RTAA
Representation Theory of Algebras and Applications
Fridays at 16:00 ( Zoom)
Organizers: Kostiantyn Iusenko, John MacQuarrie and Eduardo Marcos.
Seminar Mailing List: RTAA — Representações das Álgebras e Aplicações
FORTHCOMING WEBINARS
PAST WEBINARS
16 December, 2022 
Viktor HugoICMCUSPSome conjectures in homological algebraIn this talk we shall discuss some homological problems, mostly motivated by the celebrated AuslanderReiten Conjecture on the freeness of finitely generated modules over commutative Noetherian local rings by means of the vanishing of Ext modules. We shall give cohomological criteria for prescribed bounds on the projective dimension of such a module, and we shall conclude with some AuslanderReiten type freeness criteria and others open problems. Show abstract 
09 December, 2022 
Samuel LopesUniversidade do PortoGeneralized Heisenberg algebras, quantizations and Poisson semiclassical limitQuantum generalized Heisenberg algebras (qGHA for short) we introduced as deformations and as generalizations of the generalized Heisenberg algebras profusely studied in the Physics literature. The class of qGHA includes all generalized downup algebras, the enveloping algebra of the Heisenberg Lie algebra and its quantum deformation as well as generalized Heisenberg algebras. We show that these can all be studied uniformly, highlighting their common properties. 
02 December, 2022 
Luís Augusto de MendonçaUFMGThe weak commutativity construction for Lie algebrasS. Sidki's weak commutativity construction $\chi(G)$ in group theory is a certain quotient of the free product $G \ast G$, designed to contain the Schur multiplier $H_2(G,\mathbb{Z})$ as a subquotient. We will consider its analogue in the category of Lie algebras over a field. We will discuss the definition and basic properties, and examine it from the point of view of the homological finiteness properties $FP_m$. Show abstract 
25 November, 2022 
Tiago CruzMPIM, BonnRelative dominant dimension and quasihereditary covers of TemperleyLieb algebrasEvery finitedimensional algebra can be written as endomorphism algebra of a projective module over a quasihereditary algebra. 
18 November, 2022 
Ricardo SouzaUFMGTopological Comodules and Almostsplit SequencesConstructing the AuslanderReiten Quiver of a general coalgebra is, as usual, an easytostate but hardtodo kind of construction. Although some progress has been made by Chin, Kleiner and Quinn, as well as Simson, we still don't have the means to generate almostsplit sequences for general comodules over general algebras, due to the size constraints. 
11 November, 2022 
Jorge VitóriaUniversità degli Studi di PadovaQuantity vs size in representation theoryIndecomposable modules over a finitedimensional algebra $R$ are largely thought of as the building blocks of the module category $R$. A famous theorem of Auslander, FullerReiten and RingelTachikawa, states a finitedimensional algebra admits only finitely many indecomposable modules up to isomorphism if and only if every indecomposable module is finitedimensional. This establishes a correlation between quantity (of indecomposable finitedimensional modules) and size (of indecomposable modules). 
04 November, 2022 
Henning KrauseBielefeld UniversityOn the symmetry of the finitistic dimensionThe finitistic dimension of a finite dimensional algebra is conjectured to be finite. Following recent work of Charley Cummings we discuss a construction which demonstrates that this invariant behaves rather differently when passing from right to left modules, and vice versa. Show abstract 
28 October, 2022 
Bernhard KellerUniversity of Paris VIISingularity categories, Leavitt path algebras and Hochschild homologyThe singularity category of a noetherian (non commutative) algebra is the quotient of its bounded by its perfect derived category. This construction goes back to Buchweitz (1986) in this setting and, independently, to Orlov (2003) in a geometric setting. We will recall the description of the singularity category of a radicalsquare zero quiver algebra using a graded Leavitt path algebra following work of Paul Smith, XiaoWu Chen, Dong Yang and others. We will then combine this with a localization theorem for Hochschild homology to obtain a simple description of the Hochschild homology of these singularity categories (with their canonical differential graded enhancement) and of the corresponding Leavitt path algebras. Finally, we will report on recent work of XiaoWu Chen and Zhengfang Wang which yields a generalization from radicalsquare zero to arbitrary finitedimensional algebras (over an algebraically closed field). This is mainly a survey talk. The original parts are based on joint work with Umamaheswa an Arunachalam and Yu Wang. Show abstract 
21 October, 2022 
Claire AmiotInstitut FourierDerived equivalences for gentle and skewgentle algebrasIn this talk, I will present how we can use topological model introduced my Upper, Plamondon and Schroll in 2018 in order to obtain information on derived categories of gentle or skewgentle algebras. This is joint work with Brüstle, Plamondon and Schroll. Show abstract 
16 September, 2022 
Viktor ChustIMEUSPOn generalized (bound) path algebrasThe generalized path algebras were introduced in (Coelho, Liu, 2000), in order to generalize the wellknown concept of path algebras over a quiver. In order to construct a generalized path algebra, we associate an algebra to each vertex of a quiver (instead of only the base field as it happens with ordinary path algebras), and we consider paths intercalated by elements from the algebras to form a vector space basis of the generalized path algebra. Multiplication is then naturally defined by concatenation of paths and using the multiplications of the algebras in each vertex. We have recently defined the generalized bound path algebras, which are a quotient of a generalized path algebra by an ideal generated by relations. The aim of this talk is to introduce these concepts and to discuss some ideas which appear in recent works by the authors, which relate representationtheoretical properties of a given generalized (bound) path algebra with those of the algebras used in its construction. This work was produced under supervision by Dr. Flávio Ulhoa Coelho (IMEUSP) and the authors acknowledge financial support by São Paulo Research Foundation (grant FAPESP #2018/181235 and #2020/139256). Show abstract 
24 June, 2022 
Marcelo MoreiraUniversidade Federal de AlfenasO estudo da estrutura das (co)homologias de Hochschild da classe de álgebras de dimensão finita $A$ com: $Hom_{AA} (DA,A) =0$O interesse sobre essa classe de álgebras nasceu na tentativa da generalização das sequências exatas curtas de grupos de cohomologia de Hochschild dos trabalhos [1] e [2]: \begin{equation*} 0 \longrightarrow H^0(TA,DA) \longrightarrow HH^0(TA) \longrightarrow HH^0(A) \longrightarrow 0 \end{equation*} \begin{equation*} 0 \longrightarrow H^1(TA,DA)\oplus\mathcal{E}(DA) \longrightarrow HH^1(TA) \longrightarrow HH^1(A) \longrightarrow 0 \;, \end{equation*} em que $\mathcal{E}(DA)$ é o $k$subespaço de $Hom_{A\text{}A}(DA, A)$ formado por todos os morfismos de $A$bimódulos $f \colon DA \to A$ tais que, para quaisquer $x, y \in DA$, temos que $f(x)y+xf(y) =0$. 
17 June, 2022 
Marlon StefanoUFMGO método de Butler aplicado a $\mathbb Z_p[C_p\times C_p]$módulos de permutação.Seja $p$ um número primo e $G$ um $p$grupo finito com subgrupo normal $N$ de ordem $p$. Vamos denotar por $\mathbb Z_p$ o anel dos inteiros $p$ádicos. Em um trabalho recente, Zalesskii e MacQuarrie forneceram uma caracterização dos $\mathbb Z_pG$módulos de permutação em termos de módulos para $\mathbb Z_p[G/N]$. A caracterização depende de duas condições, mas a necessidade dessas condições não era conhecida. Em um trabalho junto com MacQuarrie, aplicamos uma correspondência devida a Butler, que permite associar reticulados a $n$uplas de $\mathbb Z_pG$módulos, para mostrar a necessidade dessas condições por exibir um contraexemplo não trivial para a afirmação: se ambos os $N$invariantes e $N$coinvariantes de um certo reticulado $U$ são de permutação, então $U$ também o é. 
10 June, 2022 
Flávio CoelhoIMEUSPUma trisecção das componentes do quiver de AuslanderReiten. O conceito de trisecções na categoria de módulos sobre uma álgebra tem sido bastante utilizado na teoria de representações. Uma dessas trisecções envolve as subcategorias ${\mathcal L}_{\Lambda}$ e ${\mathcal R}_{\Lambda}$ definidas como segue. Para uma álgebra $\Lambda$,
$$ {\mathcal L}_{\Lambda} \ = \ \{ X \in \mbox{ ind}\Lambda \colon \mbox{ pd}_\Lambda Y \leq 1 \mbox{ quando existir um caminho } Y \leadsto X \} $$
$$ {\mathcal R}_{\Lambda} \ = \ \{ X \in \mbox{ ind}\Lambda \colon \mbox{ id}_\Lambda Y \leq 1 \mbox{ quando existir um caminho} X \leadsto Y \} $$
onde $M \leadsto N$ significa que existe um caminho de morfismos n\~ao nulos de $M$ a $N$. Relembre também que pd$_\Lambda N$ e id$_\Lambda N$ indicam, respectivamente, as dimensões projetiva e injetiva de um módulo $N$. Desta forma, $({\mathcal L}_{\Lambda}\setminus {\mathcal R}_{\Lambda}, {\mathcal L}_{\Lambda} \cap {\mathcal R}_{\Lambda}, {\mathcal R}_{\Lambda} \setminus {\mathcal L}_{\Lambda})$ induz uma trisecção na categoria ind$\Lambda$ para classes de álgebras como quasitilted e shod. Vamos discutir quando é que $({\mathcal L}_{\Lambda}\setminus {\mathcal R}_{\Lambda}, {\mathcal L}_{\Lambda} \cap {\mathcal R}_{\Lambda}, {\mathcal R}_{\Lambda} \setminus {\mathcal L}_{\Lambda})$ induz uma trisecção no quiver de AuslanderReiten de uma álgebra.

03 June, 2022 
Manuel SaorínUniversity of Murcia$\mathcal{P}^{<\infty}$contravariant finiteness and strong tilting iteration via corner algebrasA sufficient condition for the verification of the finitistic dimension conjecture for an Artin algebra $\Lambda$ is that the subcategory $\mathcal{P}^{<\infty}(mod\Lambda)$ of (finitely generated) modules of finite projective dimension be contravariantly finite in the category $mod\Lambda$. This last condition is in turn equivalent to the existence of a strong tilting $\Lambda$module. Two natural problems arise: 1) Give methods to construct Artin algebras $\Lambda$ with the mentioned contravariant finiteness property; 2) Assuming that property, and hence also the existence of a strong tilting $\Lambda$module $T$, when is it true that the (strongly tilted) endomorphism algebra $\tilde{\Lambda}=End(T_\Lambda)$ has the mentioned contravariant property? and, if so, can this process of strong tilting be iterated indefinitely?. We will show that, by an adequate choice of an idempotent $e\in\Lambda$, the answers to these questions can already be checked by looking at the corner algebra $e\Lambda e$. Show abstract 
27 May, 2022 
Thomas BrüstleUniversité de SherbrookeHomological approximations in persistence theory Multiparameter persistence modules are defined over a wild algebra and therefore they do not admit a complete discrete invariant. One thus tries in persistence theory to “approximate” such a module by a more manageable class of modules. Using that approach we define a class of invariants for persistence modules based on ideas from homological algebra. 
20 May, 2022 
Lorna GregoryUniversità degli Studi della Campania Luigi VanvitelliMaranda's theorem for pureinjective modules Let $R$ be a discrete valuation domain with maximal ideal generated by $\pi$ and let $\Lambda$ be an $R$order inside a separable algebra. For example, $R=\mathbb{Z}_{(p)}$ and $\Lambda=\mathbb{Z}_{(p)}G$ where $G$ is a finite group. 
13 May, 2022 
Sibylle SchrollUniversity of CologneFull exceptional sequences in the derived category of gentle algebrasIn general it is difficult to determine whether the bounded derived category of a finite dimensional algebras has full exceptional sequences or not. In this talk I will focus on the class of gentle algebras and determine for which gentle algebras the bounded derived category admits full exceptional sequences in terms of an underlying geometric surface model. Gentle algebras are finite dimensional algebras that are connected to many different areas of mathematics such as cluster theory, N=2 gauge theory and homological mirror symmetry of surfaces. Show abstract 
29 April, 2022 
José Armando ViveroUniversidad de La RepúblicaTriangular LIT algebrasIn this talk I am going to present some results concerning LatIgusaTodorov algebras (LIT algebras for short). The notion of LIT algebra, given by D. Bravo, M. Lanzilotta, O. Mendoza and J. Vivero in [1], is a way of generalizing the concept of IgusaTodorov algebra given by J. Wei in [2]. The results I am going to present can be found in [2103.12120] Triangular LatIgusaTodorov algebras (arxiv.org). 
08 April, 2022 
Eduardo MarcosIMEUSP$S$homogenous triples and aplications to algebras with 2relationsThis talk is on a joint work with Yuri Volkov. We define the notion os Shomogeneous triples and $S$homogeneous algebras and give an equivalence of categories which we apply to study koszulity, etc... The results are used for the partial classifications of homogeneous algebras whose defining ideal is generated by two relations. Show abstract 
01 April, 2022 
Calin ChindrisUniversity of MissouriQuiver Radial Isotropy and Applications to the Paulsen Problem in Frame TheorySigmacritical representations are quiver representations that satisfy certain matrix equations. They arise naturally in the context of KempfNess theorem on closed orbits in Invariant Theory. After introducing all the relevant concepts, I will first present the quiver radial isotropy theorem which gives necessary and sufficient conditions for the orbit of a quiver representation to contain a sigmacritical representation. I will then explain how this result can be used to solve the Paulsen Problem for matrix frames. This is based on joint work with Jasim Ismaeel. Show abstract 
03 December, 2021 
Mark KleinerSyracuse UniversityGraph monoids and preprojective roots of Coxeter groupsA graph monoid $\mathfrak{M}$ of a finite undirected graph $\Gamma$ without loops and multiple edges was introduced in 1969 by Cartier and Foata in order to give a new proof and a noncommutative version of the celebrated MacMahon Master Theorem, which is a result in enumerative combinatorics and linear algebra. If $\Gamma$ is given an acyclic orientation $\Lambda$ and thus becomes a quiver $(\Gamma, \Lambda)$, a certain subset (not a submonoid) of $\mathfrak{M}$ is closely related to the $(+)$admissible sequences of vertices introduced in 1973 by Bernstein, Gelfand, and Ponomarev in their seminal paper on quiver representations. If $\Gamma$ is the Coxeter graph of a Coxeter group $\mathcal{W}$, we use a canonical surjective monoid homomorphism $\mathfrak{M} \rightarrow \mathcal{W}$ to study preprojective roots of $\mathcal{W}$. Show abstract 
26 November, 2021 
Rosanna LakingUniversità degli Studi di VeronaWide intervals and mutationTorsion pairs in the category $\textrm{mod} A$ of finitedimensional modules over a finitedimensional algebra have played an important role in many aspects of modern representation theory, including the study of cluster theory, $t$structures and stability conditions. If we consider the collection of all torsion pairs ordered by inclusion of the torsion class, then we obtain a complete lattice. In recent work by Asai and Pfeiffer, the socalled `wide' intervals in this lattice are studied from the perspective of lattice theory. These intervals arise naturally both in relation to stability conditions and also in $\tau$tilting theory. In this talk we will discuss how the torsion pairs in $\textrm{mod} A$ are parametrised by 2term cosilting complexes in the unbounded derived category $D(\textrm{Mod} A)$ and how wide intervals correspond to their mutations. This talk is based on ongoing joint work with Lidia Angeleri Hügel, Jan Stovicek and Jorge Vitória. Show abstract 
19 November, 2021 
Alex Sierra CárdenasUniversidade Federal do ParáOn Brauer configurations induced by finite groupsAspects of the representation theory of a Brauer configuration algebra, such as the Cartan matrix and the module length of the respective indecomposable modules, have shown the existence of combinatorial relations that are satisfied by any finite group. The aim of this talk is to present both the Cartan matrix of a Brauer configuration algebra and the module length of any indecomposable projective module associated to a Brauer configuration algebra. Then using these aspects and the concept of subgroupoccurrence of an element in a group, we demonstrate a couple of combinatorial relations satisfied by any finite group, when considering the Brauer configuration induced by a finite group of an order different from a prime number. Show abstract 
12 November, 2021 
Marco A. PérezInstituto de Matemática y Estadística "Prof. Ing. Rafael Laguardia"Relative strongly Gorenstein objects in abelian categoriesThe purpose of this talk is to present a relativization of the concept of strongly Gorenstein projective module, introduced by Bennis and Mahdou in 2007. Given a pair $(\mathcal{A,B})$ of full subcategories $\mathcal{A}$ and $\mathcal{B}$ of an abelian category $\mathcal{C}$, we say that an object $C \in \mathcal{C}$ is periodic (or strongly) $(\mathcal{A,B})$Gorenstein projective if there exists a short exact sequence $C \rightarrowtail A \twoheadrightarrow C$, with $A \in \mathcal{A}$, which remains exact after applying the contravariant functor $\text{Hom}(,B)$ for every $B \in \mathcal{B}$. We shall show several properties, characterizations and examples of these objects in the case where $(\mathcal{A,B})$ is a hereditary pair (meaning that $\textrm{Ext}^i(A,B) = 0$ for every $A \in \mathcal{A}$, $B \in \mathcal{B}$ and $i \geq 1$). For instance, we shall see a relation with relative Gorenstein objects (2021  Becerril, Mendoza and Santiago) and periodic objects (2020  Bazzoni, CortésIzurdiaga and Estrada). Concerning specific examples, we shall exhibit a characterization of noetherian rings in terms of periodic Gorenstein injective modules relative to the pair (absolutely pure modules, injective modules). If time allows, we shall comment on a more general version of periodic $(\mathcal{A,B})$Gorenstein projective objects, namely, $(\mathcal{A,B})$Gorenstein projective objects with period $m \geq 1$. For these families of objects, an object is $(\mathcal{A,B})$Gorenstein projective with periods $m$ and $n$ if,
and only if, it is $(\mathcal{A,B})$Gorenstein projective with period $\mathrm{gcd}(m,n)$. 
05 November, 2021 
Hipolito TreffingerUniversität Bonn$\tau$tilting theory and stratifying systemsOn the one hand, tautilting theory was introduced by Adachi, Iyama and Reiten in 2012 and quickly became central in representation theory of finite dimensional algebras. In this talk, after giving a brief overview of some central results in this theory, we will explain how every taurigid object in a module category induces at least one stratifying system, as defined by Erdmann and Sáenz. Time permitting, we will use these results to give a new proof of the fact that every complete stratifying system in the module category of a hereditary algebra is an exceptional sequence, first proven by Cadavid and Marcos. Show abstract 
29 October, 2021 
Luis Gabriel Rodríguez ValdésUniversidad Nacional Autónoma de MéxicoHomological theory of kidempotent ideals in dualizing varietiesIn this talk, we develop the theory of $k$idempotent ideals in the setting of dualizing varieties. Several results given previously by M. Auslander, M. I. Platzeck, and G. Todorov are extended to this context. Given an ideal $I$ (which is the trace of a projective module), we construct a canonical recollement which is the analogous to a wellknown recollement in categories of modules over artin algebras. Moreover, we study the homological properties of the categories involved in such a recollement. Consequently, we find conditions on the ideal $\mathcal{I}$ to obtain quasihereditary algebras in such a recollement. Applications to bounded derived categories are also given. (Joint work with V. Santiago Vargas and M. L. S. Sandoval). Show abstract 
22 October, 2021 
Valente SantiagoUniversidad Nacional Autónoma de MéxicoTriangular matriz categories and recollementsWe define the analogous of the triangular matrix algebra to the context of rings with several objects. Given two additive categories $\mathcal{U}$ and $\mathcal{T}$ and $M \in$ $\operatorname{Mod}\left(\mathcal{U} \otimes \mathcal{T}^{o p}\right)$ we will construct the triangular matrix category $\boldsymbol{\Lambda}:=\left[\begin{array}{ll}\mathcal{T} & 0 \\ M & \mathcal{U} \end{array}\right]$ and we prove that there is an equivalence $(\operatorname{Mod}(\mathcal{T}), \mathbb{G M o d}(\mathcal{U})) \simeq \operatorname{Mod}(\boldsymbol{\Lambda})$. We will show that if $\mathcal{U}$ and $\mathcal{T}$ are dualizing $K$varieties and $M \in \operatorname{Mod}\left(\mathcal{U} \otimes \mathcal{T}^{o p}\right)$ satisfies certain conditions then $\boldsymbol{\Lambda}:=\left[\begin{array}{ll}\mathcal{T} & 0 \\ M& \mathcal{U}\end{array}\right]$ is a dualizing variety. Finally, we will show that given a recollement between functor categories we can induce a new recollement between triangular matrix categories, this is a generalization of a result given by Chen and Zheng in [Q. Chen, M. Zheng. Recollements of abelian categories and special types of comma categories. J. Algebra. 321 (9), 24742485 (2009), Theorem 4.4]. Show abstract 
15 October, 2021 
Oliver LorscheidUniversity of GroningenRepresentation type via quiver GrassmanniansThe representation type of a quiver $Q$ can be characterized by the geometric properties of the associated quiver Grassmannians:

08 October, 2021 
Jeremy RickardUniversity of BristolGeneration of the unbounded derived category of a ringIf $R$ is a ring, recall that the derived category $D(R)$ is a category whose objects are chain complexes of $R$modules. In recent decades, $D(R)$ has been recognized to be of great importance in studying the homological algebra of R.

01 October, 2021 
RobinsonJulian SernaUPTC, ColombiaA link between representations of peak posets and cluster algebrasIn this talk, we show a link between the theory of cluster algebras and the theory of representations of posets. Particularly, we give a geometric interpretation of the category of finitely generated socleprojective representations over the incidence algebra of a poset of type $A$ as a combinatorial category of certain diagonals of a regular polygon. This construction is inspired by the realization of the cluster category of type $A$ as the category of all diagonals by CalderoChapotonSchiffler. Moreover, given a poset $P$ of type $A$, we define a subalgebra $B(P)$ of a cluster algebra $B$ and we establish a sufficient condition to conclude $B=B(P)$. This is a joint work with R. Schiffler. Show abstract 
24 September, 2021 
Fernando dos Reis NavesUFMGUm relacionamento funtorial entre álgebras e seus quocientes pelas $n$ésimas potências do radical de JacobsonA famosa construção de Gabriel provou que uma álgebra de dimensão finita pode ser vista como um quociente de uma álgebra de caminhos por um ideal admissível. A construção permitiu olhar para teoria de representação de álgebras de dimensão finita de um modo combinatório. Iusenko, MacQuarrie e Quirino exibiram uma adjunção que explica de maneira muito precisa a filosofia da construção de Gabriel. A adjunção deles é obtida utilizando uma relação de equivalência nos morfismos das álgebras. Nesta palestra, mostraremos que a construção de Gabriel pode ser obtida utilizando uma relação mais fina. Além disso, através de uma adjunção, provaremos que há uma classe de álgebras que podem ser aproximadas por álgebras quadráticas, isto é, um quociente de uma álgebra de caminhos por um ideal homogêneo de grau 2. Show abstract 
17 September, 2021 
Andrea SolotarUniversidad de Buenos AiresInvariants of gentle algebrasGentle and locally gentle algebras are quadratic Koszul algebras. The isomorphism classes of gentle
algebras are in bijection with dissections of certain types of surfaces. 
10 September, 2021 
Claudiano Henrique da Cunha MeloUFMGÁlgebras seriais sem ciclos truncadas são derivadamente equivalentes a álgebras de incidência de posetsDada uma álgebra serial sem ciclos truncada $\Lambda$, denotamos sua categoria derivada por $\mathcal{D}^b(\Lambda).$ Nesta palestra apresentaremos a construção de um complexo inclinante $T_{\Lambda}$ e definiremos um conjunto parcialmente ordenado $S_{\Lambda}$ tais que a álgebra de endomorfismos $End_{\mathcal{D}^b(\Lambda)} T_{\Lambda}$ é isomorfa à álgebra de incidência de poset $kS_{\Lambda}^{op}$. Com isso, usando o Teorema de Rickard podemos concluir que $\Lambda$ é derivadamente equivalente a $kS_{\Lambda}^{op}$. Show abstract 
03 September, 2021 
Edson Ribeiro AlvaresUniversidade Federal do ParanáAção do grupo de tranças em sequências excepcionais e aplicações para álgebras hereditárias por partesNesta palestra, vamos introduzir o conceito de mutação de sequências excepcionais em categorias de feixes coerentes. Estas mutações permitem definir a ação do grupo de tranças sobre sequências excepcionais. Com o uso eficiente do Teorema de RiemannRoch e a Teoria de AuslanderReiten, podemos tirar bons resultados sobre as órbitas desta ação. Estes resultados nos trazem um melhor entendimento sobre as álgebras que são derivadamente equivalente a categoria de feixes coerentes sobre retas projetivas com peso. Show abstract 
30 July, 2021 
Gustavo MataUniversidad de la República, UruguayTopics on the IgusaTodorov functionsOne of the most important conjecture in the representation theory of Artin algebras is the finitistic dimension conjecture. It states that $sup\{pd(M) : M\ \text{is a f.g module of finite projective dimension}\}$ is finite. In an attempt to prove the conjecture this conjecture Igusa and Todorov defined in “On finitistic global dimension conjecture for artin algebras”, two functions from the objects of modA to the natural numbers, which generalize the notion of projective dimension. Nowadays they are known as the IgusaTodorov functions. In this talk I will introduce the IgusaTodorov functions and their main properties. We will also see how to use these functions to prove the finitistic dimension conjecture in several contexts. Show abstract 
23 July, 2021 
Danilo Dias da SilvaUniversidade Federal de SergipeFeixes instantons e representações de aljavasO seminário terá como tema apresentar uma nova compactificação para o espaço de módulos (moduli spaces) de feixes intantons de carga $1$ sobre $\mathbb P^3$. Isto será feito identificando estes feixes com representações de uma aljava com três vértices e oito flechas que atendem certas propriedades e olhando essas representações no espaço de módulos de King de representações tetaestáveis sobre esta aljava. Show abstract 
16 July, 2021 
Mariano SuárezÁlvarezUniversidad de Buenos AiresOn the modular automorphism of twisted CalabiYau algebrasA twisted CalabiYau algebra $A$ is, by definition, endowed with an automorphism $\sigma:A\to A$, welldefined only up to inner automorphisms, that controls the duality theory for representations of $A$. The algebra is CalabiYau, and not only twistedly so, precisely when $\sigma$ can be taken to be inner and even the identity map of $A$, but in general it cannot. The objective of the talk will be to present some results that give information about this automorphism in the general situation, and show how it can be used to construct interesting and nontrivial invariants of the algebra, of automorphisms and derivations of the algebra, and of related objects. Some applications of these invariants to the problem of computing Hochschild cohomology and the automorphism groups of our algebras will be discussed. Show abstract 
25 June, 2021 
Eduardo MarcosIMEUSPVariety defined by the Groebner basis of a moduleThis is a joint project with Ed. Green and Schroll Sibylle. 
18 June, 2021 
Ricardo FranquizUFMGÁlgebra de Árvore de Brauer e Blocos de Grupos ProfinitosSejam $G$ um grupo profinito , $k$ um corpo de característica $p> 0$. A álgebra de grupo completa de G, $k[[G]]$, possui uma decomposição como um produto direto de álgebras pseudocompactas indecomponíveis, que chamaremos de blocos. Cada bloco de $k[[G]]$ tem associado um pro$p$ subgrupo de $G$ chamado grupo de defeito. O grupo de defeito proporciona uma medida que tão próximo estará um bloco de ser uma álgebra semisimples. Nesta palestra explicaremos como associar a cada bloco um grupo de defeito e descreveremos os blocos cujo grupo de defeito é um grupo cíclico usando a estrutura de álgebra de árvore de Brauer.

11 June, 2021 
Joseph GrantUniversity of East AngliaPreprojective algebras: classical and higherI will give an introduction to representations of quivers, aimed at nonexperts, and then introduce preprojective algebras of quivers. Iyama showed how many nice aspects of the representations of quivers generalise to certain algebras of higher global dimension, and the preprojective algebra can be defined in this setting. I will explain some results on higher preprojective algebras obtained in joint work with Osamu Iyama. Show abstract 
04 June, 2021 
Valeriano LanzaUFFModuli of flags of sheaves: a quiver descriptionIn [1], the moduli spaces of framed flags of sheaves on $\mathbb P^2$ were described by means of representations of the socalled enhanced ADHM quiver. We first review those results, with a recent refinement concerning the chamber structure in the space of stability parameters. We shall then discuss the obstruction theory for these moduli spaces, showing in general that they have a perfect obstruction theory, and providing for specific choices of invariants a class of unobstructed points. Finally, open problems and possible further developments will be presented. This is a joint work with Rodrigo von Flach and Marcos Jardim.

14 May, 2021 
Vitor GuliszUFPRHigher AuslanderReiten theory: what is it and how to understand itHigher AuslanderReiten theory was introduced by Osamu Iyama in the 2000s as a generalization of the theory developed by Maurice Auslander and Idun Reiten in the 1970s. In this talk, we will discuss what is this theory and how to understand it. In doing so, we will examine both the definitions of $n$almost split sequence and of $n$cluster tilting subcategory. In the end, we will also look at some open problems of the theory. Show abstract 
07 May, 2021 
John MacQuarrieUFMGPropriedades homológicas de álgebras preservadas por certas extensõesUma extensão de álgebras associativas é simplesmente uma álgebra associativa $A$ com subálgebra $B$. Em uma sequência de artigos recentes, Cibils, Lanzilotta, Marcos e Solotar colocaram condições sobre a extensão (extensões "limitadas") e mostraram que, sobre essas condições, duas propriedades homológicas valem para $B$ se, e somente se, valem para $A$: nomeadamente "dimensão global finita" e "suporte da homologia de Hochschild finita". Em particular, segue disso que a "Conjectura de Han" vale para $B$ se, e somente se, vale para $A$.
