Past Seminars- Colloquium

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  • Nicolaos Kapouleas
    Thu Oct 22, 2015
    4:00 pm
    Abstract: I will discuss various geometric gluing constructions. First I will discuss constructions for Constant Mean Curvature hypersurfaces in Euclidean spaces including my earlier work for two-surfaces in three-space which settled the Hopf conjecture for surfaces of genus two and higher, and recent generalizations in collaboration with...
  • Rodrigo Banuelos
    Thu Oct 15, 2015
    4:00 pm
    Abstract
  • Yanyan Li
    Thu Apr 16, 2015
    4:00 pm
    The mathematical problem of gradient estimates for solutions of divergence form elliptic systems with piece-wise smooth coefficients arises in studying composite materials in applied science. We will start with ideas in joint works with Vogelius (2000) and Nirenberg (2003) about a decade ago, in particular an open problem in the paper with...
  • Michael Bjorklund
    Thu Apr 9, 2015
    4:00 pm
    After briefly reviewing some basic aspects of quantum probability theory, especially questions surrounding a celebrated theorem of Gleason, we turn to analogues of quantum probabilities studied in symplectic geometry known as quasi-states, which are functions on Lie algebras which are linear on abelian sub-algebras. A prototypical (and well-...
  • R. Carmona
    Thu Apr 2, 2015
    4:00 pm
    After discussing a few examples of herding and flocking, we review the mean field game paradigm as introduced by Lasry and Lions. Using a probabilistic reformulation of the problem, we demonstrate how the solutions of these models can be identified with solutions of forward - backward stochastic differential equations (FBSDEs) of McKean-Vlasov...
  • Alan Newell
    Thu Mar 5, 2015
    4:00 pm
    Phyllotaxis, the arrangement of phylla (leaves, bracts, seeds) near the shoot apical meristems of plants has intrigued and mystified natural scientists for over two thousand years. It is surprising that only within the last two decades have quantitative explanations emerged that describe the wonderful architectures which are observed. I will give...
  • Xiaojun Huang
    Thu Feb 26, 2015
    4:00 pm
    We discuss the global property of a local holomorphic isometry into the product of projective spaces. We prove global extension and rigidity properties for such a map when the source is a Hermitian symmetric space  of compact type. Our work is along the lines of the previous work of Calabi, Clozel-Ullmo and Mok. This is a joint work with Yuan...