Events
Department of Mathematics and Statistics
Texas Tech University
In 1983, Costa discovered a complete embedded minimal surface in three-dimensional Euclidean space with genus one and three embedded ends. Building on this result, Hoffman and Meeks later constructed complete embedded minimal surfaces with three embedded ends and arbitrary genus. These surfaces can be viewed as desingularizations of the union of a catenoid and a plane along their intersection circle. In this talk, we aim to explore analogous constructions in four-dimensional Euclidean space. Specifically, we discuss the desingularization of the union of a Lagrangian catenoid and a two-dimensional plane, highlighting both the similarities to and the differences from the Costa–Hoffman–Meeks surfaces in three-dimensional space.
This Differential Geometry, PDE and Mathematical Physics seminar is available over zoom.
Differential categories use category theory to provide the foundations of differential calculus. In this talk, I will give you guided tour of the world of differential categories. We will see (1) differential categories, which give the algebraic foundations of differentiation; Cartesian differential categories, which give the foundations of multivariable differential calculus; and (3) tangent categories, which give the foundations of differential geometry. In particular we will look at the map of differential categories and see how these three concepts relate to each other. Moreover, the theory of differential categories has been successful in formalising various important concepts related to differentiation. In particular, this talk will set the table for next week’s talk, where Chiara Sava will explain how differential categories capture differential graded algebras.  | Wednesday
Sep. 24
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| Algebra and Number Theory
No Seminar
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Abstract. Convergent of a finite element discretization of Chorin's projection method for the incompressible Navier-Stokes equations to Leray-Hopf solutions
Abstract: We consider Chorin's projection method combined with a finite element spatial discretization for the time-dependent incompressible Navier-Stokes equations. The projection method advances the solution in two steps: A prediction step which computes an intermediate velocity field that is generally not divergence-free, and a projection step which enforces (approximate) incompressibility by projecting this velocity onto the (approximately) divergence-free subspace. We establish convergence, up to a subsequence, of the numerical approximations generated by the projection method with finite element spatial discretization to a Leray-Hopf solution of the incompressible Navier-Stokes equations, without any additional regularity assumptions beyond square-integrable initial data and square-integrable forcing. A discrete energy inequality yields a priori estimates, which we combine with a new compactness result to prove precompactness of the approximations in $L^2([0,T]\times\Omega)$, where $[0,T]$ is the time interval and $\Omega$ is the spatial domain. Passing to the limit as the discretization parameters vanish, we obtain a weak solution of the Navier–Stokes equations. A central difficulty is that different a priori bounds are available for the intermediate and projected velocity fields; our compactness argument carefully integrates these estimates to complete the convergence proof.
When: 4:00 pm (Lubbock's local time is GMT -5)
Where: room Math 011 (Math Basement)
ZOOM details:
- Choice #1: use this link
Direct Link that embeds meeting and ID and passcode.
- Choice #2: join meeting using this link
Join Meeting, then you will have to input the ID and Passcode by hand:
* Meeting ID: 915 2866 2672
* Passcode: applied
abstract noon CDT (UT-5)
Zoom link available from Dr. Brent Lindquist upon request.