BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Emine Yıldırım (Queen's University) DTSTART:20200812T160000Z DTEND:20200812T173000Z DTSTAMP:20260315T021505Z UID:UCGEN/1 DESCRIPTION:Title: Cl uster Categories\nby Emine Yıldırım (Queen's University) as part of UCGEN - Uluslararası Cebirsel GEometri Neşesi\n\n\nAbstract\nCluster Ca tegories are introduced to understand cluster dynamics from the representa tion theory point of view. The subject has its roots in two important resu lts in the literature that give us a glimpse of a relationship between clu ster dynamics and representation theory. The first is that there is an one -to-one correspondence between the cluster variables of a finite type clus ter algebra and the almost positive roots of the corresponding root system . The second is a well-known result by Gabriel that classifies finite repr esentation type quivers by using positive roots of the corresponding root system. In this talk\, after giving an overview of cluster categories\, I will talk about a recent joint work with Charles Paquette on the generaliz ation of discrete cluster categories.\n LOCATION:https://researchseminars.org/talk/UCGEN/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Emre Sertöz (Leibniz University Hannover) DTSTART:20200819T160000Z DTEND:20200819T173000Z DTSTAMP:20260315T021505Z UID:UCGEN/2 DESCRIPTION:Title: Se parating periods of quartic surfaces\nby Emre Sertöz (Leibniz Univers ity Hannover) as part of UCGEN - Uluslararası Cebirsel GEometri Neşesi\n \n\nAbstract\nKontsevich--Zagier periods form a natural number system that extends the algebraic numbers by adding constants coming from geometry an d physics. Because there are countably many periods\, one would expect it to be possible to compute effectively in this number system. This would re quire an effective height function and the ability to separate periods of bounded height\, neither of which are currently possible.\n\nIn this talk\ , we introduce an effective height function for periods of quartic surface s defined over algebraic numbers. We also determine the minimal distance b etween periods of bounded height on a single surface. We use these results to prove heuristic computations of Picard groups that rely on approximati ons of periods. Moreover\, we give explicit Liouville type numbers that ca n not be the ratio of two periods of a quartic surface. This is ongoing wo rk with Pierre Lairez (Inria\, France).\n LOCATION:https://researchseminars.org/talk/UCGEN/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Yusuf Barış Kartal (Princeton University) DTSTART:20200826T160000Z DTEND:20200826T173000Z DTSTAMP:20260315T021505Z UID:UCGEN/3 DESCRIPTION:Title: p- adic analytic actions on Fukaya categories and iterates of symplectomorphi sms\nby Yusuf Barış Kartal (Princeton University) as part of UCGEN - Uluslararası Cebirsel GEometri Neşesi\n\n\nAbstract\nA theorem of Bell\ , Satriano and Sierra state that for a given smooth complex surface $X$ wi th an automorphism $\\phi$ the set of natural numbers $n$ such that $Ext^i (F\,(\\phi^*)^n(F'))\\neq 0$ is a union of finitely many arithmetic progre ssions and finitely many other numbers. Due to homological mirror symmetry conjecture\, one can expect a symplectic version of this statement. In th is talk\, we will present such a theorem for a class of symplectic manifol ds and symplectomorphisms isotopic to identity. The technique is analogous to its algebro-geometric counterpart: namely we construct p-adic analytic action on a version of the Fukaya category\, interpolating the action of the iterates of the symplectomorphism.\n LOCATION:https://researchseminars.org/talk/UCGEN/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Özge Ülkem (Heidelberg University) DTSTART:20200902T160000Z DTEND:20200902T173000Z DTSTAMP:20260315T021505Z UID:UCGEN/4 DESCRIPTION:Title: Un iformization of the moduli space of generalized $\\mathcal{D}$-elliptic s heaves\nby Özge Ülkem (Heidelberg University) as part of UCGEN - Ulu slararası Cebirsel GEometri Neşesi\n\n\nAbstract\nDrinfeld defined the n otion of elliptic modules\, which are now called Drinfeld modules\, as an analogue of elliptic curves in the function field setting. To prove the La nglands correspondence in this context\, Drinfeld studied moduli spaces of elliptic sheaves. The categories of elliptic sheaves and Drinfeld modules are equivalent under certain conditions. Since then\, many generalization s of elliptic sheaves have been studied\, such as $\\mathcal{D}$-elliptic sheaves defined by Laumon\, Rapoport and Stuhler and Frobenius-Hecke sheav es defined by Stuhler. In this talk\, we will give a brief introduction to the function field world and introduce a new generalization of elliptic s heaves\, called generalized $\\mathcal{D}$-elliptic sheaves. We will state a uniformization theorem for the moduli space of the latter and talk abou t the proof if time permits. This builds on work of Laumon-Rapoport-Stuhle r\, of Hartl and of Rapoport-Zink.\n LOCATION:https://researchseminars.org/talk/UCGEN/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Mehmet Kıral (RIKEN AIP) DTSTART:20200909T160000Z DTEND:20200909T173000Z DTSTAMP:20260315T021505Z UID:UCGEN/5 DESCRIPTION:Title: Kl oosterman Sums for SL3 Long Word Element\nby Mehmet Kıral (RIKEN AIP) as part of UCGEN - Uluslararası Cebirsel GEometri Neşesi\n\n\nAbstract\ nUsing the reduced word decomposition of the long word element of the Weyl group element of SL3\, we give a nice expression for the long word Kloost erman sum. First classical Kloosterman sums\, their importance\, and matri x formulation will be introduced. This is joint work with Maki Nakasuji of Sophia University (Tokyo).\n LOCATION:https://researchseminars.org/talk/UCGEN/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Hülya Argüz (University of Versailles Saint-Quentin-En-Yvelines) DTSTART:20200916T150000Z DTEND:20200916T163000Z DTSTAMP:20260315T021505Z UID:UCGEN/6 DESCRIPTION:Title: An algebro-geometric view on mirror symmetry\nby Hülya Argüz (Universi ty of Versailles Saint-Quentin-En-Yvelines) as part of UCGEN - Uluslararas ı Cebirsel GEometri Neşesi\n\n\nAbstract\nMirror symmetry is a phenomeno n discovered by string theorists\, which relates physical theories obtaine d using different deformation families of Calabi-Yau manifolds. An algebro --geometric approach to mirror symmetry\, which uses tropical and log geom etric tools to construct such families of Calabi--Yau manifolds\, is provi ded by the Gross-Siebert program. In this talk we will review the most rec ent advances in this program\, and particularly report on our joint work w ith Mark Gross.\n LOCATION:https://researchseminars.org/talk/UCGEN/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Umut Varolgüneş (Stanford University) DTSTART:20200923T160000Z DTEND:20200923T173000Z DTSTAMP:20260315T021505Z UID:UCGEN/7 DESCRIPTION:Title: Ho mological mirror symmetry for chain type invertible polynomials\nby Um ut Varolgüneş (Stanford University) as part of UCGEN - Uluslararası Ceb irsel GEometri Neşesi\n\n\nAbstract\nI will start by giving a quick intro duction to classical and symplectic Picard-Lefschetz theory. Then\, I will explain the homological mirror symmetry (HMS) conjecture regarding invert ible polynomials. Finally\, I will sketch the A-side computation that goes into proving HMS in the chain type case. This is joint work with A. Polis hchuk.\n LOCATION:https://researchseminars.org/talk/UCGEN/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Kadri Ilker Berktav (Middle East Technical University) DTSTART:20200930T150000Z DTEND:20200930T163000Z DTSTAMP:20260315T021505Z UID:UCGEN/8 DESCRIPTION:Title: Hi gher Structures in Physics\nby Kadri Ilker Berktav (Middle East Techni cal University) as part of UCGEN - Uluslararası Cebirsel GEometri Neşesi \n\n\nAbstract\nThis is an overview of higher structures in physics. In th is talk\, we intend to outline the basics of derived algebraic geometry an d its essential role in encoding the formal geometric aspects of moduli sp aces of solutions to certain differential equations. Throughout the talk\, we always study objects with higher structures in a functorial perspectiv e\, and we shall focus on algebraic local models for those structures. To be more precise\, we shall be interested in derived geometric construction s and higher spaces for certain moduli problems associated with classical field theories and their defining equations\, the so-called Euler-Lagrange equations. \nTo this end\, the talk is organized into two main parts: In the first part of the talk\, we shall revisit the naïve and algebro-geome tric definition of a classical field theory together with some examples\, and then we will establish the connection between classical field theories and moduli problems. In the second part of the talk\, we first recall the basic aspects of moduli theory in a categorical perspective and explain h ow higher-categorical notions like stacks come into play to overcome certa in technical problems naturally arising in many moduli problems. In the sp irit of these discussions\, we shall also give some examples from gauge th eory and Einstein gravity.\n LOCATION:https://researchseminars.org/talk/UCGEN/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Selvi Kara (University of South Alabama) DTSTART:20201007T150000Z DTEND:20201007T163000Z DTSTAMP:20260315T021505Z UID:UCGEN/9 DESCRIPTION:Title: Mo nomial Ideals of Graphs and Their Syzygies\nby Selvi Kara (University of South Alabama) as part of UCGEN - Uluslararası Cebirsel GEometri Neşe si\n\n\nAbstract\nGiven a homogeneous ideal $I$\n in a polynomial ring \n$ R=k[x_1\,…\,x_n]$\,\n we can describe the structure of $I$\n by using it s minimal free resolution. All the information related to the minimal free resolution of $I$\n is encoded in its Betti numbers. However\, it is a di fficult problem to express Betti numbers of any homogeneous ideal in a gen eral way. Due to this difficulty\, it is common to focus on coarser invari ants of \n$I$ or particular classes of ideals. \n\nIn this talk\, we consi der monomial ideals associated to graphs. We will discuss the Castelnuovo- Mumford regularity\, projective dimension\, and extremal Betti numbers of such ideals and provide formulas for these invariants in terms of the comb inatorial data of their associated graphs. Results presented in this talk are from joint works with Biermann\, O’Keefe\, Lin\, and Casiday.\n LOCATION:https://researchseminars.org/talk/UCGEN/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Enis Kaya (University of Groningen) DTSTART:20201014T150000Z DTEND:20201014T163000Z DTSTAMP:20260315T021505Z UID:UCGEN/10 DESCRIPTION:Title: E xplicit Vologodsky Integration for Hyperelliptic Curves\nby Enis Kaya (University of Groningen) as part of UCGEN - Uluslararası Cebirsel GEomet ri Neşesi\n\n\nAbstract\nLet X be a curve over a p-adic field with semi-s table reduction and let ω be a meromorphic 1-form on X. There are two not ions of p-adic integration one may associate to this data: the Berkovich –Coleman integral which can be performed locally\; and the Vologodsky in tegral with desirable number-theoretic properties. In this talk\, we prese nt a theorem comparing the two\, and describe an algorithm for computing V ologodsky integrals in the case that X is a hyperelliptic curve. We also i llustrate our algorithm with a numerical example computed in Sage. This ta lk is partly based on joint work with Eric Katz.\n LOCATION:https://researchseminars.org/talk/UCGEN/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Irem Portakal (Otto von Guericke University Magdeburg) DTSTART:20201021T150000Z DTEND:20201021T163000Z DTSTAMP:20260315T021505Z UID:UCGEN/11 DESCRIPTION:Title: R igid toric matrix Schubert varieties\nby Irem Portakal (Otto von Gueri cke University Magdeburg) as part of UCGEN - Uluslararası Cebirsel GEomet ri Neşesi\n\n\nAbstract\nIn this talk\, we introduce the usual torus acti on on matrix Schubert varieties. In the toric case we show that these vari eties arise from a bipartite graph. We study the first order deformations of toric matrix Schubert varieties and we prove that it is rigid if and on ly if the three-dimensional faces of its associated (edge) cone are all si mplicial.\n LOCATION:https://researchseminars.org/talk/UCGEN/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Özhan Genç (Jagiellonian University) DTSTART:20201028T150000Z DTEND:20201028T163000Z DTSTAMP:20260315T021505Z UID:UCGEN/12 DESCRIPTION:Title: U lrich Trichotomy on del Pezzo Surfaces\nby Özhan Genç (Jagiellonian University) as part of UCGEN - Uluslararası Cebirsel GEometri Neşesi\n\n \nAbstract\nA vector bundle $\\mathcal{E}$ on a projective variety $X$ in $\\mathbb{P}^N$ is Ulrich if $\\rm{H}^∗(X\,E(−k))$ vanishes for $1 ≤ k ≤\\dim(X)$. It has been conjectured by Eisenbud and Schreyer that ever y projective variety carries an Ulrich bundle. Even though this conjecture has not been proved or disproved\, another interesting question is worth considering: classify projective varieties as Ulrich finite\, tame or wild type with respect to families of Ulrich bundles that they support. In thi s talk\, we will show that this trichotomy is exhaustive for certain del P ezzo surfaces with any given polarization. This talk is based on a joint w ork with Emre Coşkun.\n LOCATION:https://researchseminars.org/talk/UCGEN/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Oğuz Şavk (Boğaziçi University) DTSTART:20201104T150000Z DTEND:20201104T163000Z DTSTAMP:20260315T021505Z UID:UCGEN/13 DESCRIPTION:Title: B rieskorn spheres\, homology cobordism and homology balls\nby Oğuz Şa vk (Boğaziçi University) as part of UCGEN - Uluslararası Cebirsel GEome tri Neşesi\n\n\nAbstract\nA classical question in low-dimensional topolog y asks which \nhomology $3$-spheres bound homology $4$-balls. This questio n is fairly \naddressed to Brieskorn spheres $\\Sigma(p\,q\,r)$. Since the y are defined \nto be links of singularities $x^p+y^q+z^r=0$\, Brieskorn s pheres are \nalgebro-geometric originated $3$-manifolds.\n\nOver the years \, Brieskorn spheres also have been the main objects for \nthe understandi ng of the algebraic structure of the integral homology \ncobordism group. In this talk\, we will present several families of \nBrieskorn spheres whi ch do or do not bound integral and rational \nhomology balls. Also\, we wi ll investigate their positions in both \nintegral and rational homology co bordism groups.\n LOCATION:https://researchseminars.org/talk/UCGEN/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Bahar Acu (Northwestern University) DTSTART:20201111T150000Z DTEND:20201111T163000Z DTSTAMP:20260315T021505Z UID:UCGEN/14 DESCRIPTION:Title: U nderstanding symplectic fillings of contact manifolds via algebraic variet ies\nby Bahar Acu (Northwestern University) as part of UCGEN - Uluslar arası Cebirsel GEometri Neşesi\n\n\nAbstract\nThis talk is an attempt fo r a (pandemic-conscious) invitation to contact topology via an algebro-ge ometric approach with the caveat that we admit having little to no under standing of many concepts in algebraic geometry. A very useful strategy in studying topological manifolds is to factor them into smaller pieces.  Briefly\, an "open book decomposition" on an $n$-dimensional manifold (the open book) is a type of fibration over a circle that helps us stud y our manifold in terms of its $(n-1)$-dimensional fibers (the pages) a nd $(n-2)$-dimensional boundary of these fibers (the binding). Open book s provide a natural framework for studying the topological properties of a geometric phenomenon called "contact structures" on smooth manifolds . In this talk\, we aim to provide an exposition of results\, some of wh ich are fruits of several joint works\, concerning "symplectic fillings"  of contact manifolds given by certain classes of algebraic varieties u sing their "supporting" open books.\n LOCATION:https://researchseminars.org/talk/UCGEN/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Kadri İlker Berktav (Middle East Technical University) DTSTART:20201125T150000Z DTEND:20201125T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/15 DESCRIPTION:Title: H igher Structures in Einstein Gravity\nby Kadri İlker Berktav (Middle East Technical University) as part of UCGEN - Uluslararası Cebirsel GEome tri Neşesi\n\n\nAbstract\nThis is a talk on a recent investigation about higher structures in the theory of General Relativity. It can be also seen as a direct sequel of the previous talk “Higher Structures in Physics. ” However\, for the sake of completeness\, the talk will include a brief summary of key ideas from the aforementioned talk. In that respect\, we s hall begin with revisiting the basics of moduli theory and derived algebra ic geometry. Next\, we will report some relevant constructions and results from our work encoding various stacky formulations of Einstein Gravity.\n \nThis talk is a continuation of a previous talk of the speaker\, which yo u may find in the following link:\nhttps://www.youtube.com/watch?v=gmUfTPc M7Go&t=2060s\n LOCATION:https://researchseminars.org/talk/UCGEN/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Ayşegül Öztürkalan (Abdullah Gül University) DTSTART:20201118T150000Z DTEND:20201118T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/16 DESCRIPTION:Title: L oops in moduli spaces of real plane projective curves\nby Ayşegül Ö ztürkalan (Abdullah Gül University) as part of UCGEN - Uluslararası Ceb irsel GEometri Neşesi\n\n\nAbstract\nThe space of real algebraic plane pr ojective curves of a fixed degree has a natural stratification. The strata of top dimension consists of non-singular curves and are known up to curv es of degree 6. Topology and\, in particular\, fundamental groups of indiv idual strata have not been studied systematically. We study the stratum fo rmed by non-singular sextics with the real part consisting of 9 ovals whic h lie outside each other and divide the set of complex points. Apparently this stratum has one of the most complicated fundamental groups. In the ta lk I will study its subgroups which come from strata of singular curves an d originates from spaces of linear equivalent real divisors on a real cubi c curve.\n LOCATION:https://researchseminars.org/talk/UCGEN/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Sema Güntürkün (University of Massachusetts Amherst) DTSTART:20201202T150000Z DTEND:20201202T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/17 DESCRIPTION:Title: O n the Eisenbud-Green-Harris conjecture.\nby Sema Güntürkün (Univers ity of Massachusetts Amherst) as part of UCGEN - Uluslararası Cebirsel GE ometri Neşesi\n\n\nAbstract\nA generalization of the Macaulay’s theorem on the growth of Hilbert functions of homogeneous ideals in $K[x_1\,\\ldo ts\, x_n]$ is conjectured by Eisenbud\, Green and Harris in the 90s. The c onjecture\, also known as the EGH conjecture\, states that the lex-plus-po wers ideals show an extremal behavior among the homogeneous ideals contain ing regular sequences in terms of their Hilbert functions. In this talk\, our focus will be on a case of the EGH conjecture for the homogeneous ide als containing a regular sequence of quadratic forms. This is a joint work with Mel Hochster.\n LOCATION:https://researchseminars.org/talk/UCGEN/17/ END:VEVENT BEGIN:VEVENT SUMMARY:İzzet Coşkun (University of Illinois at Chicago) DTSTART:20201209T150000Z DTEND:20201209T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/18 DESCRIPTION:Title: B rill-Noether Theorems for moduli spaces of sheaves on surfaces\nby İz zet Coşkun (University of Illinois at Chicago) as part of UCGEN - Uluslar arası Cebirsel GEometri Neşesi\n\n\nAbstract\nIn this talk\, I will desc ribe several results on the cohomology of the general sheaf in a moduli sp ace of sheaves on a projective surface. I will discuss joint work with Jac k Huizenga on rational surfaces such as Hirzebruch surfaces and joint work with Howard Nuer and Kota Yoshioka on K3 surfaces.\n LOCATION:https://researchseminars.org/talk/UCGEN/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Burçin Güneş (Sabancı University) DTSTART:20201216T150000Z DTEND:20201216T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/20 DESCRIPTION:Title: O n nilpotent automorphism groups of function fields\nby Burçin Güneş (Sabancı University) as part of UCGEN - Uluslararası Cebirsel GEometri Neşesi\n\n\nAbstract\nWe study the automorphisms of a function field of g enus $g\\geq 2$ over an algebraically closed field of positive characteris tic $p$. More precisely\, we show that the order of a nilpotent subgroup $ G$ of its automorphism group is bounded by $16(g−1)$ when $G$ is not a $ p$-group. We show that if $|G|=16(g−1)$\, then $g−1$ is a power of $2$ . Furthermore\, we provide an infinite family of function fields attaining the bound. This is a joint work with Nurdagül Anbar.\n LOCATION:https://researchseminars.org/talk/UCGEN/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Sümeyra Sakallı (University of Arkansas) DTSTART:20210106T150000Z DTEND:20210106T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/21 DESCRIPTION:Title: S ymplectic 4-Manifolds on the Noether Line and between the Noether and Half Noether Lines\nby Sümeyra Sakallı (University of Arkansas) as part of UCGEN - Uluslararası Cebirsel GEometri Neşesi\n\n\nAbstract\nIn this talk\, first we will review some main concepts and techniques in the smoot h and symplectic 4-manifolds theory. Then we will discuss our construction s of exotic\, simply connected and symplectic 4-manifolds on the Noether l ine and between the Noether and half Noether lines via pencils of complex curves of genus one and via symplectic surgeries. We will also present a c ompletely geometric way of constructing certain configurations of Kodaira ’s singularities in the rational elliptic surfaces\, without using any m onodromy arguments.\n LOCATION:https://researchseminars.org/talk/UCGEN/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Levent Doğan (Technical University of Berlin) DTSTART:20210113T150000Z DTEND:20210113T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/22 DESCRIPTION:Title: P olynomial Time Algorithms for Torus Actions\nby Levent Doğan (Technic al University of Berlin) as part of UCGEN - Uluslararası Cebirsel GEometr i Neşesi\n\n\nAbstract\nIn this talk\, we will consider three algorithmic problems\, namely orbit equivalence\, orbit closure intersection and orbi t containment problem for actions of tori. We will describe the related in variant theory and show that all three problems admit polynomial time algo rithms.\n LOCATION:https://researchseminars.org/talk/UCGEN/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Kürşat Sözer (University of Lille) DTSTART:20210120T150000Z DTEND:20210120T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/23 DESCRIPTION:Title: T wo-dimensional extended HQFTs with arbitrary targets\nby Kürşat Söz er (University of Lille) as part of UCGEN - Uluslararası Cebirsel GEometr i Neşesi\n\n\nAbstract\nInspired by theoretical physics\, topological qua ntum field theories (TQFTs) produce manifold invariants behaving well unde r gluing. Homotopy quantum field theories (HQFTs)\, introduced by Turaev\, generalize TQFTs to manifolds equipped with continuous maps to fixed targ et space. A different generalization of TQFTs is given by extended TQFTs w hich includes lower-dimensional manifolds utilizing higher categories. In this talk\, we define and classify 2-dimensional extended HQFTs with arbit rary targets generalizing the earlier work on K(G\,1)-targets using the me thods introduced for TQFTs by Chris Schommer-Pries in 2009.\n LOCATION:https://researchseminars.org/talk/UCGEN/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Emre Şen (University of Iowa) DTSTART:20210127T150000Z DTEND:20210127T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/24 DESCRIPTION:Title: Q uivers in Algebraic Geometry: Various Examples\nby Emre Şen (Universi ty of Iowa) as part of UCGEN - Uluslararası Cebirsel GEometri Neşesi\n\n \nAbstract\nThis will be an expository talk about quivers\, and their repr esentations. We will see why quivers naturally appear in the context of al gebraic geometry and how they are useful to solve algebrogeometric problem s. In this manner\, we discuss various subjects: group actions with finit ely many orbits\, derived categories of coherent sheaves\, toric vector bu ndles\, exceptional sequences\, quiver moduli etc.\n LOCATION:https://researchseminars.org/talk/UCGEN/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Oğuzhan Yürük (TU Braunschweig) DTSTART:20210203T150000Z DTEND:20210203T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/25 DESCRIPTION:Title: U nderstanding the Regions of Multistaionarity via Symbolic Nonnegativity Ce rtificates\nby Oğuzhan Yürük (TU Braunschweig) as part of UCGEN - U luslararası Cebirsel GEometri Neşesi\n\n\nAbstract\nParameterized ordina ry differential equation systems are crucial for modeling in biochemical r eaction networks under the assumption of mass-action kinetics. Various que stions concerning the signs of multivariate polynomials in positive orthan t arise from studying the solutions' qualitative behavior with respect to parameter values. In this work\, we utilize circuit polynomials to find sy mbolic certificates of nonnegativity in order to provide further insight i nto the number of positive steady states of the n-site phosphorylation cyc le model. This is a joint work with Elisenda Feliu\, Nidhi Kaihnsa and Tim o de Wolff.\n LOCATION:https://researchseminars.org/talk/UCGEN/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Özgür Esentepe (University of Connecticut) DTSTART:20210210T150000Z DTEND:20210210T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/26 DESCRIPTION:Title: A nnihilation of cohomology over curve singularities\nby Özgür Esentep e (University of Connecticut) as part of UCGEN - Uluslararası Cebirsel GE ometri Neşesi\n\n\nAbstract\nHilbert's syzygy theorem implies that the se cond syzygy of every module over a polynomial ring S in two variables is p rojective. In fancy language\, this means that $Ext_S^3(M\,N)$ vanishes fo r every pair of modules $M\,N$. This is no longer true when we consider a quotient $R$ of $S$ by an ideal generated by a single polynomial $f$. In f act\, for every $i>0$ there is at least one pair $M\,N$ such that $Ext_R^i (M\,N)\\neq 0$. We investigate the ideal consisting of ring elements which uniformly annihilate all $Ext_R^i(M\,N)$ for sufficiently large $i$. I am dedicating this talk to students and academics of Boğaziçi University w ho are protesting against a rector appointed by the 12th president of Turk ey and I will try my best to keep it accessible to a broad audience.\n LOCATION:https://researchseminars.org/talk/UCGEN/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Sinem Odabaşı (Universidad Austral de Chile) DTSTART:20210217T150000Z DTEND:20210217T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/27 DESCRIPTION:Title: O n induced cotorsion pairs in functor category.\nby Sinem Odabaşı (Un iversidad Austral de Chile) as part of UCGEN - Uluslararası Cebirsel GEom etri Neşesi\n\n\nAbstract\nThe question of interest that motivates our wo rk is how to ensure that the category Add (A\,R-Mod) of additive functors has a projective / injective model structure without putting any condition s on the ring R. Essentially\, it is motivated by the classical projective /injective/flat model structures on the category Ch(R) of chain complexes of left R-modules.\n\n While we have been working on this problem with my collegues\, in a recent work of Henrik Holm and Peter Jorgensen published in arXiv arXiv:2101.06176\, this problem is handled by using techniques/re sults in Gorenstein Homological Algebra. \n\nFortunately\, our approach di ffers from theirs\, and includes other contexts such as module category ov er a formal triangular matrix ring.\n\nWith this objective in mind\, in th is talk we will talk about how to build "possible" Hovey cotorsion pairs^1 in Add (A\, R-Mod)\, and later we will present an explicit characterizati on of their objects. The results obtained on these cotorsion pairs in Add (A\, R-Mod) generalize the known results in the categories of chain comple xes of R-modules and modules over a formal triangular matrix ring. It is a work in progress with Sergio Estrada and Manuel Cortes Izurdiaga.\n\n1: T here is a close relation between abelian model structures in abelian categ ories and Hovey pairs\; see [Hov02]. That's why we focus on finding suitab le Hovey pairs in Add (A\, R-Mod).\n\n[Hov02] Hovey\, M. Cotorsion pairs\, model category structures\, and representation theory. Math Z 241\, 553 –592 (2002).\n LOCATION:https://researchseminars.org/talk/UCGEN/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Büşra Sert (TU Dresden) DTSTART:20210224T150000Z DTEND:20210224T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/28 DESCRIPTION:Title: C ombinatorial Methods for Minkowski Tensors of Polytopes\nby Büşra Se rt (TU Dresden) as part of UCGEN - Uluslararası Cebirsel GEometri Neşesi \n\n\nAbstract\nIntrinsic volumes of a convex body provide scalar data (vo lume\, surface area\, Euler characteristic etc. ) about the geometry of a convex body intrinsically\, i.e.\, the data doesn't depend on the ambient space. Minkowski tensors are the tensor valued generalization of intrinsic volumes. They give not only scalar data on the geometry of a convex body\ , but also information about its shape\, orientation etc..\nMoreover\, gen erating functions for moments of the uniform distribution on convex bodies provide us a way to extract entries of Minkowski volume tensors.\n\nIn t his talk\, we first give necessary background on Minkowski tensors and the ir connection to moments on polytopes. Then\, we describe Minkowski "surfa ce tensors"\, and focus on some methods to obtain their entries in the ca se of simplicial polytopes.\n\nThis is a joint work with Niklas Livchitz a nd Amy Wiebe.\n LOCATION:https://researchseminars.org/talk/UCGEN/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Emrah Sercan Yılmaz (Boğaziçi University) DTSTART:20210303T160000Z DTEND:20210303T173000Z DTSTAMP:20260315T021505Z UID:UCGEN/29 DESCRIPTION:by Emrah Sercan Yılmaz (Boğaziçi University) as part of UCG EN - Uluslararası Cebirsel GEometri Neşesi\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/UCGEN/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Habermann (London School of Geometry and Number Theory) DTSTART:20210324T160000Z DTEND:20210324T173000Z DTSTAMP:20260315T021505Z UID:UCGEN/30 DESCRIPTION:Title: H omological mirror symmetry for nodal stacky curves\nby Matthew Haberma nn (London School of Geometry and Number Theory) as part of UCGEN - Ulusla rarası Cebirsel GEometri Neşesi\n\n\nAbstract\nIn this talk I will expla in the proof of homological mirror symmetry where the B-side is a ring or chain of stacky projective lines joined nodally\, and where each irreducib le component is allowed to have a non-trivial generic stabiliser\, general ising the work of Lekili and Polishchuk. The key ingredient of the proof i s to match categorical resolutions on the A- and B-sides by identifying th em both with an intermediary category given by the derived category of mod ules of a gentle algebra. I will explain the strategy of constructing thes e resolutions on the A-- and B--sides\, as well as how to deduce homologic al mirror symmetry from this.\n LOCATION:https://researchseminars.org/talk/UCGEN/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Nursel Erey DTSTART:20210331T160000Z DTEND:20210331T173000Z DTSTAMP:20260315T021505Z UID:UCGEN/31 DESCRIPTION:Title: E dge ideals and some numerical invariants of graded resolutions\nby Nur sel Erey as part of UCGEN - Uluslararası Cebirsel GEometri Neşesi\n\nAbs tract: TBA\n LOCATION:https://researchseminars.org/talk/UCGEN/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Olgür Çelikbaş (West Virginia University) DTSTART:20210407T150000Z DTEND:20210407T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/32 DESCRIPTION:Title: O n torsion in tensor products of modules\nby Olgür Çelikbaş (West Vi rginia University) as part of UCGEN - Uluslararası Cebirsel GEometri Neş esi\n\n\nAbstract\nTensor products are fundamental objects used in many ar eas including mathematics\, physics\, and engineering.\nIn 1961 Maurice Au slander initiated the study of torsion in tensor products of finitely gene rated modules in his pioneering paper\, \nModules over unramified regular local rings (Illinois J. Math. 5\, 1961\, 631-647). Subsequently\, in 1994 \, Craig Huneke and Roger Wiegand \nextended and studied Auslander’s res ults over hypersurface rings in their influential paper\, Tensor products of modules and the rigidity of Tor \n(Math. Ann. 299\, 1994\, no. 3\, 449 –476).\n\nIn this talk I will discuss some of the results of Auslander\, and Huneke and Wiegand\, concerning the existence of torsion in tensor pr oducts\nof finitely generated modules over commutative Noetherian local ri ngs. I also plan to talk about my work on the reflexivity of tensor produc ts\, \nwhich was motivated by the second rigidity theorem of Huneke and Wi egand.\n LOCATION:https://researchseminars.org/talk/UCGEN/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Sergio Estrada (University of Murcia) DTSTART:20210414T150000Z DTEND:20210414T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/33 DESCRIPTION:Title: T he big singularity category of a non-affine scheme\nby Sergio Estrada (University of Murcia) as part of UCGEN - Uluslararası Cebirsel GEometri Neşesi\n\n\nAbstract\nA classic result of Buchweitz shows that the singul arity category of a Gorenstein local ring A is triangulated equivalent to the stable category of finitely generated Gorenstein projective A-modules and to the homotopy category of totally acyclic complexes of finitely gene rated projective A-modules. In this talk we present a non-affine version o f this result. To achieve this we will define a "big" version of Orlov´s singularity category.The talk is based on a project developed with Lars Ch ristensen (Texas Tech University) and Peder Thompson (Norwegian University of Science and Technology).\n LOCATION:https://researchseminars.org/talk/UCGEN/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Tim Tribone DTSTART:20210421T150000Z DTEND:20210421T160000Z DTSTAMP:20260315T021505Z UID:UCGEN/34 DESCRIPTION:Title: M atrix factorizations with more than two factors\nby Tim Tribone as par t of UCGEN - Uluslararası Cebirsel GEometri Neşesi\n\n\nAbstract\nGiven an element f in a regular local ring\, a matrix factorization of f is a pa ir of square matrices such that their product is $f$ times an identity mat rix of the appropriate size. These objects were originally introduced by E isenbud to study the hypersurface ring defined by f. We will discuss some of the basic theory of matrix factorizations and then specialize to a gene ralization where the factorizations have more than two factors.\n LOCATION:https://researchseminars.org/talk/UCGEN/34/ END:VEVENT END:VCALENDAR