Date: | July 24, 2017 |

Time: | 3:00PM - 4:00PM |

Location: | BLOC 628 |

Speaker: | Bongsuk Kwon, Ulsan National Institute of Science and Technology |

Title: | Quasi-neutral limit for the Euler-Poisson system |

Abstract: | We first briefly talk about the formation of a plasma sheath near the surface of a ball-shaped material immersed in a bulk plasma. To mathematically investigate this, we study existence, stability and the quasi-neutral limit of the boundary layer solutions for the Euler-Poisson equations in a three-dimensional annular domain. Under a suitable condition on the velocity at the sheath edge, referred as to Bohm criterion for the annulus, we show that there exists a unique stationary spherical symmetric solution. Then, we show the quasi-neutral limit behavior by establishing $H^1$ estimate of the difference of the solutions to the Euler-Poisson equations and its quasi-neutral limiting equations. If time permits, the stability and asymptotic behavior will be also discussed. |

Date: | July 26, 2017 |

Time: | 2:00PM - 2:50PM |

Location: | BLOC 220 |

Speaker: | Cleon Da Silva Barroso, Universidade Federal do CearĂˇ |

Title: | Existence of shift basic sequences and its implications |

Abstract: | It is shown that every seminormalized sequence with no weakly convergent subsequences admits a wide-(s) subsequence which is shift equivalent. Also, basic sequences with shiftable properties are studied. They give rise to a generalized form of the Pelczynski's property (u), called property (su). It is shown that every Banach space with a conditional spreading basis has property (su). As a consequence the classical Jamesâ€™ space J2 has property (su), which nicely contrast with the fact that it does not have Pelczynski's property (u). |

Date: | July 27, 2017 |

Time: | 2:00PM - 2:50PM |

Location: | BLOC 220 |

Speaker: | Richard Lechner, Johannes Kepler University Linz |

Title: | Factorization of the identity operator in classical Banach spaces: recent results |

Abstract: | We discuss several recent results on factors of the identity operator in mixed norm Hardy spaces, bi-parameter BMO and $SL^\infty$. As a consequence of these factorization results, we obtain that those spaces are primary. The methods used are either infinite dimensional, or finite dimensional quantitative methods, centered around the geometry and the combinatorics of colored dyadic intervals and rectangles. |

Date: | July 28, 2017 |

Time: | 2:00PM - 2:50PM |

Location: | BLOC 220 |

Speaker: | Kevin Ford, The University of Illinois at Urbana-Champaign |

Title: | Probabilistic methods in the study of prime gaps |

Abstract: | We describe how probabilistic tools and reasoning are used to study problems about gaps between prime numbers in various sequences, for example the sequence of all primes, and the sequence of prime values of a polynomial. This is joint work with Ben Green, Sergei Konyagin, James Maynard, Carl Pomerance and Terence Tao. |