Speaker: Junyi Xie (CNRS Rennes)
Time: 15:00–16:00 3/05/2021
Title: Some boundedness problems in Cremona group
Abstract: This talk is based on a work with Cantat and Deserti. According to the degree sequence, there are 4 types (elliptic, Jonquieres, Halphen and Loxodromic) of elements f in Bir(P^2). For a fixed degree d>=1, we study the set of these 4 types of elements of degree d. We show that for Halphen twists and Loxodromic transformations, such sets are constructible. This statement is not true for elliptic and Jonquieres elements.We also show that for a Jonquieres or Halphen twist f of degree d, the degree of the unique f-invariant pencil is bounded by a constant depending on d. This result may be considered as a positive answer to the Poincare problem of bounding the degree of first integrals,but for birational twists instead of algebraic foliations. As a consequence of this, we show that for two Halphen twists f and g, if they are conjugate in Bir(f), then they are conjugate by some element of degree bounded by a constant depending on deg(f)+deg(g). This statement is not true for Jonquieres twists.
Speaker: Guolei Zhong(National University of Singapore)
Time: 16:15–17:15 3/05/2021
Title: Fano threefolds and fourfolds admitting non-isomorphic endomorphisms.
Abstract: In this talk, we first show that a smooth Fano threefold X admits a non-isomorphic surjective endomorphism if and only if X is either toric or a product of a smooth rational curve and a del Pezzo surface. Second, we show that a smooth Fano fourfold Y with a conic bundle structure is toric if and only if Y admits an amplified endomorphism. The first part is a joint work with Sheng Meng and De-Qi Zhang, and the second part is a joint work with Jia jia.
Speaker: Zhiyuan Li ( Shanghai Center for Mathematical Sciences)
Time: 9:00–10:00 3/19/2021
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Speaker: Michael Kemeny (University of Wisconsin-Madison)
Time: 10:15–11:15 3/19/2021
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Speaker: Weizhe Zheng (Morningside Center of Mathematics)
Time: 15:00–16:00 4/02/2021
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Speaker: Kestutis Cesnavicius (U. Paris Sud)
Time: 16:15–17:15 4/02/2021
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Speaker: Kuan-Wen Lai (University of Massachusetts Amherst)
Time: 9:00–10:00 4/16/2021
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Speaker: Yu-Shen Lin (Boston University)
Time: 10:15–11:15 4/16/2021
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Speaker: Yi Gu (Suzhou University)
Time: 15:00–16:00 4/30/2021
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Speaker: Takehiko Yasuda (Osaka University)
Time: 16:15–17:15 4/30/2021
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Speaker: Yuji Odaka (Kyoto University)
Time: 15:00–16:00 5/14/2021
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Speaker: YongJoo Shin (Chungnam National University)
Time: 16:15–17:15 5/14/2021
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Speaker: Zhiyu Tian (BICMR-Beijing University)
Time: 15:00–16:00 5/28/2021
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Speaker: Joao Pedro dos Santos (Universite de Paris)
Time: 16:15–17:15 5/28/2021
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