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February 5, 2019

  

Tuesday, February 05, 2019

SOURCE;s Tri-School Household Cleaning Supply Donation Drive: Mon, Feb 4 - Fri, Feb 15 (Multi-Day Event)
All Day

East Baltimore

Some families go without the basic essentials. Items such as cleaning supplies can make a difference. Donate to SOURCE's Tri-School Household Cleaning Supply Donation Drive! SOURCE is accepting new and unopened cleaning supplies for Baltimore families in need. Items will be donated and distributed to families through our community-based partner organizations. Collection boxes will be located in JHSPH Student Lounge and Student Affairs (E1002), SON Lobby and SOM Armstrong Building Lobby. Items can also be dropped off at SOURCE – 615 N. Wolfe St., W1600. Questions? Email SOURCE, SOURCE@jhu.edu.
Strictly localisable measure spaces.
3:30 PM - 4:30 PM

Speaker. Thierry De Pauw (East China Normal University, Shanghai)

Abstract. This lecture will explore a general setting in which the Radon-Nikodym theorem holds after classical work of I. Segal, and its potential link to the calculus of variations. It turns out, for instance, that 1 dimensional Hausdorff measure in the plane be strictly localisable is undecidable in ZFC. We will mention applications to the dual of the space BV and beyond.

The lecture will be held in Krieger 300.
Category Theory Seminar
4:00 PM - 5:30 PM

Title: Higher categories from higher-dimensional manifolds
Christoph Dorn, Oxford University
Abstract:
     While higher groupoids have a natural model in spaces, higher categories have no such well-accepted model. This makes the question of correctness of a given definition of higher categories difficult to answer. We argue that the question has a simple answer “locally”, namely, categories are locally modelled on so-called manifold diagrams. The corresponding “local model" for spaces/groupoids can be formulated in classical terms by a generalised Thom-Pontryagin construction. The idea of locally modelling higher categories by manifold diagrams (most prominently in the case of Gray-categories) is not new and has been proposed by multiple authors. However, the niceness of this manifold-based perspective on higher categories has been somewhat obfuscated by the complexity of manifold geometry in higher dimensions in the past. We will discuss a fully algebraic formulation of this manifold perspective. Interestingly, the model of higher categories that is based on this algebraic formulation is not fully weak: It is a generalisation of (unbiased) Gray-categories to higher dimensions. This is the starting point of a wealth of further research, which reaches from a (version of) Simpson’s conjecture to presentations of the extended cobordism n-category and the homotopy and cobordism hypotheses.

This will be held in Gilman 377. More information for upcoming lectures can be found here.
Math Department Colloquium
5:00 PM - 6:00 PM

Boundary regularity for area minimizing surfaces and a question of Almgren
Camillo de Lellis (IAS)

Consider an area minimizing oriented surface which has a smooth boundary $\Gamma$ of multiplicity $1$ in some smooth Riemannian ambient manifold $\Sigma$. The celebrated work of Federer and Fleming guarantees the existence of one such minimizer in a suitable class of generalized oriented surfaces, called integral currents.

In codimension $1$ a famous work of Hardt and Simon gives full regularity of this object at the boundary, which is thus a classical oriented hypersurface (with boundary) in a neighborhood of $\Gamma$. In higher codimension the work of Allard can be used to conclude regularity under some geometric assumptions, but for general smooth $\Gamma$ even the existence of a single boundary regular point was open. In a recent joint work with Guido De Philippis, Jonas Hirsch and Annalisa Massaccesi we show that boundary regular points are always dense in $\Gamma$. This has some interesting consequences on the structure of the minimizer and in particular it allows us to answer positively to a question raised by Almgren at the end of his `` Big regularity paper''.

Room: tba

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