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Title: The polynomial method over varieties
Author: Rovira Cisterna, Sergi
Director/Tutor: Sombra, Martín
Keywords: Varietats algebraiques
Geometria algebraica
Treballs de fi de màster
Algebraic varieties
Algebraic geometry
Master's theses
Issue Date: 11-Sep-2019
Abstract: [en] In 2010, Guth and Katz introduced the polynomial partitioning theorem as a tool in incidence geometry and in additive combinatorics. This allowed the application of results from algebraic geometry (mainly on intersection theory and on the topology of real algebraic varieties) to the solution of long standing problems, including the celebrated Erdős distinct distances problem. Recently, Walsh has extended the polynomial partitioning method to an arbitrary subvariety. This result opens the way to the application of this method to control the point-hypersurface incidences and, more generally, of variety-variety incidences, in spaces of arbitrary dimension. This final project consists in studying Walsh’s paper, to explain its contents and explore its applications to t his kind of incidence problems.
Note: Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2019, Director: Martín Sombra
Appears in Collections:Màster Oficial - Matemàtica Avançada

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