DIFFERENTIAL GEOMETRY SEMINAR: | Jonathan WeitsmanNortheastern University |
Quantization of b-symplectic manifolds |

on Tuesday, February 09, 2016, at 4:15 PM in Science Center 507 | ||

b-symplectic (or log-symplectic) manifolds are Poisson manifolds with the property that the Poisson bivector field arises from a symplectic structure on the complement of a real hypersurface, and has a prescribed vanishing on that hypersurface. This is a "least degenerate" case of Poisson geometry which we can try to use as a laboratory to apply techniques developed in symplectic geometry to obtain intuition about quantization in the Poisson setting. Recent work with V. Guillemin and E. Miranda on desingularization of b-symplectic forms leads to a proposed scheme for quantization of these manifolds in the case where the b-symplectic form has certain integrality properties and where an abelian group acts in a Hamiltonian fashion and satisfies a technical nondegeneracy condition. We show that in this case we obtain a finite quantization, which we conjecture should arise from the index of a Fredholm operator acting on sections of an appropriate line bundle. This is joint work with V. Guillemin and E. Miranda. |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR: | Valentino TosattiNorthwestern University |
Non-Kahler Calabi-Yau manifolds |

on Tuesday, February 09, 2016, at 9:50 - 10:50 am in CMSA Building, 20 Garden Street, Room G02 | ||

Calabi-Yau manifolds are often defined as compact Kahler manifolds with vanishing real first Chern class. Yau's theorem shows that these are precisely the compact complex manifolds which admit a Ricci-flat Kahler metric. What happens if we do not demand that the manifold be Kahler? It turns out that to obtain a meaningful theory one needs to require that the first Chern class vanishes in a stronger sense. I will present various results on the geometry of these manifolds, including a result (joint with Szekelyhidi and Weinkove) that shows that these are precisely the compact complex manifolds which admit a Gauduchon Hermitian metric with vanishing Chern-Ricci curvature. |

NUMBER THEORY SEMINAR: | Paul Frank BaumPennsylvania State University |
Geometric Structure in Smooth Dual |

on Wednesday, February 10, 2016, at 3:00 PM in Science Center 507 | ||

Let G be a connected split reductive p-adic group. Examples are GL(n, F) , SL(n, F) , SO(n, F), and Sp(n, F) where n can be any positive integer and F can be any finite extension of the field Qp of p-adic numbers. The smooth (or admissible) dual of G is the set of equivalence classes of smooth irreducible representations of G. The smooth dual of G is the disjoint union of subsets known as the Bernstein components. The talk will explain the ABPS (Aubert-Baum-Plymen-Solleveld) conjecture which states that each Bernstein component is a complex affine variety. Each of these complex affine varieties is explicitly identified as the extended quotient associated to the given Bernstein component. The ABPS conjecture has been proved for GL(n, F ), SL(n, F ), SO(n, F ), and Sp(n, F ). The talk will conclude with an exposition of the connection between ABPS and the local Langlands conjecture. The above is joint work with Anne-Marie Aubert, Roger Plymen, and Maarten Solleveld. |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM: | Chunpeng WangJilin University |
Continuous Subsonic-Sonic Flows in a Convergent Nozzle |

on Wednesday, February 10, 2016, at 4:00 PM in CMSA Building, 20 Garden Street, Room G10 | ||

This talk concerns continuous subsonic-sonic flows in a convergent nozzle with straight solid walls. It is shown that for the given inlet being a perturbation of an arc centered at the vertex of the nozzle and the given incoming mass flux belonging to an open interval depending only on the adiabatic exponent and the length of the arc, there is a unique continuous subsonic-sonic flow from the given inlet with the angle of the velocity orthogonal to the inlet line and the given incoming mass flux. Furthermore, the sonic curve of this continuous subsonic-sonic flow is a free boundary, where the flow is singular in the sense that while the speed is Holder continuous at the sonic state, yet the acceleration blows up at the sonic state. |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR: | Lydia BieriUniversity of Michigan |
Einstein's Equations, Energy and Gravitational Radiation |

on Thursday, February 11, 2016, at 9:50 - 10:50 am in CMSA Building, 20 Garden Street, Room G02 | ||

The Einstein equations of General Relativity (GR) govern the laws of the universe. They can be written as a set of constraints on the initial data and a set of evolution equations. A major goal in the study of these equations is to investigate the analytic properties and geometries of the solution spacetimes.In particular, fluctuations of the curvature of the space time, known as gravitational waves, have been a highly active research topic, as we are believed to be on the verge of their detection. Understanding gravitational radiation is tightly interwoven with the study of the Cauchy problem in GR. I will address recent work with David Garfinkle on gravitational radiation in asymptotically flat as well as cosmological spacetimes. |

HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR: | Dhruv RanganathanYale University |
TBA |

on Tuesday, February 16, 2016, at 3:00 PM in Science Center 507 | ||

TBA |

DIFFERENTIAL GEOMETRY SEMINAR: | Lydia BieriUniversity of Michigan |
The Shape of the Universe |

on Tuesday, February 16, 2016, at 4:15 PM in Science Center 507 | ||

In General Relativity, a major branch of research is devoted to the study of the geometric properties of solutions to the Einstein equations. Gravitational waves, which are predicted by the theory of General Relativity and expected to be detected in the near future, are fluctuations of the spacetime curvature. These waves leave a footprint in the spacetime regions they travelled through. We investigate the geometric-analytic properties of various spacetimes with gravitational radiation. |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR: | Camillo DeLellisInstitut für Mathematik Universität Zürich |
Approaching Plateau's problem with minimizing sequences of sets |

on Tuesday, February 16, 2016, at 9:50 - 10:50 am in CMSA Building, 20 Garden Street, Room G02 | ||

In a joint paper with Francesco Ghiraldin and Francesco Maggi we provide a compactness principle which is applicable to different formulations of Plateau's problem in codimension one and which is exclusively based on the theory of Radon measures and elementary comparison arguments. Exploiting some additional techniques in geometric measure theory, we can use this principle to give a different proof of a theorem by Harrison and Pugh and to answer a question raised by Guy David. |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR: | Florent BekermanMIT |
Transport Methods and Universality for beta-matrix models |

on Wednesday, February 17, 2016, at 2:30 PM in CMSA Building, 20 Garden Street, Room G02 | ||

We use transport methods to show universality of local statistics for non-critical beta-matrix models. We construct an approximate transport map between the densities of the eigenvalues under two different potentials , obtained as the flow of an approximate solution of a linearized Monge-Ampère equation. The transport map enjoys accurate estimates in the dimension and can be used to show some universality results in the bulk and at the edge. This is based on a work with A. Figalli and A. Guionnet. |

HARVARD LOGIC SEMINAR: | John BaldwinUniversity of Illinois at Chicago |
The divorce of set theory and first order model theory |

on Wednesday, February 24, 2016, at 4:00 - 6:00 PM in 2 Arrow Street, Room #420 | ||

Around 1970 there seemed to be inevitable ties between axiomatic set theory and even first order model theory. The advent of stability theory erased this impression, by showing that while cardinality is deeply entangled with first order model theory, the niceties of cardinal arithmetic are not. We describe the types of entanglement as oracular (consistency inspires a ZFC proof), transitory (the hypothesis is eliminable), and full (there is an equivalence with an independent set theoretic proposition). In the last case, set theoretic pluralism entails model theoretic pluralism. |