|Shuai Guo||School of Mathematical Sciences, Peking University, China|
Bio: Shuai Guo got Ph. D in Tsinghua University, 2011 and now is an associate professor in SMS of Peking University.
Research interests: Higher genus enumerative geometry and mirror symmetry.
Honors: 2019 "QiuShi" Outstanding Youth Award (2019), Selected as the national youth talent support program of China (2019).
Polynomial structures in higher genus enumerative geometry
It is important to calculate the enumerative invariants from various moduli theories in mirror symmetry. The polynomial structure is often appeared in those quantum theories, including the Calabi-Yau type and the Fano type theories. Such conjectural structure is also called the finite generation conjecture in the literature. For each genus, it is conjectured that the computation of infinite many enumerative invariants can be converted to a finite computation problem. The original motivation of studying such structures will also be mentioned. This talk is based on the joint work with Janda-Ruan, Chang-Li-Li, Bousseau-Fan-Wu and Zhang respectively.
|Alexander Efimov||professor, Steklov Mathematical Institute of Russian Academy of Sciences, Russia|
Research interests: algebraic geometry, mirror symmetry, non-commutative geometry.
Honors: European Mathematical Society Prize (2020), Russian Academy of Sciences Medal with the Prize for Young Scientists (2017), Moscow Mathematical Society award (2016).
Smooth compactifications of differential graded categories
We will give an overview of results on smooth categorical compactifications, the questions of theire existence and their construction. The notion of a smooth categorical compactification is closely related with the notion of homotopy finiteness of DG categories.
First, we will explain the result on the existence of smooth compactifications of derived categories of coherent sheaves on separated schemes of finite type over a field of characteristic zero. Namely, such a derived category can be represented as a quotient of the derived category of a smooth projective variety, by a triangulated subcategory generated by a single object. Then we will give an example of a homotopically finite DG category which does not have a smooth compactification: a counterexample to one of the Kontsevich's conjectures on the generalized Hodge to de Rham degeneration.
Finally, we will formulate a K-theoretic criterion for existence of a smooth categorical compactification, using DG categorical analogue of Wall's finiteness obstruction from topology.
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