# Singularity Theory and Related Topics 2021

Workshop will be held on November 20-21, 2021, in east campus of USTC (University of Science and Technology of China). This workshop is supported by the institute of Geometry and Physics (IGP).

### 王振建(USTC)

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The mission of the Institute of Geometry and Physics (IGP) is to advance the understanding of geometry and its interface with theoretical physics, to nurture the next generation of original mathematicians and ultimately to build a top notch institution for the subject area. We thus endeavor to provide a quiet, comfortable and inspiring environment, where talentedresearchers in geometry and related fields from all over the world are invited to visit, be it short term or long, to work and to thrive; and where academic freedom, diligence and originality are promoted and valued. The center provides strong funding for our faculty research including support for doctoral students and postdoctoral researchers.

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## Schedule

Conference Schedule

 Time Speaker Title Abstract November 20 9:00-10:00 左怀青 Derivation algebras associated to isolated singularities Let R be a positively graded algebra which define an isolated singularity. A long-standing conjecture in algebraic geometry and singularity theory is the non-existence of negative weight derivations on certain R. Halperin and Alexsandrov conjectured that there are no negative weight derivations when R is a complete intersection graded Artinian algebra, and Wahl conjectured there are no negative weight derivations on R when R is isolated normal singularity admits a good $C^*$ action. This problem is also important in rational homotopy theory. In this talk, we will briefly review the background and present our recent progress on some problems of several derivations algebras associated to isolated singularities. 10:20-11:20 陈伟彦 Choosing points on cubic plane curves It is a classical topic to study structures of certain special points on smooth complex cubic plane curves, for example, the 9 flex points and the 27 sextactic points. We consider the following topological question asked by Farb: Is it true that the known algebraic structures give all the possible ways to continuously choose n distinct points on every smooth cubic plane curve, for each given integer n? This work is joint with Ishan Banerjee. 11:20-14:00 Lunch Break 14:00-15:00 魏传豪 Kodaira-type vanishings via Nonabelian Hodge Theory In the past decade, Mochizuki has completed the spectacular theory of mixed Twistor D-modules. In this talk, I will first briefly introduce this result. Then, I will show that Kodaira-type vanishing still holds under the setting of mixed Twistor D-modules, which generalizes Saito’s vanishing under the setting of mixed Hodge Modules. Furthermore, I will also talk about a version of Kawamata-Viehweg vanishing, under this general setting. 15:20-16:20 张希平 On Milnor Classes of Determinantal Hypersurfaces The local Milnor fibration of a complex hypersurfaces is one of the essential objects in singularity theory, and the topological invariants assigned to them (the local Milnor numbers and the L\'e numbers) are important invariants of study. In this talk we will discuss these invariants on determinantal hypersurfaces, from the angle of their characteristic classes: the Milnor class and the L\'e class. We provide a new definition to the L\'e class for polarized hypersurfaces, and show that this definition matches the involution formula between Milnor class and L\'e class given in [Callejas-Bedregal-Morgado-Seade 2014]. Then we give a new approach to the computation of these local invariants, mainly on building a connection between the local Euler obstructions and the Milnor numbers for these hypersurfaces. This is a joint work with Terrence Gaffney 18:00 Banquet November 21 9:00-10:00 陈智 “Free elements” in Artin groups Coxeter groups and Artin groups could be viewed as natural generalizations of the permutation group and the braid group respectively. There is a natural lifting map from Coxeter group to (positive part of) the corresponding Artin group, whose image are certain elements constitute the generating set of the so called “dual braid monoid” structure. As a generalization, we would introduce some kind of elements of the Artin groups which we called “Free elements”, and discuss application of these elements in some problems of the Artin group. 10:20-11:20 刘晔 Survery on the $K(\pi,1)$ conjecture(tte) for Artin groups We survey the $K(\pi,1)$ conjecture for Artin groups which asserts that an arbitrary Artin group admits a $K(\pi,1)$ space coming from the free action of the corresponding Coxeter group on the Tits cone minus the associated hyperplane arrangement. In particular, we will mention several equivalent formulations of the conjecture as well as some important proved cases. If time permits, we will explain why a result of Digne-Michel implies a much weaker form, the $K(\pi,1)$ conjecturette, which asserts that the second homotopy group of the conjectured space vanishes.

Accommodation: All invited speakers will be arranged to live at Guest House (USTC).

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University of Science and Technology of China

96 Jinzhai Road, Hefei, 230026, Anhui, P.R. China

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