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.

Talk Title: Leveraging molecular symmetry to explore unique magnetochemical properties of iron-sulfur clusters

Struggling to stay on track with your writing? This four-session workshop series will help you navigate common challenges and develop strategies for a more productive writing process. We will explore how to manage your time and set realistic expectations, harness perfectionism to your advantage, build a strong working relationship with your dissertation advisor or PI, and use constructive procrastination as a tool for maintaining a healthy writing routine. Each session will be interactive and designed to equip you with practical skills to improve your writing habits.Pre-registration is required to participate and light refreshments will be served.