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Events happening on October 16, 2018

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Oct. 16, 2018 10am (MATH 350)	Geometry/Analysis Sema Salur (University of Rochester) X Let $N2n$ be a smooth symplectic manifold equipped with a closed, nondegenerate differential 2-form $ω$ . An $n$ -dimensional submanifold $L^{n}$ of $N2n$ is called Lagrangian if the restriction of $ω$ to $L$ is zero. Lagrangian submanifolds and their deformations have important applications in symplectic geometry and mathematical physics. In partciular, they play a role in establishying the correspondence between “Calabi-Yau mirror pairs” in string theory. In this talk we first study the deformations of (special) Lagrangian submanifolds and then extend the theory to “Lagrangian Type” submanifolds inside $G2$ manifolds. If time permits, we will also discuss relations between $G2$ and contact structures. Deformation Theory of Calibrated Submanifolds Sponsored by the Meyer Fund
Oct. 16, 2018 12pm (MATH 350)	Geometry/Analysis Catherine Searle (Wichita State University) X The classification of compact Riemannian manifolds with positive or non-negative sectional curvature is a long-standing problem in Riemannian geometry. One successful approach has been the introduction of symmetries, and an important first case to understand is that of continuous abelian symmetries. In recent work with Escher, we obtained an equivariant diffeomorphism classification of closed, simply-connected non-negatively curved Riemannian manifolds admitting an isotropy-maximal torus action, with implications for the Maximal Symmetry Rank Conjecture for non-negatively curved manifolds. I will discuss joint work with Escher and Dong, that builds on this work to extend the classification to those manifolds admitting an almost isotropy-maximal action. Torus actions, maximality, and non-negative curvature Sponsored by the Meyer Fund
Oct. 16, 2018 12:10pm (MATH …	Kempner Geometry and Analysis Day TBA
Oct. 16, 2018 1pm (MATH 220)	Peter Mayr X We discuss the third step in Zhuk's algorithm where constraints are replaced by all their weaker constraints. CSP weaker relations
Oct. 16, 2018 2pm (MATH 350)	Lie Theory Mandi Schaeffer-Fry (MSU) X Galois automorphisms act naturally on the irreducible characters of a finite group. But, it is in general a difficult problem to describe this action, say, in terms of known parameters for the characters of a given group. We discuss this problem in the case of finite symplectic and special orthogonal groups. This is joint work with Jay Taylor. Galois Actions and Classical Groups
Oct. 16, 2018 3pm (MATH 350)	Geometry/Analysis James P. Kelliher (UC Riverside) X We say that the regularity of a function in $ℝ^{d}$ is \textit{striated} if it has higher regularity along certain hypersurfaces than it does in directions normal to those hypersurfaces. In the context of active transport equations, we say that striated regularity is propagated if such regularity is maintained as both the scalar and the hypersurfaces are transported by the flow map for the velocity field. (Being active scalars, the velocity field at time $t$ is a function of the scalar at time $t$ , making the underlying PDE nonlinear.) We first discuss briefly the transport of vorticity by the 2D Euler equations. Two simplifying properties of these equations are that the transport is by a divergence-free vector field, and the transport equations related to the hypersurfaces are pure transport. We outline how the propagation of striated regularity was first established for the 2D Euler equations in a landmark 1991 result of Jean-Yves Chemin. We place Chemin's approach and subsequent approaches by later authors in a larger framework that we then apply to a seemingly very similar active transport equation: the aggregation equation with Newtonian potential (the inviscid form of a limiting case of the Keller-Segel equation). Such equations lack, however, the two simplifying properties of the 2D Euler equations. We explain how we overcome these difficulties to obtain the propagation of the regularity of level sets of the active scalar, a restricted form of propagation of striated regularity. This extends a recent result of Bertozzi, Garnett, Laurent, and Verdera for patch boundary regularity for the aggregation equation. This is joint work with Hantaek Bae of Ulsan National Institute of Science and Technology (UNIST). Striated regularity for a class of active transport equations Sponsored by the Meyer Fund

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