2018.4.13-4.19 学术活动预告
2018/4/12 11:00:06 中国科学院数学与系统科学研究院

     Speaker:

     Prof. Zhengyu Hu, National Taiwan University

     Title:

     Complements on log canonical Fano varieties

     Time & Venue:

     2018.4.13 9:00-11:00 N913

     Abstract:

     Let {(X, B)} be a set of log canonical Fano pairs of dimension ≤ 3 such that the coefficients of the boundary divisors B belong to a hyperstandard set. Then we prove the boundedness of their Q-complements. I will also discuss the theory of complements in the LC category for an arbitrary dimension.

     Speaker:

     江 辰 博士, IPMA，东京大学

     Title:

     Noether inequality for algebraic threefolds

     Time & Venue:

     2018.4.17 9:00-10:00 N913

     Abstract:

     For varieties of general type, it is natural to study the distribution of birational invariants and relations between invariants. We are interested in the relation between two fundamental birational invariants: the geometric genus and the canonical volume. For a minimal projective surface S, M. Noether proved that $K_S^2\geq 2p_g(S)-4,$ which is known as the Noether inequality. It is thus natural and important to study the higher dimensional analogue. In this talk, we will talk about our recent work on the Noether inequality for projective 3-folds. We will show that the inequality $\text{vol}(X)\geq \frac{4}{3}p_g(X)-{\frac{10}{3}}$ holds for all projective 3-folds X of general type with either $p_g(X)\leq 4$ or $p_g(X)\geq 27$, where $p_g(X)$ is the geometric genus and $\text{vol}(X)$ is the canonical volume. This inequality is optimal due to known examples found by M. Kobayashi in 1992. This proves that the optimal Noether inequality holds for all but finitely many families of projective 3-folds (up to deformation and birational equivalence). I will briefly recall the history on this problem and give some idea of the proof. This is a joint work with Jungkai A. Chen and Meng Chen.

     Speaker:

     任盼盼 博士, swansea university

     Title:

     Least Squares Estimator for path-distribution dependent SDEs via Discrete-time Observations

     Time & Venue:

     2018.4.16 16:00-17:00 N613

     Abstract:

     In this talk, we study a least squares estimator for an unknown parameter in the drift coefficient of a path-distribution dependent stochastic differential equation involving a small dispersion parameter. Our estimator is based on discrete time observations of the path-distribution dependent SDEs involved. More precisely, if the coefficients satisfy global Lipschitz condition, the estimator is based on classical Euler-Maruyama scheme, whereas, in the case that the coefficients follow the weak monotone condition, the estimator is established on tamed Euler-Maruyama algorithm. We show that the least squares estimator obtained is consistent with the true value, we also obtain the rate of convergence and derive the asymptotic distribution of least squares estimator.

     来源：中国科学院数学与系统科学研究院

     中国科学院数学与系统科学研究院

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