The Spatial Distribution of Income in Cities: Cross-Country Evidence and Theory | David Lagakos

Ten minutes for your mind@2:50 every day at 2:50 pm in multiple time zones:Europa@2:50, EET, Athens, Helsinki (UTC+2) (7:50 am EST) https://us02web.zoom.us/j/88298032734Atlantica@2:50, EST, New York, Toronto (UTC-4) https://us02web.zoom.us/j/85349851047Pacifica@2:50, PST, Los Angeles, Vancouver (UTC=7) (5:50 pm EST) https://us02web.zoom.us/j/85743543699Almost everything works better again if you unplug it for a bit, including your mind. Stop by and unplug. Get the benefits of mindfulness without the fuss.@2:50 meets at the same time every single day for ten minutes of quiet together.No pre-requisite, no registration needed.Visit the website to view all @2:50 time zones each day.at250.org or at250.mit.edu

MIT Program in Polymers and Soft Matter (PPSM) Seminar

Come relax with us and enjoy some fun conversation! No need to RSVP: just show up with your friends!

Speaker: Zhenhua Liu (Princeton)Title: General behavior of area-minimizing subvarietiesAbstract:We will review some recent progress on the general geometric behavior of homologically area-minimizing subvarieties, namely, objects that minimize area with respect to homologous competitors. They are prevalent in geometry, for instance, as holomorphic subvarieties of a Kahler manifold, or as special Lagrangians on a Calabi-Yau, etc. A fine understanding of the geometric structure of homological area-minimizers can give far-reaching consequences for related problems.Camillo De Lellis and his collaborators have proven that area-minimizing integral currents have codimension two rectifiable singular sets. A pressing next question is what one can say about the geometric behavior of area-minimizing currents beyond this. Almost all known examples and results point towards that area-minimizing subvarieties are subanalytic, generically smooth, and calibrated. It is natural to ask if these hold in general. In this direction, we prove that all of these properties thought to be true generally and proven to be true in special cases are totally false in general. We prove that area-minimizing subvarieties can have fractal singular sets. Smoothable singularities are non-generic. Calibrated area minimizers are non-generic. Consequently, we answer several conjectures of Frederick J. Almgren Jr., Frank Morgan, and Brian White from the 1980s.

Speaker: Cris Negron (University of Southern California)Title: 3-dimensional field theories for derived categories of quantum group representationsAbstract: I will discuss existence, and constructions, of 3-dimensional field theories for derived categories of quantum group representations. The distinguishing point here is that the state spaces in these theories will be infinite dimensional, and the theory will only be defined on 3-manifolds with nonvanishing outgoing boundary. I will emphasize motivations from mathematical physics and implications for representation theory. (Physics predicts, for example, the existence of deformations of quantum group representations along the relevant Langlands dual group, which then enables deformations of the corresponding theory by local systems.) This is joint work with Agustina Czenky.