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Texas A&M University

Events for 10/21/2019 from all calendars

Geometry Seminar

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Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Donghao Wang, MIT

Title: Finite Energy Monopoles on $\C \times \Sigma$

Abstract: The Seiberg-Witten (monopole) equations and the monopole invariants introduced by Witten have greatly influenced the study of smooth 4-manifolds since 1994. By studying its dimensional reduction in dimension 3, Kronheimer-Mrowka defined the monopole Floer homology for any closed 3-manifolds. In this talk, we continue this reduction process and consider the moduli space of solutions on $X=\mathbb{C}\times\Sigma$, where $\Sigma$ is a compact Riemann surface. We will classify solutions to the Seiberg-Witten equations on $X$ with finite analytic energy and estimate their decay rates at infinity according to the algebraic input. The motivation is to extend the construction of Kronheimer-Mrowka for compact 3-manifolds with boundary, and this work is the first step towards this goal.


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Time: 6:00PM - 7:00PM

Location: BLOC 220

Speaker: Matthias Maier, Dept of Mathematics, Texas A&M University

Title: Potential flow: Why does an airplane fly?

Abstract: Flight has fascinated mankind for millennia. It was not until the beginning of the 20th century that "lift" could be used for the first heavier-than-air flight. Even though airplanes are nowadays a central tool of transportation, the notion of flight remains a fascinating topic with a number of questions still unresolved today. In this talk we will examine a classical theory of flight based on "potential flows". These are flows that can be described (in 2D) as a complex-valued function defined on the complex number plane. Based on this representation we will derive two fundamental theorems for potential flow, Blasius' Thorem and the Kutta-Joukowsky Theorem, that describe the "lift'" of a body in potential flow.