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Geometrically continuous splines are piecewise polynomials defined on a collection of patches stitched together through transition maps. In this talk, we introduce an algebraic framework to study geom...
The topic for 2017 Tianyuan Spring School is: higher dimensional algebraic varieties and moduli theory, including biraitonal geometry, stability theory and the geometry of Fano varieties. The topics o...
Algebraic Geometry is a subject moving forward rapidly in the recent years. This conferences aims to encourage the communication among the algebraic geometers from the two institutes and others. Besid...
Algebraic Geometry is a subject moving forward rapidly in the recent years. This conferences aims to encourage the communication among the algebraic geometers from the two institutes and others. Besid...
The topic for 2017 Tianyuan Spring School is: higher dimensional algebraic varieties and moduli theory, including biraitonal geometry, stability theory and the geometry of Fano varieties. The topics o...
For smooth families of projective algebraic curves, we extend the notion of intersection pairing of metrized line bundles to a pairing on line bundles with flat relative connections. In this setting, ...
In topology, the notions of the fundamental group and the universal cover are closely intertwined. By importing usual notions from topology into the algebraic and arithmetic setting, we construct a ...
We consider the question: “How bad can the deformation space of an object be?” The answer seems to be: “Unless there is some a priori reason otherwise, the deformation space may be as bad as possible...
In this paper, we show that the presentation of affine $\mathbb{T}$-varieties of complexity one in terms of polyhedral divisors holds over an arbitrary field. We describe also a class of multigraded a...
These three lectures present some fundamental and classical aspects of microlocal analysis. Starting with the Sato's microlocalization functor and the microsupport of sheaves, we then construct a micr...
Abstract: We construct explicit G4 fluxes in F-theory compactifications. Our method relies on identifying algebraic cycles in the Weierstrass equation of elliptic Calabi-Yau fourfolds. We show how to ...
Abstract: We relate R-equivalence on tori with Voevodsky's theory of homotopy invariant Nisnevich sheaves with transfers and effective motivic complexes.
Abstract: We study the geometry underlying the difference between non-negative polynomials and sums of squares. The hypersurfaces that discriminate these two cones for ternary sextics and quaternary q...
Abstract: Given a non-rational real space curve and a tolerance $\epsilon>0$, we present an algorithm to approximately parametrize the curve. The algorithm checks whether a planar projection of the sp...
In this paper, we produce topologized versions of two theorems. One is due to Borel and Tits [2] and is concerned with abstract homomorphisms of absolutely almost simple algebraic groups.

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