Algebraic Geometry Graduate Seminars (AG-GS)

AG-GS is a weakly organized graduate seminar series on algebraic geometry and its related fields. Our goal is to provide an interactive environment and to bring together graduate students working on algebraic geometry and its related fields, such as number theory, geometry/topology, mathematical physics, etc… Each week involves either a colloquium or a mini-lecture series on a particular topic. Lecture series may cover two or more sessions depending on the topic.

Talks are held on each Thursday at 11:00-12:00 in Gündüz İkeda seminar room, Department of Mathematics, METU.

To subscribe to the mail list, please send an email to hsuluyer@metu.edu.tr

You are cordially invited to this week general seminar :

1) February 20, 2020: Sadık TERZI (METU)“Weierstrass Points over Complex Numbers”

Abstract: Let X be a “closed” compact Riemann surface (non-singular proper algebraic curve over complex numbers). Weierstrass points of X are defined as a consequence of the important theorem of Riemann-Roch in the theory of algebraic curves. As an immediate application, the set of Weierstrass points is an invariant of a curve which is useful in the study of the curve’s automorphism group and the fixed points of automorphism. The talk will include some prerequisite material for theory, concepts of (higher-order) Weierstrass points, and applications.

2) February 27, 2020: Sadık TERZI (METU) Weierstrass Points over Positive Characteristics

Abstract: Let X be smooth projective curve of genus g>1 over algebraically closed field k of positive characteristic p and L be (non-special) line bundle of degree d on X. We will give definition(s) of L-weierstrass points like complex case. In the characteristic p>0, linearly independent functions may have identically zero Wronskian determinants. Therefore, to determine L-weierstrass points on a curve X as points where the gap sequence differs from the generic gap sequence on X, one modifies the classical Wronskian by using Hasse-derivatives. Then, usual det=0 approach applies to give finitely many L-weierstrass points. At the end of the talk, we will see examples which bring diverse pathologies.





3) March 05, 2020: Kadri İlker BERKTAV (METU)Homotopy Theory of Stacks I

Abstract: This is a mini-lecture series on the homotopy theoretical formulation of stacks. In this series, we always consider higher structures in algebraic geometry in a functorial perspective. In the first lecture, we shall
provide a suitable language in order to define the notion of a pre-stack in
a functorial manner. In that respect, the basics of 2-category theory will
be introduced. In order to encode the so-called local-global properties (as
in the case of standard sheaf theoretical constructions), on the other hand, we like to employ the homotopy theory of stacks. To this end, we shall study the main ingredients of model categories, the concept of simplicial objects, and the manifestation of the desired local-to-global aspects in terms of “homotopy limits”. These will be the main topics of interest in the second lecture of the series.

4) March 12, 2020: Kadri İlker BERKTAV (METU)Homotopy Theory of Stacks II

Abstract: This is a mini-lecture series on the homotopy theoretical formulation of stacks. In this series, we always consider higher structures in algebraic geometry in a functorial perspective. In the first lecture, we shall
provide a suitable language in order to define the notion of a pre-stack in
a functorial manner. In that respect, the basics of 2-category theory will
be introduced. In order to encode the so-called local-global properties (as
in the case of standard sheaf theoretical constructions), on the other hand, we like to employ the homotopy theory of stacks. To this end, we shall study the main ingredients of model categories, the concept of simplicial objects, and the manifestation of the desired local-to-global aspects in terms of “homotopy limits”. These will be the main topics of interest in the second lecture of the series.

5) March 19, 2020: “TBA”

Abstract: