Phenomena with Curvature Effects and its Applications
Abstract:One Day Workshop on Differential Equations For the structure of the thin electrical double layer (EDL), we analyze boundary layer solutions of a nonlocal electrostatic model with small Debye screening length. The model is an elliptic type with nonlocal dependence on its unknown variable, and it is known that the limiting profiles of solutions asymptotically blow up near the boundary. In this work, a series of fine estimates that combine the Pohozaev's identity, the inverse H\"{o}lder type estimates and some technical comparison arguments is developed for establishing boundary asymptotics for solutions in arbitrary bounded domains. The concept of inverse H\"{o}lder type estimates seems novel, and rarely appears in previous related literatures. Moreover, to gain a clear picture on the curvature effect of the thin boundary layer, we concentrate on the physical domain being a ball with the simplest geometry. The current study involves three contributions. The first one is about the boundary concentration phenomena. We show that the net charge density behaves exactly as Dirac delta measures concentrated at boundary points, which presents that the extra charges are accumulated near the boundary (charged surface), and the ionic distribution approaches electroneutrality in the bulk. For the second one, the boundary asymptotic blow-up behavior is completely illustrated. An interesting outcome shows that the significant curvature effect merely occurs in the part of the boundary layer sufficiently close to the boundary, and this part is quite thinner than the whole boundary layer. The third contribution is a connection to physical applications. Using such pointwise descriptions, we calculate the corresponding EDL capacitance and provides a theoretical way to support that the EDL has higher capacitance in a quite thin region near the charged surface, not in the whole EDL.

   
 


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