Schedule 2022
Previous talks - March to July 2022
Friday 01/07/2022
3:30pm UTC-3
Friday 24/06/2022
3:30pm UTC-3
A different way to generalize the Weierstrass semigroup
Brady Ali (University of Waterloo)
Abstract: In this talk we propose a different way to generalize the Weierstrass semigroup in a curve of genus g to a vector bundle F and we prove that when the vector bundle is semistable the largest gap is less than 2g − μ(F), where μ(F) denotes the slope of F. Also, when F is a line bundle we find the cardinality of the set of gaps, which is a theorem analogous to the Weierstrass Gap Theorem.
Friday 17/06/2022
3:30pm UTC-3
No seminar
Friday 10/06/2022
3:30pm UTC-3
Geometric Group Theory and Algebraic Geometry
Luize D'Urso (IMPA)
Abstract: We will analyze the GGT theorem behind the theorem about the non-simplicity of the Cremona group over any field. We will try to understand how is possible to use GGT to help answer questions of algebraic geometry and convince the audience to participate with us of the lecture course "Reflexões em Geometria Algébrica".
Friday 03/06/2022
3:30pm UTC-3
Castelnuovo's rationality criterion
Daniela Paiva (IMPA)
Abstract: The problem of classification of varieties up to birational equivalence is a well known problem in algebraic geometry. In this talk we will prove Castelnuovo's rationality criterion theorem: if X is a complex smooth projective surface over the with P_2(X)=0 and q(X)=0, then X is a rational surface.
Friday 27/05/2022
3:30pm UTC-3
Moduli Space and Geometric Invariant Theory
Ana Quedo (IMPA)
Abstract: In this talk, we will speak about quotients of the Geometric Invariant Theory (GIT). In the first part, we will introduce the basic concepts related to the moduli space to understand examples that motivate the construction of the GIT quotients, and after we will see that the Kempf Theorem ensures a relation of the GIT quotients with the quotients that comes from symplectic geometry, that is obtained via symplectic reduction.
Friday 20/05/2022
3:30pm UTC-3
Automorphism group of Artin-Schreier
Abraham Rojas Vega (ICMC - USP)
Abstract: It is well known the equivalence between the category of (finitely generated) Algebraic Function Fields and the category of algebraic varieties over a given algebraically closed field. So, the theory of Algebraic Function Fields is an important tool in Algebraic Geometry, specially in the case of curves.
In this talk, we follow a paper of Valentini and Madan, who use the Theory of Algebraic Function Fields (specially ramified coverings) to determine the automorphism group of Artin-Schreier curves. Other important results are shown in the process, such as the automorphism group of PGL(2,K), where K is an algebraically closed field of positive characteristic.
Slides & Video
Friday 13/05/2022
3:30pm UTC-3
Complete intersections and Weierstrass points
Sarah Faria
Abstract: There are many advances related to the rationality of the moduli space M_{g,1}^{S} parametrizing pointed smooth projective curves of genus g>=0 and Weierstrass semigroup S at the marked point. The semigroups studied in the results have genus g<=6 or they are symmetric semigroups generated by at most four elements. Will be shown two results about the geometry of M_{g,1}^{S} that can be described as follows: given a numerical semigroup S of genus g>=1, if the monomial affine curve Spec(k[S]) is a complete intersection, then M_{g,1}^{S} admits a compactification that is isomorphic to the projetivization of the negatively graded part of the first cohomology moduli of k[S]. The complete intersection hypothesis can be interchanged by the hypothesis that the curve Spec(k[S]) is a local complete intersection, but in this case we have to assume that M_{g,1}^{S} is non-empty. Under these new conditions we show the same conclusion as the first result. A classical result of realizable semigroups is obtained independently through a simple application of the Jacobian criterion.
Friday 06/05/2022
3:30pm UTC-3
On the representability of Chow groups of 0-cycles
Rina Paucar Rojas (IMCA/University of Göttingen)
Abstract: In this talk I will give a brief introduction to algebraic cycles and some equivalence relations defined on them, then I will discuss the notion of representability of Chow groups of 0-cycles on surfaces and state Bloch’s conjecture. Finally, I will present a result on the kernel of the Gysin homomorphism of Chow groups of 0-cycles, induced by the closed embedding of a curve into a surface, which is related with the study of 0-cycles on surfaces especially in the context of Bloch’s conjecture.
Friday 29/04/2022
3:30pm UTC-3
Locally Recoverables Codes from a Tower of Garcia Stichtenoth
Francisco Galluccio (Universidad Nacional del Litoral/Universidad de Valladolid)
Abstract: Locally Recoverable Codes (LRC Codes) were developed in the last years as a solution for distributed storage as the recovery of any erased coordinates using only a small fraction of the codeword. The most recent constructions came from Algebraic-Geometric Codes, in particular from coverings of curves and fiber product of curves. In this talk we will talk about Function Fields, and trying to adapt these constructions to this category, and describing a way to generalize the construction to some Towers of Function Fields. In particular, we will show an example using the Garcia-Stichtenoth Tower to see the properties of this construction.
Friday 22/04/2022
3:30pm UTC-3
No seminar
Friday 15/04/2022
3:30pm UTC-3
No seminar
Friday 08/04/2022
3:30pm UTC-3
A survey on non-symplectic automorphisms on K3 surfaces
Aline Zanardini (Leiden University)
Abstract: An automorphism of a K3 surface induces an action on the one- dimensional space of holomorphic 2-forms on the surface, so there are two kinds of automorphisms on K3 surfaces: symplectic and non-symplectic ones. The automorphism is called symplectic if the induced action is trivial. Otherwise, it is called non-symplectic. In this expository talk I will present some general results about non-symplectic automorphisms of finite order on K3 surfaces.
Time permitting I will report on some recent joint work in progress with R. Bell, P. Comparin, J. Li, A. Rincón-Hidalgo and A. Sarti.
Friday 01/04/2022
5:00pm UTC-3
Enumerative Geometry and Physics
Felipe Espreafico Guelerman Ramos (IMPA)
Abstract: Enumerative geometry concerns the computation of the numbers of geometric structures subjected to certain conditions. In the end of the 20th century, physicists studying String Theory were able to solve enumerative problems that mathematicians couldn't. We give a short introduction to the topic and explain the relations between Physics and Geometry.
Talk in person without slides and video
Friday 25/03/2022
3:30pm UTC-3
Quotients of K3 Surfaces vs Quotients of 2-Complex Tori
Yulieth Prieto (Leibniz Universität Hannover)
Abstract: Inspired by Kummer quartic surfaces, we study K3 surfaces that are birational to quotients of 2-complex tori by a finite automorphism preserving their periods. We will see that these K3 surfaces can be also obtained as quotients of K3 surfaces by finite automorphisms known as symplectic automorphisms. We will examine the role of such automorphisms, and if time permits, we will discuss some constructions for higher dimensional analogous of K3 surfaces and their quotients which are examples of irreducible holomorphic symplectic orbifolds.
Friday 18/03/2022
3:30pm UTC-3
Polynomial maps and unimodular domains
Wodson Mendson (IMPA)
Abstract: In this expository talk we will consider topics around affine algebraic geometry. The talk will be divided into two parts. In the first part, we will do a brief discussion about Keller polynomial maps in the n-dimensional affine space and we will present some results about the classical Jacobian Conjecture (1939). In the second part, we will explore the notion of the unimodular domains and we will establish an arithmetic version of the Jacobian Conjecture, result due to Essen and Lipton.
Previous talks - Summer 2022
Friday 25/02/2022
3:30pm UTC-3
Degenerations of linear series to curves with three components, using quiver representations
Eduardo Vital (IMPA)
Abstract: General degenerations of linear series to nodal curves with n+1 components yield exact linked nets of vector spaces with finite support, which are special quiver representations of pure dimension. We study some properties of linked net and their linked projective spaces.
Friday 18/02/2022
3:30pm UTC-3
A group action on multivariate polynomials over finite fields
Lucas da Silva Reis (UFMG)
Abstract: In this talk we consider the natural action of the (group) of transformations z --> az+b on multivariate polynomials over finite fields. We discuss the basics of the invariant theory for this group action and, in particular, we completely describe the fixed point subring for special groups (cyclic and Sylow).
Friday 11/02/2022
3:30pm UTC-3
0-dimensional compactifications are spectra
Lucas Henrique Rocha de Souza (UFMG)
Abstract: Let X be a Hausdorff locally compact locally connected space. Abels proved that there is a correspondence of the set of compactifications of X with 0-dimensional boundary and a family of subalgebras of some boolean algebra. This talk is about this theorem and a version of it for groups, proved also by Abels. These compactifications of groups have some applications in group theory such as the solution of Serre's conjecture about finitely generated groups, proved by Stallings.
Friday 04/02/2022
3:30pm UTC-3
Restrictions and extensions of foliations
Mateus Gomes Figueira (IMPA)
Abstract: Let X be a smooth projective surface contained in the 3-dimensional projective space. We prove that X is a plane if and only if every codimension one holomorphic foliation on X extends to a foliation on projective space.
Friday 21/01/2022
3:30pm UTC-3
On invariance of plurigenera
Xia Xiao (UQAM - Université du Quebec à Montreal)
Abstract: The purpose of the talk is to give a survey of Siu’s theorem of invariance of plurigenera for the pluricanonical bundle twisted with a line bundle which admits a singular positive metric that is well-defined on the central fiber.
Friday 10/06/2022
3:30pm UTC-3
TBA
Luize D'Urso (IMPA)
Abstract: TBA
Slides & Video