**Visitors:**

- Øyvind Solberg (Trondheim): May 2019
- Alexandros Grosdos (Osnabrück): 17 December 2018 - 22 December 2018
- Ioannis Zachos (Michigan): 17 December 2018 - 22 December 2018
- William Crawley-Boevey (Bielefeld): 3 December 2018 - 22 December 2018
- Julia Sauter (Bielefeld): 3 December 2018 - 22 December 2018
- Steffen Oppermann (Trondheim): 14 October 2018 - 20 October 2018
- Torkil Stai (Trondheim): 14 October 2018 - 20 October 2018

**Algebra Seminar in Thessaloniki:**

**Algebra Evening in Thessaloniki****,**Tuesday, 18 December 2018, Room M2.

**17.30 - 18.15: **William Crawley-Boevey (Bielefeld)

** Title**: My Struggle with the Deligne Simpson Problem

**Abstract: **The Deligne Simpson problem (DSP) arises in the classification of linear ODEs in the complex domain, but it is elementary to state: given k conjugacy classes in GL(n,C), determine whether or not there are matrices in these classes with no common invariant subspace and product equal to the identity. Work I did on quiver algebras led to a conjectural answer for the DSP, I proved one direction in 2006 with P. Shaw, and although I announced a proof of the other direction, it never got written up. In this talk I will explain the background to the DSP and discuss recent work with A. Hubery aimed at completing the other direction.

** 18.30 - 19.00: **Kostas Karagiannis (Thessaloniki)

** Title**: On the canonical embedding of the Kummer-Artin-Schreier-Witt family of curves

**Abstract: ***Arithmetic Geometry*, the discipline that bridges Algebraic Geometry and Number Theory, mainly studies algebraic curves over fields of prime characteristic p>0. Technical difficulties led Serre, Tate and Grothendieck to develop *lifting techniques* to fields of characteristic 0, over which curves are better understood. Applying these techniques, Oort-Sekiguchi-Suwa (1989) and Bertin-Mézard (2000), unified Artin-Schreier theory and Kummer theory, by introducing an appropriate family of curves over the ring of Witt vectors. Using results of Karanikolopoulos-Kontogeorgis (2014) on the sheaf of holomorphic differentials Ω, we study the family's induced canonical embedding into projective space. In particular, in joint work with professors Charalambous and Kontogeorgis, we give explicit generators for the embedding's defining ideal, combining lifting techniques with elements of combinatorial commutative algebra and the theory of Gröbner bases.

** 19.00 - 19.30: **Ioannis Zachos (Michigan)

** Title**: Introduction to Local Models

**Abstract: **In this talk we will try to define the local models and give a small sketch of the historical development of the theory. The importance of the local models lies in the fact that under some assumptions they model the singularities that arise in the reduction modulo p of Shimura varieties. The Shimura varieties are often moduli spaces of abelian varieties with additional structure. Understanding the structure of local models will help us to have a better understanding of the moduli spaces of the abelian varieties with some additional structure. In this talk we will try to give most of the background needed in order to understand the above mathematical objects. Time permitted, we will state some open problems.

** 19:45 - 20:15: **Alexandros Grosdos (Osnabrück)

** Title**: Moment Ideals of Mixture Distributions

**Abstract: **Moments are quantities that measure the shape of statistical or stochastic objects and have recently been studied from an algebraic and combinatorial point of view. We start this talk by introducing (local) mixture distributions and their moment ideals. We explain how mixing distributions on the statistical side corresponds to taking secants of the algebraic varieties on the geometric one and we compute generators for the ideals involved. Furthermore, we apply elimination theory and Prony's method in order to do parameter estimation, and showcase our results with an application in signal processing. A main goal of this talk is to highlight the natural connections between algebraic statistics, geometry, combinatorics and applications in analysis throughout the talk.

- Thursday, 13 December 2018, Room M2, 12:15 - 13:00.

** Speaker: **Julia Sauter (Bielefeld)

** Title**: Going relative with faithfully balanced modules

**Abstract: **We briefly revisit faithfully balanced modules for finite-dimensional algebras and the well-known correspondences they induce (for (co)-generators and (co)tilting modules). Relative homological algebra (RHA) replaces the usual exact structure on finitely generated modules with another one which is easily defined - this has been introduced by Auslander and Solberg. We explain how the previously mentioned correspondences interplay with RHA and their relative versions. This is work in progress with Biao Ma.

** **

- Thursday, 22 November 2018, Room M2, 12:15 - 13:00.

** Speaker: **Chrysostomos Psaroudakis (Thessaloniki)

** Title**: Explicit right adjoints between homotopy categories

** Abstract: **Let T be a triangulated category with coproducts and let X be a set of compact objects. Then X generates a certain t-structure, and in particular describes explicitly a left adjoint to the inclusion of the coaisle. Unfortunately, it does not make much sense to consider the naive dual of this setup; cocompact objects rarely appear in categories which occur naturally. Motivated by this, we introduce a weaker version of cocompactness called 0-cocompactness, and show that in a triangulated category with products these objects cogenerate a t-structure. As an application, we provide explicit right adjoints between certain homotopy categories. This is joint work with Steffen Oppermann and Torkil Stai.

- Thursday, 18 October 2018, Room M2, 12:15 - 13:00.

** Speaker: **Steffen Oppermann (Trondheim)

** Title**: Auslander-Reiten quivers and higher dimensional analogs

** Abstract: **In my talk I will first discuss some classical concepts in representation theory of finite dimensional algebras. In particular we will look at Auslander Reiten quivers, and what information these quivers contain. I will then focus on a more recent twist: the generalization of Auslander Reiten theory to a “higher dimensional” version, and discuss some aspects that generalize nicely (as well as possibly some that don’t).

- Thursday, 18 October 2018, Room M2, 13:15 - 14:00.

** Speaker: **Torkil Stai (Trondheim)

**Title**: Triangulated categories and orbit categories

**Abstract**: The concept of a *triangulated category* comes up everywhere, in particular in mathematics! Our primary objective is to provide some very basic intuition for this notion, with an emphasis on connections and similarities with the more familiar abelian categories. For instance, taking *subcategories* and *quotients* of triangulated categories is straightforward. A much more mysterious construction is that of an *orbit category* of a triangulated category with respect to an automorphism; there is no a priori reason why this gadget should be triangulated. The secondary aim of this talk is to explain how algebraists have coped with this nightmare over the last decade. Time permitting, I will report on ongoing work with Steffen Oppermann on the topic.