Title: TBA
Speaker: Casey Kelleher [Princeton University]
Abstract:
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Dzmitry Dudko, Stony Brook University
mini-course: A priori bounds for neutral quadratic polynomials
Title: TBA
Title: mini-course: A priori bounds for neutral quadratic polynomials
Speaker: Dzmitry Dudko [Stony Brook University]
Abstract: Douady-Ghys's surgery implies that a neutral quadratic polynomial with a bounded type rotation number has a Siegel quasidisk containing the critical point on its boundary. In this minicourse, we will show that such a Siegel quasidisk degenerates in a controllable way as the rotation number becomes unbounded. This unifies (in a certain sense) the Inou-Shishikura near-parabolic and the Pacman near-Siegel renormalization theories for neutral quadratic polynomials (parametrized by the main cardioid).
Joint work with Misha Lyubich.
The first lecture will give a general introduction to the near-neutral renormalization theories. We will also outline the main steps of proving the new a priori bounds and discuss some consequences previously known only in the Innou-Shishikura class.
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Title: Holomorphic 1-forms on the moduli space of curves
Speaker: Gian Pietro Pirola [$\text{Universit\`a}$ degli studi di Pavia ]
Abstract: It is well known that there are no nontrivial closed 1-forms on the moduli space of curves of genus g>2. We show that if g>4 there are no nontrivial holomorphic one forms. We use both Satake and Deligne-Mumford compactifications of the moduli space and an extension result for the sections of a vector bundle F. More precisely we give a characterization for the surjectivety of the restriction map H^0(F)->H^0(F_D), here D is a divisor in a linear system |nH|, where n>>0 and H is a big and semiample line bundle. These results were obtained in collaboration with Filippo Favale and Sara Torelli.
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Title: Random matrix statistics---A new class of statistical laws for highly correlated systems.
Speaker: Horng-Tzer Yau [Harvard University]
Abstract: In this lecture, we will review recent works concerning spectral statistics of random matrices and related conjectures. We’ll explain the underlying mechanism for the universality of random matrix statistics. The dynamics of eigenvalues and eigenvectors for random matrices will also be discussed.
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Last day for Fall/Winter degree candidates to apply for graduation via SOLAR. Applications submitted after11/11/20 will not appear in the Commencement Publication.
Title: TBA
Speaker: Jack Burkart [Stony Brook University]
Abstract: TBA
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Dzmitry Dudko, Stony Brook University
mini-course: A priori bounds for neutral quadratic polynomials
Title: TBA
Title: mini-course: A priori bounds for neutral quadratic polynomials
Speaker: Dzmitry Dudko [Stony Brook University]
Abstract: Douady-Ghys's surgery implies that a neutral quadratic polynomial with a bounded type rotation number has a Siegel quasidisk containing the critical point on its boundary. In this minicourse, we will show that such a Siegel quasidisk degenerates in a controllable way as the rotation number becomes unbounded. This unifies (in a certain sense) the Inou-Shishikura near-parabolic and the Pacman near-Siegel renormalization theories for neutral quadratic polynomials (parametrized by the main cardioid).
Joint work with Misha Lyubich.
In the second lecture, we will overview principles of the near-degenerate regime and show how the Covering Lemma can be applied to Siegel maps. We will then discuss a mechanism of how a priori bounds' failure on a given scale can lead to even bigger failure on a deeper scale.
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Last day to take a leave of absence or withdraw from the University. Students can process via SOLAR.
Last day students can select Grade/Pass/No Credit (GPNC). Changes must be processed by 4:00 PM. Non-petitionable
Title: TBA
Speaker: Christine Breiner [Fordham University]
Abstract:
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