Thursday, January 30 (lecture room K1)  

09:00  09:10  Welcome and opening 
09:10  10:00  Lidia Angeleri Hügel 
coffee break  
10:30  11:20  Manuel Cortés Izurdiaga 
11:30  12:20  George Ciprian Modoi 
lunch break  
14:00  14:50  Xianhui Fu 
coffee break  
15:30  16:20  Simion Breaz 
16:30  17:20  Dolors Herbera 
social dinner (from 19:30)  


Friday, January 31 (lecture room K1)  
10:00  10:50  Silvana Bazzoni 
11:00  11:50  Sylvia Wiegand 
coffee break  
12:20  13:10  Alberto Facchini 
13:20  14:10  Mike Prest 
Enochs Conjecture (or Enochs question) asks if a class of modules providing for covers is necessarily closed under direct limits.
In a recent paper in collaboration with Leonid Positselski and Jan Šťovíček (http://arxiv.org/abs/1911.11720) it is shown that every direct limit presentation has locally split kernel (even quasi split) and this plays a key role in connection with precovers and covers. In particular, this allows to obtain a simple elementary proof of Enochs Conjecture for the left class of an ntilting cotorsion pair in a Grothendieck category.
The paper deals also with covers and precovers of direct limits in AB3 categories, but in this talk I will mostly deal with module categories and I will discuss some classes of modules over commutative rings providing for minimal approximations, that is covers and/or envelopes.
In this talk we will focus on the problem of when, for a given Torpair (𝒯, 𝒮) in the categories of modules over a ring R, the class 𝒯 is closed under products or, more generally, products of modules in 𝒯 have finite projective dimension relative to 𝒯. As we will see, this property is related with some MittagLeffler conditions satisfied by the modules belonging to 𝒮. As a particular case of our results, we will obtain the characterization of those rings for which the class of all modules with finite flat dimension is closed under products.
This work is motivated by the study of right Gorenstein regular rings, that is, rings with finite right global Gorenstein projective dimension (equivalently, rings for which the classes of right modules with finite projective and with finite injective dimensions coincide).
In Geometry and Topology there are several functors between geometric spaces or topological spaces on the one hand, and commutative rings on the other. The most famous of these functors are probably the ring C(X) of real continuous functions of a topological space X and the spectrum Spec(R) of a commutative ring R. We will discuss the possibility of extending these classical ideas to the noncommutative setting. I will try to speak in a language understandable to everybody (i.e., to any mathematician...)
References:
Let M be a finitely generated module, and let Add_{ℵ0}(M) denote the category of the direct summands of M^{(ω0)}. Let V^{*}(M) denote the monoid of isomorphism classes of the objects in Add_{ℵ0}(M).
We will describe a process of "gluing" together the quotients of the category Add_{ℵ0}(M) by the ideal generated by an object of Add_{ℵ0}(M), to construct a submonoid B(M) of V^{*}(M). What makes B(M) particularly interesting, is that in the case of a module finite algebra over commutative noetherian ring, B(M)=V^{*}(M).
The particular way we found these monoids, motivated us to name them as monoids defined by a system of supports. We will develop some theory about them, mainly in the case of monoids defined by a full system of supports, which is the one appearing when R is a commutative local noetherian ring.
The talk is based on joint work with P. Příhoda and R. Wiegand.