RESEARCH SEMINARS
UBB-UTCN Algebra seminar - Thursdays, 10:00 - 12:00
Geometry seminar - Fridays, 12:00 - 14:00

INVITED LECTURERS
Dr. Jonathan Gruber, National University of Singapore
Introduction to tilting theory in highest weight categories
Joi 25 mai 2023, ora 10:20, Zoom, Mathematica Sala pi

Abstract. In this talk, I will explain the notion of tilting objects in highest weight categories and discuss some of their key properties. Some important examples that we will see are the tilting modules in category O for a complex simple Lie algebra, in the category of rational representations of a reductive algebraic group, and in the category of representations of a quantum group at a root of unity. Towards the end of the talk, I will also discuss some of my own recent results on minimal tilting complexes.

Join Zoom Meeting
https://zoom.us/j/98588250468?pwd=eUtFdzQybWFMd1hXbjBaVDRsOXd6UT09
Meeting ID: 985 8825 0468
Passcode: 499898

Assoc. Prof. Dr. Emil Horobet, Sapientia University Tg. Mures
When does subtracting a rank-one approximation decrease tensor rank?
Joi 11 mai 2023, ora 10:00, Zoom, Mathematica Sala pi

Abstract. Subtracting a critical rank-one approximation from a matrix always results in a matrix with a lower rank. This is not true for tensors in general. We ask the question: what is the closure of the set of those tensors for which subtracting a rank-one approximation does result in lowering the rank? In this talk, we show how to construct this variety of tensors and we show how this is connected to the bottleneck points of the variety of rank-one tensors and in general to the singular locus of the hyperdeterminant and to orthogonally decomposable tensors.
Prof. Dr. Tomasz Brzezinski, Swansea University
Towards deformation theory of trusses
Joi 4 mai 2023, ora 10:00, Mathematica Sala pi

Abstract. In 2006 Carinena, Grabowski and Marmo proposed a specific deformation of multiplication of an associative algebra by a Nijenhuis-type operator. The associativity of the deformed product is controlled by Hochschild cohomology. This deformation has an “affine” flavour and can be extended to trusses (abelian heaps with distributing associative multiplication), which requires one to develop Hochschild cohomology for trusses. In this talk I will describe deformation of trusses through Nijenhuis operators and the corresponding modification of Hochschild cohomology.
Dr. Patrick Serwenne, TU Dresden
Exotic and block-exotic fusion systems
Joi 27 aprilie 2023, ora 10:00, Microsoft Teams. Event Link: shorturl.at/gwDY4, Mathematica Sala pi

Abstract. One of the main problems in the theory of fusion systems is the question whether a fusion system arises in the form of a finite group if and only if it arises in the form of a p-block of a finite group. There is a conjecture saying that both methods to obtain these categories are equivalent. We present ongoing work concerning our strategy to prove the conjecture.
Dr. Yuta Kozakai, Tokyo University of Science
τ-Tilting theory for group algebras of finite groups
Joi 13 aprilie 2023, ora 10:20, Zoom, Mathematica Sala pi

Abstract. Since τ-tilting theory was introduced in 2014, the theory continues to develop rapidly. One of the main themes of the theory is giving a classification of support τ-tilting modules, which have become very popular for various reasons.
In this talk, we introduce a recent result giving a relationship between the sets of support τ-tilting modules over two group algebras of certain finite groups.


Join Zoom Meeting
https://zoom.us/j/6513958939?pwd=RitMc0FlYkU3QmFQZDFQakorL29qdz09
Meeting ID: 651 395 8939
Passcode: 4ALW1H

Dr. Ipek Tuvay, Mimar Sinan Fine Arts University, Turkey
Brauer indecomposability of Scott modules
Joi 6 aprilie 2023, ora 10:00, MicrosoftTeams. Event Link: shorturl.at/gwDY4, Mathematica Sala pi

Abstract. In this talk, we will first introduce the notion of Brauer indecomposability of Scott modules, and then discuss its relationship with saturated fusion systems. Then we will present a recent result from a joint work with S. Koshitani which gives an equivalent condition for the Scott module to be Brauer indecomposable. In the end, we will demonstrate an application on constructing splendid Morita equivalences between principal blocks of two finite groups with isomorphic defect groups.
Dr. Lleonard Rubio y DeGrassi, Uppsala University
Maximal tori in HH1 and applications
Joi 9 martie 2023, ora 10:00, MicrosoftTeams. Event Link: shorturl.at/gwDY4, Mathematica Sala pi

Abstract. Hochschild cohomology is a fascinating invariant of an associative algebra which possesses a rich structure. In particular, the first Hochschild cohomology group HH1(A) of an algebra A is a Lie algebra, which is a derived invariant and, among selfinjective algebras, an invariant under stable equivalences of Morita type. This establishes a bridge between finite dimensional algebras and Lie algebras, however, aside from a few exceptions, fine Lie theoretic properties of HH1(A) are not often used. In this talk, I will show some results in this direction. More precisely, I will explain how maximal tori of HH1(A), together with fundamental groups associated with presentations of A, can be used to deduce information about the shape of the Gabriel quiver of A: In particular, I will show that every maximal torus in HH1(A) arises as the dual of some fundamental group of A: By combining this, with known invariance results for Hochschild cohomology, I will deduce that (in rough terms) the largest rank of a fundamental group of A is a derived invariant quantity, and among self-injective algebras, an invariant under stable equivalences of Morita type. Time permitting, I will also provide various applications. This is joint work with Benjamin Briggs.
Prof. Dr. Kenny De Commer, Vrije Universiteit Brussel
The braid equation and the reflection equation
Joi 3 noiembrie 2022, ora 10:30, Mathematica Sala pi

Abstract. There is currently a lot of interest in algebraic structures which can mimic topological operations. One particular such operation is braiding: take the ends of two strands which are hanging down, and turn around 180 degrees. If we replace each strand by a set X, one mimics the braiding operation by an invertible map r from the Cartesian square X˛ to itself. The crucial requirement of this map is that it satisfies the braid equation (also known as Yang-Baxter equation). It turns out that such a map r leads to a wealth of interesting algebraic structures. We will give an overview of the different incarnations of these structures, and their surprising relation with other well-known areas of algebra (Galois theory, radical rings, ...) We then look at a closely related topological operation: take the ends of two strands and turn around 360 degrees! Transferring this operation to the set-theoretic world, we are now looking at maps satisfying a different equation, known as the reflection equation. As our own small contribution to this area, we will comment on some algebraic structures associated to this equation.
Dr. Attila Maróti, Alfréd Rényi Institute of Mathematics, Budapesta, Ungaria
A generalization of the diameter bound of Liebeck and Shalev for finite simple groups
Joi 13 octombrie 2022, ora 10:30, Mathematica Sala pi

Abstract. We will study conditions on when a finite group can be expressed as a product of some of its conjugacy classes. The talk is based on two papers. We will first discuss a work on simple groups joint with Laszlo Pyber and then a work on alternating groups joint with Martino Garonzi.
Dr. Attila Maróti, Alfréd Rényi Institute of Mathematics, Budapesta, Ungaria
Normalizers of primitive permutation groups
Joi 18 ianuarie 2022, ora 13:00, Mathematica Sala pi

Abstract. Given a transitive permutation group G of degree n. We may consider the normalizer A of G in Sym(n) and ask how big can the index |A : G| be? The most difficult case is when G is a primitive group. In this situation it is shown that |A : G| is less than n unless n is 34, 54, 38, 58, or 316. We will also discuss other results of similar flavor for both permutation groups and linear groups. This is joint work with Robert M. Guralnick and László Pyber.
Prof. Dr. Tomasz Brzeziński, Swansea University, UK
Enter truss
Joi 14 ianuarie 2021, ora 11:00, Zoom

Abstract. The talk introduces trusses, i.e. algebraic systems consisting of a set with a ternary operation (making it into an abelian heap) and an associative binary operation distributing over the ternary one. We begin by explaining what heaps are and how are they related to groups. Next, we introduce trusses and give elementary examples. Finally, we show that trusses appear in a natural way in many algebra considerations, e.g. they can be employed to analyze isomorphisms of abelian groups and equivalence classes of extensions of rings.
Prof.Dr. Alexander Ivanov, Imperial College London
Locally Projective Graphs, Majorana Theory and the Monster Group
Vineri, 6 decembrie 2019, ora 13:00, Mathematica Sala pi

  • Abstract


  • Prof.Dr. Silvana Bazzoni, Universitŕ degli Studi di Padova
    Flat Mittag-Leffler modules and approximations
    Joi 1 iulie 2010, ora 12:00, Mathematicum Sala e

    Abstract. Drinfeld in 2006 defined an infinite dimensional vector bundle over a scheme to be a quasi-coherent sheaf whose sections in each open affine subset are projective modules. Gillespie (2007) replaced projective by flat and defined a Quillen model structure on the category of unbounded complexes over the category of quasi-coherent sheaves on a scheme. Drinfeld proposed to use an intermediate class between the classes of flat and projective modules, that is the class D of flat Mittag-Leffler modules. We will present recent results proved by Herbera-Trlifaj on the structure of flat Mittag-Leffler modules and then we will focus on the problem of deciding when the double Ext-orthogonal of D coincides with the class of all flat modules. Deconstructibility and precovering properties of the class D will also be discussed.
    Prof.Dr. Kulumani M. Rangaswamy, University of Colorado System, Colorado Springs
    The theory of Leavitt path algebras of arbitrary graphs
    Joi 24 iunie 2010, ora 12:30, Cladirea Centrala Sala 5/I


    Prof.Dr. Kulumani M. Rangaswamy, University of Colorado System, Colorado Springs
    Unions of projective modules
    Marti 22 iunie 2010, ora 17:00, Mathematicum Sala gamma


    Prof.Dr. Mihai Ciucu, Georgia Institute of Technology, Atlanta
    Monomer correlations on the square lattice
    Joi 10 iunie 2010, ora 12:00, Mathematicum Sala e

    Abstract. In 1963 Fisher and Stephenson conjectured that the correlation function of two oppositely colored monomers in a sea of dimers on the square lattice is rotationally invariant in the scaling limit. More precisely, the conjecture states that if one of the monomers is fixed and the other recedes to infinity along a fixed ray, the correlation function is asymptotically C d^(-1/2), where d is the Euclidean distance between the monomers and C is a constant independent of the slope of the ray. Shortly afterward Hartwig rigorously determined C when the ray is in a diagonal direction, and this remains the only direction settled in the literature. We generalize Hartwig's result to any finite collection of monomers along a diagonal direction. This can be regarded as a counterpart of a result of Zuber and Itzykson on n-spin correlations in the Ising model. A special case proves that two same-color monomers interact the way physicists predicted.
    Prof.Dr. Christopher Deninger, Universität Münster
    How to count points on singular surfaces over finite fields
    Marti 27 octombrie 2009, ora 12:15, Mathematicum Sala pi

    Abstract. For a smooth projective variety X over a finite field F the zeta function is a generating series for the numbers of points of X in the finite extension fields of F. If X is given by system of polynomial equations in several variables over F, a point of X in an extension field F' is a solution of the equations with coordinates in F'. Thus the zeta function encodes the number of solutions of equations over finite fields which is very interesting from a number theoretical point of view. One can think of the condition that X is smooth and projective as being analogous to being a compact manifold. A part of the famous Weil-conjectures which was proved by Grothendieck and Verdier asserts that the zeta function is in fact rational and has a simple functional equation. If the variety is no longer smooth, i.e. if it has singularities the zeta function obtained by counting points naively is still rational but it no longer has a functional equation. The talk explains with what weights one has to count the singular points -at least on surfaces- in order to obtain a new zeta function which is again rational but does have a functional equation. I will try to explain all concepts in the talk and also the required ideas from etale (intersection) cohomology.
    Dr. Dan Ciubotaru, University of Utah
    Corespondente Langlands pentru grupuri definite peste corpuri locale
    Miercuri 3 iunie 2009, ora 12:00, Mathematicum Sala e

    Abstract. In programul Langlands, reprezentarile unui grup reductiv G definit peste un corp local de caracteristica zero (real sau p-adic) sint intr-o corespondenta de dualitate cu anumite obiecte geometrice (categorii de fascicule) atasate unui grup dual, complex, \check G. Voi incerca sa explic principalele elemente ale acestei corespondente, iar apoi voi prezenta o conexiune noua intre unele reprezentari (si parametri lor Langlands) ale grupurilor clasice reale (precum GL(n,R)) si reprezentari pentru grupurile clasice p-adice (precum GL(n,Q_p)).
    Mr. Dan Salajan, Ecole Polytechnique Fédérale de Lausanne, Faculté des Sciences de Base
    Around Thompson group F
    Miercuri 7 ianuarie 2009, ora 12:00, Mathematicum Sala e

    Abstract. We present some general research problems in the theory of infinite groups together with some examples. We discuss then Banach Tarski paradox and the notion of amenability. We focus on the quite famous R. Thompson's F group of piecewise linear homeomorphisms of the unit interval, with finitely many breakpoints in the dyadic rationals, and with all derivatives powers of 2. We present some basic properties of this group: it satisfies no laws and doesn't contain copies of the free group. In the end, we discuss around the well known conjecture concerning the amenability of F.
    Prof. Dr. Stefaan Caenepeel, Vrije Universiteit Brussel
    Monoidal categories, quasi-bialgebras and the third cohomology group
    Miercuri 6 iunie 2007, ora 12:00, Mathematicum Sala e

    Abstract. We introduce quasi-bialgebra from the point of view of monoidal categories. It is explained how these notions are connected to third order cohomology groups. We give an explicit computation of the third cohomology groups of the cyclic group of order 2 and of the Klein 4 group.
    Prof.Dr. Klaus Dohmen, Dekan FB Mathematik/Physik/Informatik, Hochschule Mittweida (FH)
    Improved Bonferroni Inequalities via Graphs and Abstract Tubes
    Miercuri 9 mai 2007, ora 12:00, Mathematicum Sala e


    Abstract. Many problems in combinatorics, number theory, probability theory, reliability theory, and statistics can be solved by applying a unifying method, which is known as the principle of inclusion-exclusion. The principle of inclusion-exclusion expresses the indicator function of a union of finitely many sets as an alternating sum of indicator functions of their intersections. In probability theory, the associated truncation inequalities are widely known as Bonferroni's inequalities (although they are due to Ch. Jordan). Numerous extensions of the classical Bonferroni inequalities were established in the second half of the 20th century. Roughly, they can be divided into generally valid and non-generally valid inequalities. In this talk we deal with both kinds of extension where the selection of intersections in the estimate is determined by a graph or more generally, by an abstract simplicial complex. Applications are given to graph colouring and network reliability.
    Dr. Cristian M. Litan, Universidad Carlos III de Madrid, Departamento de Economia
    On the generic finiteness of equilibrium outcomes for bimatrix games
    Miercuri 7 februarie 2007, ora 12, Sala e (Mathematicum)


    Abstract. It is well known that if the entries of the normal form of a game with any number of players can be perturbed independently, then generically there is a finite number of (Nash) equilibria. Kreps-Wilson criticize this result as not being very helpful when the normal form is derived from an extensive form since then many strategies lead to the same final node. If the payoffs of the final nodes can be perturbed independently the finiteness of the number of equilibria is not a generic property. In fact, the criticism of Kreps-Wilson to the normal form result can be reiterated: it is very strong to assume that final nodes utilities can be perturbed independently. Typically, in economic applications many final nodes will correspond to the same final position of a game and a natural assumption may be that the final utilities depend on the position and not on the particular history of the play (i.e. the node). When the final utilities depend on the position, the finiteness of the number of equilibria is not a generic property, again. However, a natural question rises: is the finiteness of the number of equilibrium payoffs or equilibrium outcomes a generic property in games where the payoffs of final nodes are tied together by linear constraints in whatever way? Govidnan-McLenan proved that for such games with more than two players, it is not the case. But the generic finiteness of equilibrium outcomes for bimatrix games is still an open question. We provide different mathematical problems to which such a conjecture can be reduced.
    Prof.dr. Stipsicz András (Alfred Renyi Institute of Mathematics, Budapest)
    Exotic structures on 4-dimensional manifolds
    Miercuri 24 ianuarie 2007, ora 12, Sala e (Mathematicum)
    Prof.dr. Némethi András (Alfred Renyi Institute of Mathematics, Budapest)
    Poincare series with applications to geometry and number theory
    Luni, 6 noiembrie 2006, Sala e (Mathematicum)

    Prof. Dr. Stefaan Caenepeel, Vrije Universiteit Brussel
    Cohomology over commutative Hopf algebroids
    Miercuri 21 iunie 2006, ora 12:00, Mathematicum Sala e
    Dr. Virginia Niculescu, UBB, Department of Computer Science
    Building an Object Oriented Computational Algebra System Based on Design Patterns
    Miercuri 24 mai 2006, ora 12:30, Mathematicum Sala e
    Dr. Alin Bostan, INRIA Paris
    Computer algebra: a bird's-eye view
    Miercuri 10 mai 2006, ora 12:00, Mathematicum Sala e

    Abstract. Computer algebra is a relatively young area of scientific computation, which develops, analyzes, implements and uses algebraic algorithms. It is an interdisciplinary field, complementary to numerical analysis; it is located at the border between computer science and mathematics, with various domains of application, from effective algebraic geometry to combinatorics, from mathematical physics and control theory to computational number theory and cryptology. The aim of this talk is to describe, along with a survey of some historical and sociological aspects of Computer algebra, typical examples of current research directions, theoretical open questions and computational challenges.
    Dr. Gergely Bérczi, Eötvös Loránd University Budapest
    Localization theorems in topology
    Miercuri 20 aprilie 2005, ora 12:00, Mathematicum Sala e
    Prof. dr. András Szenes, Budapest University of Technology and Economics
    Toric quotients and enumerative geometry
    Joi 7 aprilie 2005, ora 14:00, Cladirea centrala 5/I
    Dr. Jan Žemlicka, Charles University Prague
    Semiartinian rings
    Miercuri 23 martie 2005, ora 12:00, Mathematicum Sala e
    Prof. dr. Markus Linckelmann, CNRS - Université Paris 7
    Derived and Morita Equivalences for Blocks of p-Solvable Groups
    Marti 23 aprilie 1996, ora 12:00, Cladirea centrala 5/I
    Miercuri 24 aprilie 1996, ora 12:00, Sala 57 (Echinox)
    Joi 25 aprilie 1996, ora 12:00, Sala 57 (Echinox)
    Vineri 26 aprilie 1996, ora 12:00, Cladirea centrala 5/I