BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ilia Itenberg (imj-prg) DTSTART:20220304T124000Z DTEND:20220304T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/1 DESCRIPTION:Title: Re al enumerative invariants and their refinement\nby Ilia Itenberg (imj- prg) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nTh e talk is devoted to several real and tropical enumerative problems. We su ggest new invariants of the projective plane (and\, more generally\, of to ric surfaces) that arise as results of an appropriate enumeration of real elliptic curves.\nThese invariants admit a refinement (according to the qu antum index) similar to the one introduced by Grigory Mikhalkin in the rat ional case. We discuss tropical counterparts of the elliptic invariants un der consideration and establish a tropical algorithm allowing one to compu te them.\nThis is a joint work with Eugenii Shustin.\n LOCATION:https://researchseminars.org/talk/OBAGS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Degtyarev (Bilkent) DTSTART:20220311T124000Z DTEND:20220311T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/2 DESCRIPTION:Title: To wards 800 conics on a smooth quartic surfaces\nby Alexander Degtyarev (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstrac t\nThis will be a technical talk where I will discuss a few computational aspects of my work in progress towards the following conjecture.\n\nConjec ture: A smooth quartic surface in P3 may contain at most 800 conics.\n\nI will suggest and compare several arithmetical reductions of the problem. T hen\, for the chosen one\, I will discuss a few preliminary combinatorial bounds and some techniques used to handle the few cases where those bounds are not sufficient.\n\nAt the moment\, I am quite confident that the conj ecture holds. However\, I am trying to find all smooth quartics containing 720 or more conics\, in the hope to find the real quartic maximizing the number of real lines and to settle yet another conjecture (recall that we count all conics\, both irreducible and reducible).\n\nConjecture: If a s mooth quartic X⊂P3 contains more than 720 conics\, then X has no lines\; in particular\, all conics are irreducible.\n\nCurrently\, similar bounds are known only for sextic K3-surfaces in P4.\n\nAs a by-product\, I have found a few examples of large configurations of conics that are not Barth- -Bauer\, i.e.\, do not contain\na 16-tuple of pairwise disjoint conics or\ , equivalently\, are not Kummer surfaces with all 16 Kummer divisors conic s.\n LOCATION:https://researchseminars.org/talk/OBAGS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthias Schütt (Hannover) DTSTART:20220318T124000Z DTEND:20220318T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/3 DESCRIPTION:Title: Fi nite symplectic automorphism groups of supersingular K3 surfaces\nby M atthias Schütt (Hannover) as part of ODTU-Bilkent Algebraic Geometry Semi nars\n\n\nAbstract\nAutomorphism groups form a classical object of study i n algebraic geometry. In recent years\, a special focus has been put on au tomorphisms of K3 surface\, the most famous example being Mukai’s classi fication of finite symplectic automorphism groups on complex K3 surfaces. Building on work of Dolgachev-Keum\, I will discuss a joint project with H isanori Ohashi (Tokyo) extending Mukai’s results to fields positive char acteristic. Notably\, we will retain the close connection to the Mathieu g roup M23 while realizing many larger groups compared to the complex settin g.\n LOCATION:https://researchseminars.org/talk/OBAGS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Emre Can Sertöz (Hannover) DTSTART:20220325T124000Z DTEND:20220325T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/4 DESCRIPTION:Title: He ights\, periods\, and arithmetic on curves\nby Emre Can Sertöz (Hanno ver) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nTh e size of an explicit representation of a given rational point on an algeb raic curve is captured by its canonical height. However\, the canonical he ight is defined through the dynamics on the Jacobian and is not particular ly accessible to computation. In 1984\, Faltings related the canonical hei ght to the transcendental "self-intersection" number of the point\, which was recently used by van Bommel-- Holmes--Müller (2020) to give a general algorithm to compute heights. The corresponding notion for heights in hig her dimensions is inaccessible to computation. We present a new method for computing heights that promises to generalize well to higher dimensions. This is joint work with Spencer Bloch and Robin de Jong.\n LOCATION:https://researchseminars.org/talk/OBAGS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Halil İbrahim Karakaş (Başkent) DTSTART:20220401T124000Z DTEND:20220401T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/5 DESCRIPTION:Title: Ar f Partitions of Integers\nby Halil İbrahim Karakaş (Başkent) as par t of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nThe colection of partitions of positive integers\, the collection of Young diagrams and the collection of numerical sets are in one to one correspondance with ea ch other. Therefore any concept in one of these collections has its counte rpart in the other collections. For example the concept of Arf numerical s emigroup in the collection of numerical sets\, gives rise to the concept o f Arf partition of a positive integer in the collection of partitions. Sev eral characterizations of Arf partitions have been given in recent works. In this talk we wil characterize Arf partitions of maximal length of posit ive integers.\nThis is a joint work with Nesrin Tutaş and Nihal Gümüşb aş from Akdeniz University.\n LOCATION:https://researchseminars.org/talk/OBAGS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Yıldıray Ozan (ODTÜ) DTSTART:20220408T124000Z DTEND:20220408T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/6 DESCRIPTION:Title: Pi card Groups of the Moduli Spaces of Riemann Surfaces with Certain Finite A belian Symmetry Groups\nby Yıldıray Ozan (ODTÜ) as part of ODTU-Bil kent Algebraic Geometry Seminars\n\n\nAbstract\nIn 2021\, H. Chen determin ed all finite abelian regular branched covers of the 2-sphere with the pro perty that all homeomorphisms of the base preserving the branch set lift t o the cover\, extending the previous works of Ghaswala-Winarski and Atalan -Medettoğulları-Ozan. In this talk\, we will present a consequence of th is classification to the computation of Picard groups of moduli spaces of complex projective curves with certain symmetries. Indeed\, we will use th e work by K. Kordek already used by him for similar computations. During t he talk we will try to explain the necessary concepts and tools following Kordek's work.\n LOCATION:https://researchseminars.org/talk/OBAGS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Ali Ulaş Özgür Kişisel (ODTÜ) DTSTART:20220415T124000Z DTEND:20220415T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/7 DESCRIPTION:Title: An upper bound on the expected areas of amoebas of plane algebraic curves\nby Ali Ulaş Özgür Kişisel (ODTÜ) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nThe amoeba of a complex plane algebraic curve has an area bounded above by $\\pi^2 d^2/2$. This is a deterministic upper bound due to Passare and Rullgard. In this talk I will argue that i f the plane curve is chosen randomly with respect to the Kostlan distribut ion\, then the expected area cannot be more than $\\mathcal{O}(d)$. The re sults in the talk will be based on our joint work in progress with Turgay Bayraktar.\n LOCATION:https://researchseminars.org/talk/OBAGS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Muhammed Uludağ (Galatasaray) DTSTART:20220422T124000Z DTEND:20220422T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/8 DESCRIPTION:Title: He yula\nby Muhammed Uludağ (Galatasaray) as part of ODTU-Bilkent Algebr aic Geometry Seminars\n\n\nAbstract\nThis talk is about the construction o f a space H and its boundary on which the group PGL(2\,Q) acts. The ultima te aim is to recover the action of PSL(2\,Z) on the hyperbolic plane as a kind of boundary action.\n LOCATION:https://researchseminars.org/talk/OBAGS/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Melih Üçer (Yıldırım Beyazıt) DTSTART:20220429T124000Z DTEND:20220429T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/9 DESCRIPTION:Title: Bu rau Monodromy Groups of Trigonal Curves\nby Melih Üçer (Yıldırım Beyazıt) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstrac t\nFor a trigonal curve on a Hirzebruch surface\, there are several notion s of monodromy ranging from a very coarse one in S_3 to a very fine one in a certain subgroup of Aut(F_3)\, and one group in this range is PSL(2\,Z) . Except for the special case of isotrivial curves\, the monodromy group ( the subgroup generated by all monodromy actions) in PSL(2\,Z) is a subgrou p of genus-zero and conversely any genus-zero subgroup is the monodromy gr oup of a trigonal curve (This is a result of Degtyarev).\n\nA slightly fin er notion in the same range is the monodromy in the Burau group Bu_3. The aforementioned result of Degtyarev imposes obvious restrictions on the mon odromy group in this case but without a converse result. Here we show that there are additional non-obvious restrictions as well and\, with these re strictions\, we show the converse as well.\n LOCATION:https://researchseminars.org/talk/OBAGS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Sutherland (MIT) DTSTART:20221014T124000Z DTEND:20221014T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/10 DESCRIPTION:Title: S ato-Tate groups of abelian varieties\nby Andrew Sutherland (MIT) as pa rt of ODTU-Bilkent Algebraic Geometry Seminars\n\nLecture held in ODTÜ Ma thematics department Room M-203.\n\nAbstract\nLet A be an abelian variety of dimension g defined over a number field K. As defined by Serre\, the S ato-Tate group ST(A) is a compact subgroup of the unitary symplectic group USp(2g) equipped with a map that sends each Frobenius element of the abso lute Galois group of K at primes p of good reduction for A to a conjugacy class of ST(A) whose characteristic polynomial is determined by the zeta f unction of the reduction of A at p. Under a set of axioms proposed by Ser re that are known to hold for g <= 3\, up to conjugacy in Usp(2g) there is a finite list of possible Sato-Tate groups that can arise for abelian var ieties of dimension g over number fields. Under the Sato-Tate conjecture (which is known for g=1 when K has degree 1 or 2)\, the asymptotic distrib ution of normalized Frobenius elements is controlled by the Haar measure o f the Sato-Tate group.\n\nIn this talk I will present a complete classific ation of the Sato-Tate groups that can and do arise for g <= 3.\n\nThis is joint work with Francesc Fite and Kiran Kedlaya.\n\nThis is a hybrid talk . To request Zoom link please write to sertoz@bilkent.edu.tr\n LOCATION:https://researchseminars.org/talk/OBAGS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Emre Coşkun (METU) DTSTART:20221021T124000Z DTEND:20221021T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/11 DESCRIPTION:Title: M cKay correspondence I\nby Emre Coşkun (METU) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\nLecture held in ODTÜ Mathematics departmen t Room M-203.\n\nAbstract\nJohn McKay observed\, in 1980\, that there is a one-to-one correspondence between the nontrivial finite subgroups of SU(2 ) (up to conjugation) and connected Euclidean graphs (other than the Jorda n graph) up to isomorphism. In these talk\, we shall first examine the fin ite subgroups of SU(2) and then establish this one-to-one correspondence\, using the representation theory of finite groups.\n\nThis is a hybrid tal k. To request a Zoom link please write to sertoz@bilkent.edu.tr\n LOCATION:https://researchseminars.org/talk/OBAGS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Emre Coşkun (METU) DTSTART:20221104T124000Z DTEND:20221104T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/12 DESCRIPTION:Title: M cKay correspondence II\nby Emre Coşkun (METU) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\nLecture held in ODTÜ Mathematics Departme nt Room M-203.\n\nAbstract\nLet $G \\subset SU(2)$ be a finite subgroup co ntaining $-I$\, and let \n$Q$ be the corresponding Euclidean graph. Given an orientation on $Q$\, \none can define the (bounded) derived category of the representations \nof the resulting quiver. Let $\\bar{G} = G / {\\pm I}$. Then one can \nalso define the category $Coh_{\\bar{G}}(\\mathbb{P}^1 )$ of \n$\\bar{G}$-equivariant coherent sheaves on the projective line\; t his \nabelian category also has a (bounded) derived category. In the secon d \nof these talks dedicated to the McKay correspondence\, we establish an \nequivalence between the two derived categories mentioned above.\n\nThis is a hybrid talk. To request Zoom link please write to sertoz@bilkent.edu .tr.\n LOCATION:https://researchseminars.org/talk/OBAGS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Emre Can Sertöz (Hannover) DTSTART:20221111T124000Z DTEND:20221111T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/13 DESCRIPTION:Title: C omputing limit mixed Hodge structures\nby Emre Can Sertöz (Hannover) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nConside r a smooth family of varieties over a punctured disk that is extended to a flat family over the whole disk\, e.g.\, consider a 1-parameter family of hypersurfaces with a central singular fiber. The Hodge structures (i.e. p eriods) of smooth fibers exhibit a divergent behavior as you approach the singular fiber. However\, Schmid's nilpotent orbit theorem states that thi s divergence can be "regularized" to construct a limit mixed Hodge structu re. This limit mixed Hodge structure contains detailed information about t he geometry and arithmetic of the singular fiber. I will explain how one c an compute such limit mixed Hodge structures in practice and give a demons tration of my code.\n LOCATION:https://researchseminars.org/talk/OBAGS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Müfit Sezer (Bilkent) DTSTART:20221118T124000Z DTEND:20221118T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/14 DESCRIPTION:Title: V ector invariants of a permutation group over characteristic zero\nby M üfit Sezer (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\ n\n\nAbstract\nWe consider a finite permutation group acting naturally on a vector space V​​ over a field k​​. A well known theorem of Göbe l asserts that the corresponding ring of invariants k[V]^G​​ is genera ted by invariants of degree at most dim V choose 2​​. We point out th at if the characteristic of k​​ is zero then the top degree of the vec tor coinvariants k[mV]_G​​ is also bounded above by n choose 2​​ i mplying that Göbel's bound almost holds for vector invariants as well in characteristic zero.\nThis work is joint with F. Reimers.\n LOCATION:https://researchseminars.org/talk/OBAGS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Cesare Veniani (Stuttgart) DTSTART:20221125T124000Z DTEND:20221125T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/15 DESCRIPTION:Title: N on-degeneracy of Enriques surfaces\nby Davide Cesare Veniani (Stuttgar t) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nEnri ques' original construction of Enriques surfaces involves a 10-dimensional family of sextic surfaces in the projective space which are non-normal al ong the edges of a tetrahedron. The question whether all Enriques surfaces arise through Enriques' construction has remained open for more than a ce ntury.\n\nIn two joint works with G. Martin (Bonn) and G. Mezzedimi (Hanno ver)\, we have now settled this question in all characteristics by studyin g particular configurations of genus one fibrations\, and two invariants c alled maximal and minimal non-degeneracy. The proof involves so-called `tr iangle graphs' and the distinction between special and non-special 3-seque nces of half-fibers.\n\nIn this talk\, I will present the problem and expl ain its solution\, illustrating further possible developments and applicat ions.\n LOCATION:https://researchseminars.org/talk/OBAGS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Fatma Karaoğlu (Gebze Teknik) DTSTART:20221202T124000Z DTEND:20221202T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/16 DESCRIPTION:Title: S mooth cubic surfaces with 15 lines\nby Fatma Karaoğlu (Gebze Teknik) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIt is w ell-known that a smooth cubic surface has 27 lines over an algebraically c losed field. If the field is not closed\, however\, fewer lines are possib le. The next possible case is that of smooth cubic surfaces with 15 lines. This work is a contribution to the problem of classifying smooth cubic su rfaces with 15 lines over fields of positive characteristic. We present an algorithm to classify such surfaces over small finite fields. Our classif ication algorithm is based on a new normal form of the equation of a cubic surface with 15 lines and less than 10 Eckardt points. The case of cubic surfaces with more than 10 Eckardt points is dealt with separately. Classi fication results for fields of order at most 13 are presented and a verifi cation using an enumerative formula of Das is performed. Our work is based on a generalization of the old result due to Cayley and Salmon that there are 27 lines if the field is algebraically closed.\n\n Smooth cubic surfa ces with 15 lines\n LOCATION:https://researchseminars.org/talk/OBAGS/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Meral Tosun (Galatasaray) DTSTART:20221209T124000Z DTEND:20221209T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/17 DESCRIPTION:Title: J ets schemes and toric embedded resolution of rational triple points\nb y Meral Tosun (Galatasaray) as part of ODTU-Bilkent Algebraic Geometry Sem inars\n\n\nAbstract\nOne of the aims of J.Nash in an article on the arcs s paces (1968) was to understand resolutions of singularities via the arcs l iving on the singular variety. He conjectured that there is a one-to-one relation between a family of the irreducible components of the jet schemes of an hypersurface centered at the singular point and the essential divis ors on every resolution. J.Fernandez de Bobadilla and M.Pe Pereira (2011) have shown his conjecture\, but the proof is not constructive to get the r esolution from the arc space. We will construct an embedded toric resoluti on of singularities of type rtp from the irreducible components of the jet schemes.\n\nThis is a joint work with B.Karadeniz\, H. Mourtada and C.Ple nat.\n LOCATION:https://researchseminars.org/talk/OBAGS/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Özhan Genç (Jagiellonian) DTSTART:20221216T124000Z DTEND:20221216T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/18 DESCRIPTION:Title: F inite Length Koszul Modules and Vector Bundles\nby Özhan Genç (Jagie llonian) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract \nLet $V$ be a complex vector space of dimension $n\\ge 2$ and $K$ be a s ubset of $\\bigwedge^2V$ of dimension $m$. Denote the Koszul module by $W( V\,K)$ and its corresponding resonance variety by $\\mathcal R(V\,K)$. Pap adima and Suciu showed that there exists a uniform bound $q(n\,m)$ such th at the graded component of the Koszul module $W_q(V\,K)=0$ for all $q\\ge q(n\,m)$ and for all $(V\,K)$ satisfying $\\mathcal R(V\,K)=\\{0\\}$. In t his talk\, we will determine this bound $q(n\,m)$ precisely\, and find an upper bound for the Hilbert series of these Koszul modules. Then we will c onsider a class of Koszul modules associated to vector bundles.\n LOCATION:https://researchseminars.org/talk/OBAGS/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Salvatore Floccari (Hannover) DTSTART:20230303T124000Z DTEND:20230303T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/19 DESCRIPTION:Title: S ixfolds of generalized Kummer type and K3 surfaces\nby Salvatore Flocc ari (Hannover) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAb stract\nThe classical Kummer construction associates a K3 surface to any 2 -dimensional complex torus. In my talk I will present an analogue of this construction\, which involves the two most well-studied deformation types of hyper-Kähler manifolds in dimension 6. Namely\, starting from any hype r-Kähler sixfold K of generalized Kummer type\, I am able to construct ge ometrically a hyper-Kähler manifold of K3^[3]-type. When K is projective\ , the associated variety is birational to a moduli space of sheaves on a u niquely determined K3 surface. As application of this construction I will show that the Kuga-Satake correspondence is algebraic for many K3 surfaces of Picard rank 16.\n LOCATION:https://researchseminars.org/talk/OBAGS/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Dominico Valloni (Hannover) DTSTART:20230310T124000Z DTEND:20230310T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/20 DESCRIPTION:Title: R ational points on the Noether-Lefschetz locus of K3 moduli spaces\nby Dominico Valloni (Hannover) as part of ODTU-Bilkent Algebraic Geometry Sem inars\n\n\nAbstract\nLet L be an even hyperbolic lattice and denote by $\\ mathcal{F}_L$ the moduli space of L-polarized K3 surfaces. This parametriz es K3 surfaces $X$ together with a primitive embedding of lattices $L \\ho okrightarrow \\mathrm{NS}(X)$ and\, when $L = \\langle 2d \\rangle $\, one recovers the classical moduli spaces of 2d-polarized K3 surfaces. In this talk\, I will introduce a simple criterion to decide whether a given $\\o verline{ \\mathbb{Q}}$-point of $\\mathcal{F}_L$ has generic Néron-Sever i lattice (that is\, $\\mathrm{NS}(X) \\cong L$). The criterion is of arit hmetic nature and only uses properties of covering maps between Shimura va rieties.\n LOCATION:https://researchseminars.org/talk/OBAGS/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Slawomir Rams (Jagiellonian) DTSTART:20230317T124000Z DTEND:20230317T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/21 DESCRIPTION:Title: O n maximal number of rational curves of bounded degree on certain surfaces \nby Slawomir Rams (Jagiellonian) as part of ODTU-Bilkent Algebraic Ge ometry Seminars\n\n\nAbstract\nI will discuss bounds on the number of rati onal curves of fixed degree on surfaces of various types with special emph asis on polarized Enriques surfaces. In particular\, I will sketch the pro of of the bound of at most 12 rational curves of degree at most d on high -degree Enriques surfaces (based mostly on joint work with Prof. M. Schue tt (Hannover)).\n LOCATION:https://researchseminars.org/talk/OBAGS/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Türkü Özlüm Çelik (Boğaziçi) DTSTART:20230324T124000Z DTEND:20230324T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/22 DESCRIPTION:Title: S ingular curves and their theta functions\nby Türkü Özlüm Çelik (B oğaziçi) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstra ct\nRiemann's theta function becomes polynomial when the underlying curve degenerates to a singular curve. We will give a classification of such cur ves accompanied by historical remarks on the topic. We will touch on relat ions of such theta functions with solutions of the Kadomtsev-Petviashvili hierarchy if time permits.\n LOCATION:https://researchseminars.org/talk/OBAGS/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Tolga Karayayla (ODTÜ) DTSTART:20230331T124000Z DTEND:20230331T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/23 DESCRIPTION:Title: O n a class of non-simply connected Calabi-Yau 3-folds with positive Euler c haracteristic-Part 1\nby Tolga Karayayla (ODTÜ) as part of ODTU-Bilke nt Algebraic Geometry Seminars\n\n\nAbstract\nIn this talk I will present a class of non-simply connected Calabi-Yau 3-folds with positive Euler cha racteristic which are the quotient spaces of fixed-point-free group action s on desingularizations of singular Schoen 3-folds. A Schoen 3-fold is the fiber product of two rational elliptic surfaces with section. Smooth Scho en 3-folds are simply connected CY 3-folds. Desingularizations of certain singular Schoen 3-folds by small resolutions have the same property. If a finite group G acts freely on such a 3-fold\, the quotient is again a CY 3 -fold. I will present how to classify such group actions using the automor phism groups of rational elliptic surfaces with section. The smooth Schoen 3-fold case gives 0 Euler characteristic whereas the singular case result s in positive Euler characteristic for the quotient CY threefolds.\n LOCATION:https://researchseminars.org/talk/OBAGS/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Tolga Karayayla (ODTÜ) DTSTART:20230407T124000Z DTEND:20230407T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/24 DESCRIPTION:Title: O n a class of non-simply connected Calabi-Yau 3-folds with positive Euler c haracteristic-Part 2\nby Tolga Karayayla (ODTÜ) as part of ODTU-Bilke nt Algebraic Geometry Seminars\n\n\nAbstract\nIn this talk I will present a class of non-simply connected Calabi-Yau 3-folds with positive Euler cha racteristic which are the quotient spaces of fixed-point-free group action s on desingularizations of singular Schoen 3-folds. A Schoen 3-fold is the fiber product of two rational elliptic surfaces with section. Smooth Scho en 3-folds are simply connected CY 3-folds. Desingularizations of certain singular Schoen 3-folds by small resolutions have the same property. If a finite group G acts freely on such a 3-fold\, the quotient is again a CY 3 -fold. I will present how to classify such group actions using the automor phism groups of rational elliptic surfaces with section. The smooth Schoen 3-fold case gives 0 Euler characteristic whereas the singular case result s in positive Euler characteristic for the quotient CY threefolds.\n LOCATION:https://researchseminars.org/talk/OBAGS/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Craig van Coevering (Boğaziçi) DTSTART:20230414T124000Z DTEND:20230414T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/25 DESCRIPTION:Title: E xtremal Kähler metrics and the moment map\nby Craig van Coevering (Bo ğaziçi) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstrac t\nAn extremal Kähler metric is a canonical Kähler metric\, introduced b y E.\nCalabi\, which is somewhat more general than a constant scalar curva ture Kähler metric. The existence of such a metric is an ongoing research subject and expected to be equivalent to some form of geometric stability of the underlying polarized complex manifold $(M\, J\, [\\omega])$ –the Yau-Tian-Donaldson Conjecture. Thus it is no surprise that there is a mo ment map\, the scalar curvature (A. Fujiki\, S. Donaldson)\, and the probl em can be described as an infinite dimensional version of the familiar fin ite dimensional G.I.T.\n\nI will describe how the moment map can be used t o describe the local space of extremal metrics on a symplectic manifold. E ssentially\, the local picture can be reduced to finite dimensional G.I.T. In particular\, we can construct a course moduli space of extremal Kähle r metrics with a fixed polarization $[\\omega] \\in H^2(M\, \\mathbb{R})$ \, which is an Hausdorff complex analytic space\n LOCATION:https://researchseminars.org/talk/OBAGS/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Mesut Şahin (Hacettepe) DTSTART:20230428T120000Z DTEND:20230428T130000Z DTSTAMP:20260422T225757Z UID:OBAGS/26 DESCRIPTION:Title: V anishing ideals and codes on toric varieties\nby Mesut Şahin (Hacette pe) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nMot ivated by applications to the theory of error-correcting codes\, we give a n algorithmic method for computing a generating set for the ideal generate d by $\\beta$-graded polynomials vanishing on a subset of a simplicial com plete toric variety $X$ over a finite field $\\mathbb{F}_q$\, parameterize d by rational functions\, where $\\beta$ is a $d\\times r$ matrix whose co lumns generate a subsemigroup $\\mathbb{N}\\beta$ of $\\mathbb{N}^d$. We a lso give a method for computing the vanishing ideal of the set of $\\mathb b{F}_q$-rational points of $X$. We talk about some of its algebraic invari ants related to basic parameters of the corresponding evaluation code. Whe n $\\beta=[w_1 \\cdots w_r]$ is a row matrix corresponding to a numerical semigroup $\\mathbb{N}\\beta=\\langle w_1\,\\dots\,w_r \\rangle$\, $X$ is a weighted projective space and generators of its vanishing ideal is relat ed to the generators of the defining (toric) ideals of some numerical semi group rings corresponding to semigroups generated by subsets of $\\{w_1\,\ \dots\,w_r\\}$.\n LOCATION:https://researchseminars.org/talk/OBAGS/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Ekin Ozman (Boğaziçi) DTSTART:20230505T124000Z DTEND:20230505T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/27 DESCRIPTION:Title: T he p ranks of Prym varieties\nby Ekin Ozman (Boğaziçi) as part of OD TU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn this talk we will start with basics of moduli space of curves\, coverings of curves\, p-ran ks and mention the differences in characteristics 0 and positive character istics.Then we'll define Prym variety which is a central object of study i n arithmetic geometry like Jacobian variety. The goal of the talk is to u nderstand various existence results about Prym varieties of given genus\, p-rank and characteristics of the base field. This is joint work with Rach el Pries.\n LOCATION:https://researchseminars.org/talk/OBAGS/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Degtyarev (Bilkent) DTSTART:20230512T124000Z DTEND:20230512T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/28 DESCRIPTION:Title: C ounting lines on polarized K3-surfaces\nby Alexander Degtyarev (Bilken t) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nCoun ting or estimating the number of lines or\, more generally\, low degree\nr ational curves on a polarized algebraic surface is a classical problem goi ng\nback almost 1.5 centuries. After a brief historical excurse\, I will t ry to\ngive an account of the considerable progress made in the subject in the last\ndecade or so\, mainly related to various (quasi-)polarizations of\n$K3$-surfaces: \n\n$\\bullet$\nlines on $K3$-surfaces with any polariz ation\,\n\n$\\bullet$\nlines on low degree $K3$-surfaces with singularitie s\,\n\n$\\bullet$\nconics on low degree $K3$-surfaces.\n\nIf time permits\ , I will briefly discuss other surfaces/varieties as well.\n\nSome parts o f this work are joint projects\n(some still in progress) with Ilia Itenber g\, Slavomir Rams\, Ali\nSinan Sertöz.\n LOCATION:https://researchseminars.org/talk/OBAGS/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Degtyarev (Bilkent) DTSTART:20231013T124000Z DTEND:20231013T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/30 DESCRIPTION:Title: S ingular real plane sextic curves without real points\nby Alexander Deg tyarev (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\n Abstract\n(joint with Ilia Itenberg)\nIt is a common understanding that an y reasonable geometric question about K3\n-surfaces can be restated and so lved in purely arithmetical terms\, by means of an appropriately defined h omological type. For example\, this works well in the study of singular co mplex sextic curves in P2 or quartic surfaces in P3 (see [1\,2])\, as we ll as in that of smooth real ones (see [4\,6]). However\, when the two are combined (both singular and real curves or surfaces)\, the approach fails as the `"obvious'' concept of homological type does not fully reflect the geometry (cf.\, e.g.\, [3] or [5]).\n\nWe show that the situation can be repaired if the curves in question have empty real part or\, more generall y\, have no real singular points\; then\, one can indeed confine oneself t o the homological types consisting of the exceptional divisors\, polarizat ion\, and real structure.\n\nStill\, the resulting arithmetical problem is not quite straightforward\, but we manage to solve it and obtain a satisf actory classification in the case of empty real part\; it matches all know n results obtained by an alternative purely geometric approach. In the gen eral case of smooth real part\, we also have a formal classification\; how ever\, establishing a correspondence between arithmetic and geometric inva riants (most notably\, the distribution of ovals among the components of a reducible curve) still needs a certain amount of work.\n\nThis project wa s conceived and partially completed during our joint stay at the Max-Planc k-Institut für Mathematik\, Bonn. The speaker is partially supported by T ÜBİTAK project 123F111.\n\nREFERENCES\n\n[1]. Ayşegül Akyol and Alex D egtyarev\, Geography of irreducible plane sextics\, Proc. Lond. Math. Soc. (3) 111 (2015)\, no. 6\, 13071337. MR 3447795\n\n[2]. Çisem Güneş Akt aş\, Classi\ncation of simple quartics up to equisingular deformation\, H iroshima Math. J. 47 (2017)\, no. 1\, 87112. MR 3634263\n\n[3]. I. V. Ite nberg\, Curves of degree 6 with one nondegenerate double point and groups of monodromy of nonsingular curves\, Real algebraic geometry (Rennes\, 199 1)\, Lecture Notes in Math.\, vol. 1524\, Springer\, Berlin\, 1992\, pp. 2 67288. MR 1226259\n\n[4]. V. M. Kharlamov\, On the classi\ncation of nons ingular surfaces of degree 4 in RP3\n with respect to rigid isotopies\, Fu nktsional. Anal. i Prilozhen. 18 (1984)\, no. 1\, 4956. MR 739089\n\n[5]. Sébastien Moriceau\, Surfaces de degré 4 avec un point double non dég énéré dans l'espace projectif réel de dimension 3\, Ph.D. thesis\, 200 4.\n\n[6]. V. V. Nikulin\, Integer symmetric bilinear forms and some of th eir geometric applications\, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979)\, no . 1\, 111177\, 238\, English translation: Math USSR-Izv. 14 (1979)\, no. 1\, 103167 (1980). MR 525944 (80j:10031)\n LOCATION:https://researchseminars.org/talk/OBAGS/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Turgay Akyar (METU) DTSTART:20231020T124000Z DTEND:20231020T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/31 DESCRIPTION:Title: S pecial linear series on real trigonal curves\nby Turgay Akyar (METU) a s part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nFor a gi ven trigonal curve $C$\, geometric features of the Brill-Noether variety $W_d^r(C)$ parametrizing complete linear series of degree $d$ and dimensio n at least $r$ are well known. If the curve $C$ is real\, then $W_d^r(C)$ is also defined over $\\mathbb{R}$. In this talk we will see the basic pro perties of real linear series and discuss the topology of the real locus $ W_d^r(C)(\\mathbb{R})$ for some specific cases.\n LOCATION:https://researchseminars.org/talk/OBAGS/31/ END:VEVENT BEGIN:VEVENT SUMMARY:İzzet Coşkun (UIC) DTSTART:20231027T124000Z DTEND:20231027T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/32 DESCRIPTION:Title: D ense orbits of the PGL(n)-action on products of flag varieties\nby İz zet Coşkun (UIC) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\ nAbstract\nIt is a classical and very useful fact that any n+2 linearly ge neral points in P^n are projectively equivalent. In this talk\, I will con sider generalizations of this statement to higher dimensional linear space s. The group PGL(n) acts on products of Grassmannians or more generally fl ag varieties. I will discuss cases when this action has a dense orbit. Thi s talk is based on joint work with Demir Eken\, Abuzer Gündüz\, Majid Ha dian\, Chris Yun and Dmitry Zakharov.\n LOCATION:https://researchseminars.org/talk/OBAGS/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Çisem Güneş Aktaş (Abdullah Gül) DTSTART:20231103T124000Z DTEND:20231103T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/33 DESCRIPTION:Title: G eometry of equisingular strata of quartic surfaces with simple singulariti es\nby Çisem Güneş Aktaş (Abdullah Gül) as part of ODTU-Bilkent A lgebraic Geometry Seminars\n\n\nAbstract\nThe geometry of the equisingular strata of curves\, surfaces\, etc. is one of the central problems of K3-s urfaces. Thanks to the global Torelli theorem and surjectivity of the per iod map\, the equisingular deformation classification of singular projecti ve models of K3-surfaces with any given polarization becomes a mere comput ation. The most popular models studied intensively in the literature are p lane sextic curves and spatial quartic surfaces. Using the arithmetical re duction\, Akyol and Degtyarev [1] completed the problem of equisingular de formation classification of simple plane sextics. Simple quartic surfaces which play the same role in the realm of spatial surfaces as sextics do fo r curves\, are a relatively new subject\, promising interesting discoverie s.\n\nIn this talk\, we discuss the problem of classifying quartic surface s with simple singularities up to equisingular deformations by reducing th e problem to an arithmetical problem about lattices. This research [3] or iginates from our previous study [2] where the classification was given o nly for nonspecial quartics\, in the spirit of Akyol ve Degtyarev [1]. Ou r principal result is extending the classification to the whole space of s imple quartics and\, thus\, completing the equisingular deformation classi fication of simple quartic surfaces.\n\n [1] Akyol\, A. ve Degt yarev\, A.\, 2015. Geography of irreducible plane sex- tics. Proc. Lond. M ath. Soc. (3)\, 111(6)\, 13071337. ISSN 0024-6115. doi:10.1112/plms/pdv053 .\n [2] Güneş Aktaş\, Ç\, 2017. Classification of simple qu artics up to equisin- gular deformation. Hiroshima Math. J.\, 47(1)\, 8711 2. ISSN 0018-2079. doi:10.32917/hmj/1492048849.\n\n [3] Güneş Aktaş\, Ç\, to appear in Deformation classification of quartic surfaces with simple singularities. Rev. Mat. Iberoam. doi:10.4171/RMI/1431\n LOCATION:https://researchseminars.org/talk/OBAGS/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Nurömür Hülya Argüz (Georgia) DTSTART:20231110T124000Z DTEND:20231110T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/34 DESCRIPTION:Title: Q uivers and curves in higher dimensions\nby Nurömür Hülya Argüz (Ge orgia) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\n Quiver Donaldson-Thomas invariants are integers determined by the geometry of moduli spaces of quiver representations. I will describe a corresponde nce between quiver Donaldson-Thomas invariants and Gromov-Witten counts of rational curves in toric and cluster varieties. This is joint work with P ierrick Bousseau (arXiv:2302.02068 and arXiv:arXiv:2308.07270).\n LOCATION:https://researchseminars.org/talk/OBAGS/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Deniz Genlik (OSU) DTSTART:20231117T124000Z DTEND:20231117T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/35 DESCRIPTION:Title: H olomorphic anomaly equations for $\\mathbb{C}^n/\\mathbb{Z}_n$\nby Den iz Genlik (OSU) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nA bstract\nIn this talk\, we present certain results regarding the higher ge nus Gromov-Witten theory of $\\mathbb{C}^n/\\mathbb{Z}_n$ obtained by stud ying its cohomological field theory structure in detail. Holomorphic anoma ly equations are certain recursive partial differential equations predicte d by physicists for the Gromov-Witten potential of a Calabi-Yau threefold. We prove holomorphic anomaly equations for $\\mathbb{C}^n/\\mathbb{Z}_n$ for any $n\\geq 3$. In other words\, we present a phenomenon of holomorphi c anomaly equations in arbitrary dimension\, a result beyond the considera tion of physicists. The proof of this fact relies on showing that the Grom ov-Witten potential of $\\mathbb{C}^n/\\mathbb{Z}_n$ lies in a certain pol ynomial ring. This talk is based on the joint work arXiv:2301.08389 with H sian-Hua Tseng.\n LOCATION:https://researchseminars.org/talk/OBAGS/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Ali Ulaş Özgür Kişisel (METU) DTSTART:20231124T124000Z DTEND:20231124T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/36 DESCRIPTION:Title: R andom Algebraic Geometry and Random Amoebas\nby Ali Ulaş Özgür Kiş isel (METU) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstr act\nRandom algebraic geometry studies variable properties of typical alge braic varieties as opposed to invariant properties or extremal properties. For instance\, a complex algebraic projective plane curve is always topol ogically connected\, which is an invariant property\; a real algebraic pr ojective plane curve of degree $d$ has\, by a classical theorem of Harnack \, at most $\\displaystyle{g+1=(d-1)(d-2)/2+1}$ connected components where $g$ denotes genus\, which is an extremal property\; whereas a random real algebraic projective degree $d$ plane curve in a suitable precise sense ( to be explained in the talk) has an expected number of connected component s of order $d$. In this talk\, I will first present the setup and some of the main known results of the field of random algebraic geometry. I will t hen proceed to discuss some of our results on the expected properties of a moebas of random complex algebraic varieties\, based on a joint work with Turgay Bayraktar\, and another joint work with Jean-Yves Welschinger.\n LOCATION:https://researchseminars.org/talk/OBAGS/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Nil Şahin (Bilkent) DTSTART:20231201T124000Z DTEND:20231201T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/37 DESCRIPTION:Title: M onotonicity of the Hilbert Functions of some monomial curves\nby Nil Şahin (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\n Abstract\nLet $S$ be a 4-generated pseudo-symmetric semigroup generated by the positive integers $\\{n_1\, n_2\, n_3\, n_4\\}$ where $\\gcd(n_1\, n_ 2\, n_3\, n_4) = 1$. $k$ being a field\, let $k[S]$ be the corresponding s emigroup ring and\n$I_S$ be the defining ideal of $S$. $f_*$ being the hom ogeneous summand of $f$\, tangent cone of $S$ is $k[S]/{I_S}_*$ where ${I_ S}_* =< f_*|f \\in I_S >$. We will show that the "Hilbert function of the local ring (which is isomorphic to the tangent cone) for a 4 generated ps eudo-symmetric numerical semigroup $$ is always non-de creasing when $n_1K apranov's higher-dimensional Langlands reciprocity principle for GL(n) \nby Kazım İlhan İkeda (Boğaziçi) as part of ODTU-Bilkent Algebraic G eometry Seminars\n\n\nAbstract\nAbelian class field theory\, which describ es (including the arithmetic of) all abelian extensions of local and globa l fields using algebraic and analytic objects related to the ground field via Artin reciprocity laws has undergone two generalizations. The first on e\, which is still largely conjectural\, is the non-abelian class field th eory of Langlands\, is an extreme generalization of the abelian class fiel d theory\, describes the whole absolute Galois groups of local and global fields using automorphic objects related to the ground field via the celeb rated Langlands reciprocity principles\, (and more generally via functoria lity principles). The second generalization is the higher-dimensional clas s field theory of Kato and Parshin\, which describes (including the arithm etic of) all abelian extensions of higher-dimensional local fields and hig her-dimensional global fields (function fields of schemes of finite type o ver ℤ) using this time K-groups of objects related to the ground field v ia Kato-Parshin reciprocity laws.\nSo it is a very natural question to ask the possibility to construct higher-dimensional Langlands reciprocity pri nciple. In this direction\, as an answer to this question\, Kapranov propo sed a conjectural framework for higher-dimensional Langlands reciprocity p rinciple for GL(n). In this talk\, we plan to sketch this conjectural fram ework of Kapranov (where we plan to focus on the local case only).\n LOCATION:https://researchseminars.org/talk/OBAGS/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Degtyarev (Bilkent) DTSTART:20231215T124000Z DTEND:20231215T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/39 DESCRIPTION:Title: L ines on singular quartic surfaces via Vinberg\nby Alexander Degtyarev (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstrac t\nLarge configurations of lines (or\, more generally\, rational curves of low degree) on algebraic surfaces appear in various contexts\, but only in the case of cubic surfaces the picture is complete. Our principal goal is the classification of large configurations of lines on quasi-polarized K3-surfaces in the presence of singularities. To the best of our knowledge \, no attempt has been made to attack this problem from the lattice-theore tical\, based on the global Torelli theorem\, point of view\; some partial results were obtained by various authors using ``classical'' algebraic g eometry\, but very little is known. The difficulty is that\, given a polar ized N\\'eron--Severi lattice\, computing the classes of smooth rational c urves depends on the choice of a Weyl chamber of a certain root lattice\, which is not unique.\n\nWe show that this ambiguity disappears and the alg orithm becomes deterministic provided that sufficiently many classes of li nes are fixed. Based on this fact\, Vinberg's algorithm\, and a combinator ial version of elliptic pencils\, we develop an algorithm that\, in princi ple\, would list all extended Fano graphs. After testing it on octic K3-su rfaces\, we turn to the most classical case of simple quartics where\, pri or to our work\, only an upper bound of 64 lines (Veniani\, same as in the smooth case) and an example of 52 lines (the speaker) were known. We show that\, in the presence of singularities\, the sharp upper bound is indeed 52\, substantiating the long standing conjecture (by the speaker) that th e upper bound is reduced by the presence of smooth rational curves of lowe r degree.\n\nWe also extend the classification (I. Itenberg\, A.S. Sertöz \, and the speaker) of large configurations of lines on smooth quartics do wn to 49 lines. Remarkably\, most of these configurations were known befor e.\n\nThis project was conceived and partially completed during our joint stay at the Max-Planck-Institut f\\ür Mathematik\, Bonn. The speaker is p artially supported by TÜBİTAK project 123F111.\n LOCATION:https://researchseminars.org/talk/OBAGS/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Pınar Mete (Balıkesir) DTSTART:20240223T124000Z DTEND:20240223T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/40 DESCRIPTION:Title: O n some invariants of the tangent cones of numerical semigroup rings\nb y Pınar Mete (Balıkesir) as part of ODTU-Bilkent Algebraic Geometry Semi nars\n\n\nAbstract\nThe minimal free resolution is a very useful tool for extracting information about modules. Many important numerical invariants of a module such as Hilbert function and Betti numbers can be deduced from its minimal free resolution. Stamate gave a broad survey on these topics when the modules are the semigroup ring or its tangent cone for a numerica l semigroup S. He also stated the problem of describing the Betti numbers and the minimal free resolution for the tangent cone when S is 4-generated semigroup which is symmetric. In this talk\, I will first give some of ou r results\, based on a joint work with E.E. Zengin on the problem. Then\, I will talk about our ongoing study which is an application\nof the Apery table of the numerical semigroup to determine some properties of its tange nt cone.\n\nDI. STAMATE\, Betti numbers for numerical semigroup rings. Mul tigraded Algebra and Applications\,\n238\, 133-157\, Springer Proceedings in Mathematics and Statistics\, Springer\, Cham 2018.\n LOCATION:https://researchseminars.org/talk/OBAGS/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Turgay Bayraktar (Sabancı) DTSTART:20240301T124000Z DTEND:20240301T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/41 DESCRIPTION:Title: E quidistribution for Zeros of Random Polynomial Systems\nby Turgay Bayr aktar (Sabancı) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\n Abstract\nA classical result of Erdös and Turan asserts that for a univar iate complex polynomial whose middle coefficients are comparable to the ex tremal ones\, the zeros accumulate near the unit circle. We prove the ana logues result for random polynomial mappings with Bernoulli coefficients. The talk is based on the joint work with Çiğdem Çelik.\n LOCATION:https://researchseminars.org/talk/OBAGS/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Kaan Bilgin (Amsterdam) DTSTART:20240315T124000Z DTEND:20240315T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/42 DESCRIPTION:Title: T he Langlands – Kottwitz method for GSpin Shimura varieties and eigenvari eties\nby Kaan Bilgin (Amsterdam) as part of ODTU-Bilkent Algebraic Ge ometry Seminars\n\n\nAbstract\nGiven a connected reductive algebraic group G over a number field F\, the global Langlands (reciprocity) conjecture r oughly predicts that\, there should be a correspondence between (automorph ic side) the isomorphism classes of (cuspidal\, cohomological) automorphi c representations of G and (Galois side) the isomorphism classes of (irred ucible\, locally de-Rham) Galois representations for Gal(\\bar{F} / F) tak ing values in the Langlands dual group of G.\n\nIn the first part of this talk\, I will sketch the main argument of our expected theorem/proof for ( automorphic to Galois) direction of this conjecture\, for G = GSpin(n\,2)\ , n odd and F to be totally real\, under 3 technical assumptions (for time being)\, namely we assume that automorphic representations are additional ly “non-CM” and “non-endoscopic” and “std-regular”.\n\nIn the second part\, mainly following works of Loeffler and Chenevier on overconv ergent p-adic automorphic forms\, I will present an idea to remove the st d-regular assumption on the theorem via the theory of eigenvarieties.\n LOCATION:https://researchseminars.org/talk/OBAGS/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Haydar Göral (İYTE) DTSTART:20240322T124000Z DTEND:20240322T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/43 DESCRIPTION:Title: A rithmetic Progressions in Finite Fields\nby Haydar Göral (İYTE) as p art of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn 1927\, v an der Waerden proved a theorem regarding the existence of arithmetic prog ressions in any partition of the positive integers with finitely many clas ses. In 1936\, a strengthening of van der Waerden's theorem was conjecture d by Erdös and Turan\, which states that any subset of positive integers with a positive upper density contains arbitrarily long arithmetic progres sions. In 1975\, Szemeredi developed his combinatorial method to resolve t his conjecture\, and the affirmative answer to Erdös and Turan's conjectu re is now known as Szemeredi's theorem. As well as in the integers\, Szeme redi-type problems have been extensively studied in subsets of finite fiel ds. While much work has been done on the problem of whether subsets of fin ite fields contain arithmetic progressions\, in this talk we concentrate o n how many arithmetic progressions we have in certain subsets of finite fi elds. The technique is based on certain types of Weil estimates. We obtain an asymptotic for the number of k-term arithmetic progressions in squares with a better error term. Moreover our error term is sharp and best possi ble when k is small\, owing to the Sato-Tate conjecture. This work is supp orted by the Scientific and Technological Research Council of Turkey with the project number 122F027.\n LOCATION:https://researchseminars.org/talk/OBAGS/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Büşra Karadeniz Şen (Gebze Technical University) DTSTART:20240329T124000Z DTEND:20240329T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/44 DESCRIPTION:Title: B oundaries of the dual Newton polyhedron may describe the singularity\n by Büşra Karadeniz Şen (Gebze Technical University) as part of ODTU-Bil kent Algebraic Geometry Seminars\n\n\nAbstract\nWe are dealing with a hype rsurface $X\\subset\\mathbb{C}^3$\n having non-isolated singularities.We c onstruct an embedded toric resolution of $X$\n using some specific vectors in its dual Newton polyhedron. To do this\, we first define the profile o f a full dimensional cone and we establish a relation between the jet vect ors and the integer points in the profile.\n\nThis is a part of the joint work with C. Plénat and M. Tosun.\n\nReferences
\n[1] A. Altintaş Sh arland\, C. O. Oğuz\, M. Tosun and Z.aferiakopoulos\, An algorithm to find nonisolated forms of rational singularities\, In preparation.
\n[2] C. Bouvier and G. Gonzalez-Sprinberg\, Systéme générateur min imal\, diviseurs essentiels et G-désingularisations de variétés torique \, Tohoku Math. J.\, 47\, 1995.
\n[3] B. Karadeniz Şen\, C. Plén at and M. Tosun\, Minimality of a toric embedded resolution of singular ities after Bouvier-Gonzalez-Sprinberg\, Kodai Math J.\, accepted\, 20 24.\n LOCATION:https://researchseminars.org/talk/OBAGS/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Enis Kaya (KU Leuven) DTSTART:20240405T124000Z DTEND:20240405T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/45 DESCRIPTION:Title: p -adic Integration Theories on Curves\nby Enis Kaya (KU Leuven) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nFor curves ove r the field of p-adic numbers\, there are two notions of p-adic integratio n: Berkovich-Coleman integrals which can be performed locally\, and Vologo dsky integrals with desirable number-theoretic properties. These integrals have the advantage of being insensitive to the reduction type at p\, but are known to coincide with Coleman integrals in the case of good reduction . Moreover\, there are practical algorithms available to compute Coleman i ntegrals.\n\nBerkovich-Coleman and Vologodsky integrals\, however\, differ in general. In this talk\, we give a formula for passing between them. To do so\, we use combinatorial ideas informed by tropical geometry. We also introduce algorithms for computing Berkovich-Coleman and Vologodsky integ rals on hyperelliptic curves of bad reduction. By covering such a curve by certain open spaces\, we reduce the computation of Berkovich-Coleman inte grals to the known algorithms on hyperelliptic curves of good reduction. W e then convert the Berkovich-Coleman integrals into Vologodsky integrals u sing our formula. We illustrate our algorithm with a numerical example.\n\ nThis talk is partly based on joint work with Eric Katz from the Ohio Stat e University.\n LOCATION:https://researchseminars.org/talk/OBAGS/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Ichiro Shimada (Hiroshima) DTSTART:20240419T124000Z DTEND:20240419T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/46 DESCRIPTION:Title: R eal line arrangements and vanishing cycles\nby Ichiro Shimada (Hiroshi ma) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nWe investigate the topology of a double cover of a complex affine plane branc hing along a nodal real line arrangement.We define certain topological 2-c ycles in the double plane using the real structure of the arrangement.Thes e cycles resemble vanishing cycles of Lefschetz.We then calculate their i ntersection numbers.\n LOCATION:https://researchseminars.org/talk/OBAGS/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaacov Kopeliovich (Connecticut) DTSTART:20240426T124000Z DTEND:20240426T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/47 DESCRIPTION:Title: T he fundamental group of compact algebraic curve above complex numbers\ nby Yaacov Kopeliovich (Connecticut) as part of ODTU-Bilkent Algebraic Geo metry Seminars\n\n\nAbstract\nIt is well known that fundamental curves abo ve complex numbers have 2g generators where g is the genus of the curve w ith one non trivial relation that is the commutation relation. Surprisingl y I haven’t found a proof of this well known fact in the literature.\nIn this talk I will attempt to fill in the gap and show how this can be show n in a straightforward matter.\n LOCATION:https://researchseminars.org/talk/OBAGS/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Meirav Amram (SCE) DTSTART:20240503T124000Z DTEND:20240503T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/48 DESCRIPTION:Title: I nteresting methods to classify algebraic curves and surfaces\nby Meira v Amram (SCE) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbs tract\nWe present a few algebraic\, geometric and topological methods that we use in the classification of algebraic curves and surfaces. We speak about a few invariants of the classification as well. We discuss degenerat ion of algebraic surfaces\, the calculation of fundamental groups and some computational methods that help with these calculations.\n LOCATION:https://researchseminars.org/talk/OBAGS/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Degtyarev (Bilkent) DTSTART:20240510T124000Z DTEND:20240510T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/49 DESCRIPTION:Title: S ingular real plane sextic curves with smooth real part\nby Alexander D egtyarev (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n \nAbstract\nFor a change\, I will give a detailed proof of one of our join t results announced in an earlier talk\, viz. the fact that the equisingul ar equivariant deformation type of a real plane sextic curve with smooth r eal part is determined by its real homological type (in the most naïve me aning of the term)\; this theorem has been used to obtain a complete class ification of such curves. The principal goal is introducing the newer gene ration into the fascinating theory of K3-surfaces\, real aspects thereof\, and algebra/number theory involved.\n\nThis is a joint work in progress w ith Ilia Itenberg.\n LOCATION:https://researchseminars.org/talk/OBAGS/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Emre Can Sertöz (Leiden) DTSTART:20241011T124000Z DTEND:20241011T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/50 DESCRIPTION:Title: C omputing transcendence and linear relations of 1-periods\nby Emre Can Sertöz (Leiden) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\n Abstract\nI will sketch a modestly practical algorithm to compute all line ar relations with algebraic coefficients between any given finite set of 1 -periods. As a special case\, we can algorithmically decide transcendence of 1-periods. This is based on the "qualitative description" of these rela tions by Huber and Wüstholz. We combine their result with the recent work on computing the endomorphism ring of abelian varieties. This is a work i n progress with Jöel Ouaknine (MPI SWS) and James Worrell (Oxford).\n LOCATION:https://researchseminars.org/talk/OBAGS/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Veniani (Stuttgart) DTSTART:20241018T124000Z DTEND:20241018T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/51 DESCRIPTION:Title: E ntropy and non-degeneracy of Enriques surfaces\nby Davide Veniani (Stu ttgart) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\ nThe entropy of an algebraic surface serves as an invariant that quantifie s the complexity of its automorphism group. Recently\, K3 surfaces with ze ro entropy have been classified by Brandhorst-Mezzedimi and Yu. ​​​ ​​In this talk\, I will discuss joint work with Martin (Bonn) and Mezz edimi (Bonn) concerning the classification of Enriques surfaces with zero entropy. To conclude\, I will propose a conjecture on the connection betwe en zero entropy and the non-degeneracy invariant.\n LOCATION:https://researchseminars.org/talk/OBAGS/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Degtyarev (Bilkent) DTSTART:20241025T124000Z DTEND:20241025T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/52 DESCRIPTION:Title: R eal plane sextic curves with smooth real part\nby Alexander Degtyarev (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstrac t\nWe have obtained the complete deformation classification of singular re al plane sextic curves with smooth real part\, i.e.\, those without real s ingular points. This was made possible due to the fact that\, under the as sumption\, contrary to the general case\, the equivariant equisingular def ormation type is determined by the so-called real homological type in its most naïve sense\, i.e.\, the homological information about the polarizat ion\, singularities\, and real structure\; one does not need to compute th e fundamental polyhedron of the group generated by reflections and identif y the classes of ovals therein. Should time permit\, I will outline our pr oof of this theorem.\n\nAs usual\, this classification leads us to a numbe r of observations\, some of which we have already managed to generalize. T hus\, we have an Arnol’d-Gudkov-Rokhlin type congruence for close to max imal surfaces (and\, hence\, even degree curves) with certain singularitie s. Another observation (which has not been quite understood yet and may tu rn out K3-specific) is that the contraction of any empty oval of a type I real scheme results in a bijection of the sets of deformation classes.\n(j oined work with Ilia Itenberg)\n LOCATION:https://researchseminars.org/talk/OBAGS/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Enis Kaya (KU Leuven) DTSTART:20241101T124000Z DTEND:20241101T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/53 DESCRIPTION:Title: R ational curves on del Pezzo surfaces\nby Enis Kaya (KU Leuven) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn this talk\, we explore the connection between the enumerative geometry of rational cu rves on del Pezzo surfaces over a field k and the arithmetic properties of k. In particular\, we classify the number of k-rational lines and conic f amilies that can occur on del Pezzo surfaces of degrees 3 through 9 in ter ms of the Galois theory of k\, and we give partial results in degrees 1 an d 2. Our results generalize well-known theorems in the setting of smooth c ubic surfaces. This is joint work in progress with Stephen McKean\, Sam St reeter and Harkaran Uppal.\n LOCATION:https://researchseminars.org/talk/OBAGS/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Ali Ulaş Özgür Kişisel (METU) DTSTART:20241108T124000Z DTEND:20241108T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/54 DESCRIPTION:Title: I rreversible odd degree curves in $\\mathbb{RP}^2$\nby Ali Ulaş Özgü r Kişisel (METU) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\ nAbstract\nA smooth hypersurface $X\\subset \\mathbb{RP}^{n+1}$ of degree $d$ is called reversible if its defining homogeneous polynomial $f$ can be continuously deformed to $-f$ without creating singularities during the d eformation. The question of reversibility was discussed in the paper title d ``On the deformation chirality of real cubic fourfolds'' by Finashin and Kharlamov. For $n=1$\, the case of plane curves\, and $d\\leq 5$ odd\, it is known that all smooth curves of degree $d$ are reversible. Our goal in this talk is to present an obstruction for reversibility of odd degree cu rves and use it in particular to demonstrate that there exist irreversible curves in $\\mathbb{RP}^2$ for all odd degrees $d\\geq 7$. This talk is b ased on joint work in progress with Ferit Öztürk.\n LOCATION:https://researchseminars.org/talk/OBAGS/54/ END:VEVENT BEGIN:VEVENT SUMMARY:İrem Portakal (Max Planck at Leipzig) DTSTART:20241115T124000Z DTEND:20241115T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/55 DESCRIPTION:Title: N onlinear algebra in game theory\nby İrem Portakal (Max Planck at Leip zig) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nn 1950\, Nash published a very influential two-page paper proving the existe nce of Nash equilibria for any finite game. The proof uses an elegant appl ication of the Kakutani fixed-point theorem from the field of topology. Th is opened a new horizon not only in game theory\, but also in areas such a s economics\, computer science\, evolutionary biology\, and social science s. It has\, however\, been noted that in some cases the Nash equilibrium f ails to predict the most beneficial outcome for all players. To address th is\, generalizations of Nash equilibria such as correlated and dependency equilibria were introduced. In this talk\, I elaborate on how nonlinear al gebra is indispensable for studying undiscovered facets of these concepts of equilibria in game theory.\n LOCATION:https://researchseminars.org/talk/OBAGS/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Slawomir Rams (Jagiellonian]) DTSTART:20241122T124000Z DTEND:20241122T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/56 DESCRIPTION:Title: C ounting lines on projective surfaces\nby Slawomir Rams (Jagiellonian]) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn the last decade most questions concerning line configurations on degree-four surfaces in three-dimensional projective space have been answered. In cont rast\, far less is known in the case of degree-d surfaces for d>4\n even i n complex case. In my talk I will discuss the best known bound for number of lines on degree-d\n surfaces in three-dimensional projective space (b ased on joint work with Thomas Bauer and Matthias Schuett).\n LOCATION:https://researchseminars.org/talk/OBAGS/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Emre Coşkun (METU) DTSTART:20241129T124000Z DTEND:20241129T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/57 DESCRIPTION:Title: S tability Conditions I\nby Emre Coşkun (METU) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn moduli problems\, one usuall y needs to impose some sort of "stability" on the objects being classified in order to have well-behaved moduli spaces. Generalizing this concept\, in 2007\, Bridgeland defined "stability conditions" on a triangulated cate gory and proved that\, under some mild conditions\, the set of stability c onditions can be given the structure of a complex manifold. In this three- part series\, we shall explore this construction. We shall also give examp les of stability conditions when the underlying triangulated category is t he derived category of coherent sheaves on a smooth\, projective variety.\ n\nReference: Bridgeland\, Tom. Stability conditions on triangulated categ ories. Ann. of Math. (2) 166 (2007)\, no.2\, 317–345.\n LOCATION:https://researchseminars.org/talk/OBAGS/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Emre Coşkun (METU) DTSTART:20241206T124000Z DTEND:20241206T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/58 DESCRIPTION:Title: S tability Conditions II\nby Emre Coşkun (METU) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn moduli problems\, one usual ly needs to impose some sort of "stability" on the objects being classifie d in order to have well-behaved moduli spaces. Generalizing this concept\, in 2007\, Bridgeland defined "stability conditions" on a triangulated cat egory and proved that\, under some mild conditions\, the set of stability conditions can be given the structure of a complex manifold. In this three -part series\, we shall explore this construction. We shall also give exam ples of stability conditions when the underlying triangulated category is the derived category of coherent sheaves on a smooth\, projective variety. \n\nReference: Bridgeland\, Tom. Stability conditions on triangulated cate gories. Ann. of Math. (2) 166 (2007)\, no.2\, 317–345.\n LOCATION:https://researchseminars.org/talk/OBAGS/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Degtyarev (Bilkent) DTSTART:20250228T124000Z DTEND:20250228T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/59 DESCRIPTION:Title: S plit hyperplane sections on polarized K3-surfaces\nby Alexander Degtya rev (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbs tract\nI will discuss a new result which is an unexpected outcome\, follow ing a question by Igor Dolgachev\, of a long saga about smooth rational cu rves on (quasi-)polarized $K3$-surfaces. The best known example of a $K3$- surface is a quartic surface in space. A simple dimension count shows that a typical quartic contains no lines. Obviously\, some of them do and\, ac cording to B.~Segre\, the maximal number is $64$ (an example is to be work ed out). The key r\\^ole in Segre's proof (as well as those by other autho rs) is played by plane sections that split completely into four lines\, co nstituting the dual adjacency graph $K(4)$. A similar\, though less used\, phenomenon happens for sextic $K3$-surfaces in~$\\mathbb{P}^4$ (complete intersections of a quadric and a cubic): a split hyperplane section consis ts of six lines\, three from each of the two rulings\, on a hyperboloid (t he section of the quadric)\, thus constituting a $K(3\,3)$.\n\nGoing furth er\, in degrees $8$ and $10$ one's sense of beauty suggests that the graph s should be the $1$-skeleton of a $3$-cube and Petersen graph\, respectfu lly. However\, further advances to higher degrees required a systematic st udy of such $3$-regular graphs and\, to my great surprise\, I discovered t hat typically there is more than one! Even for sextics one can also imagin e the $3$-prism (occurring when the hyperboloid itself splits into two pla nes).\n\nThe ultimate outcome of this work is the complete classification of the graphs that occur as split hyperplane sections (a few dozens) and t hat of the configurations of split sections within a single surface (manag eable starting from degree $10$). In particular\, answering Igor's origina l question\, the maximal number of split sections on a quartic is $72$\, w hereas on a sextic in $\\mathbb{P}^4$ it is $40$ or $76$\, depending on th e question asked. The ultimate champion is the Kummer surface of degree~$1 2$: it has $90$ split hyperplane sections.\n\nThe tools used (probably\, n ot to be mentioned) are a fusion of graph theory and number theory\, sewn together by the geometric insight.\n LOCATION:https://researchseminars.org/talk/OBAGS/59/ END:VEVENT BEGIN:VEVENT SUMMARY:John Christian Ottem (Oslo) DTSTART:20250307T124000Z DTEND:20250307T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/60 DESCRIPTION:Title: F ano varieties with torsion in the third cohomology group\nby John Chri stian Ottem (Oslo) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n \nAbstract\nI will explain a construction of Fano varieties with torsion i n their third cohomology group. The examples are constructed as double cov ers of linear sections of rank loci of symmetric matrices\, and can be see n as higher-dimensional analogues of the Artin– Mumford threefold. As an application\, we will answer a question of Voisin on the coniveau and str ong coniveau filtrations of rationally connected varieties.\n LOCATION:https://researchseminars.org/talk/OBAGS/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Emre Coşkun (METU) DTSTART:20250314T124000Z DTEND:20250314T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/61 DESCRIPTION:Title: S tability conditions on K3 surfaces\nby Emre Coşkun (METU) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nStability conditio ns have been a topic of intense research in recent years. The present talk will review briefly their definition and basic properties as well as the existence of stability conditions on curves\, and outline the construction of stability conditions on a K3 surface.\n\n(MR2373143\, MR2376815\, MR40 93206\, MR2998828\, MR3729077)\n LOCATION:https://researchseminars.org/talk/OBAGS/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Selma Altınok Bhupal (Hacettepe) DTSTART:20250321T124000Z DTEND:20250321T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/62 DESCRIPTION:Title: T he Algebra of Generalised Splines\nby Selma Altınok Bhupal (Hacettepe ) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nClasi cal splines are piecewise polynomial functions over polyhedral complexes w ith a certain degree of smoothness at the intersections of adjacent faces. They are widely used in applications of different areas\, ranging from ap proximation theory to geometric modelling. Alternativaly\, splines can be interpreted as a collection of polynomial labeling the vertices of a (com pinatorial) graph\, with adjacent vertex-labels differing by the power of an affine line form attacthed to the edge. The concept of splines can be g eneralized to define on graphs with edge labels over arbitrary rings. Such splines are called generalized splines.\n\nIn this talk\, we give a brief description of what generalized splines are on arbitrary garphs and their properties. We explain algebraic geometric and combinatorial motivations behind studying generalized splines. In the rest of the talk\, we mainly focus on the module structure of generalized splines and discuss their bas is.\n LOCATION:https://researchseminars.org/talk/OBAGS/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Mahir Bilen Can (Tulane) DTSTART:20250328T124000Z DTEND:20250328T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/63 DESCRIPTION:Title: T wo new families of spherical varieties\nby Mahir Bilen Can (Tulane) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nMany fami liar varieties\, such as Grassmannians\, toric varieties\, symmetric space s\, and algebraic monoids\, arise naturally as representation-theoretic ob jects. Understanding their geometric and representation-theoretic distinct ions and similarities often reveals deeper underlying structures and resul ts. In this talk\, we introduce two new families of spherical varieties: n early toric and doubly spherical. We will discuss their intriguing connect ions to combinatorics and representation theory\, with a focus on their ma nifestations among Schubert varieties. This presentation is based on joint work with Nestor Diaz Morera (Fitchburg State University\, USA)\, Pinaki Saha (IIT Delhi\, India)\, and Senthamarai Kannan (Chennai Mathematical In stitute\, India).\n LOCATION:https://researchseminars.org/talk/OBAGS/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Sema Salur (Rochester/Bilkent) DTSTART:20250411T124000Z DTEND:20250411T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/65 DESCRIPTION:Title: M anifolds with Special Holonomy and Applications\nby Sema Salur (Roches ter/Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbst ract\nThe talk will focus on manifolds with special holonomy\, a class of spaces whose infinitesimal symmetries play a crucial role in M-theory comp actifications. M-theory\, often referred to as the "theory of everything\, " has emerged in recent decades as a leading candidate for unifying the fo ur fundamental forces of nature: electromagnetism\, gravity\, and the weak and strong nuclear forces.\n\nWe will begin with a brief introduction to Calabi-Yau and G₂ manifolds\, followed by an overview of my recent resea rch on the connections between symplectic\, contact\, and calibrated struc tures in these manifolds.\n LOCATION:https://researchseminars.org/talk/OBAGS/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Yves Welschinger (Institut Camille Jordan Université Lyon 1) DTSTART:20250418T124000Z DTEND:20250418T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/66 DESCRIPTION:Title: A moeba measures of random complex plane curves\nby Jean-Yves Welschinge r (Institut Camille Jordan Université Lyon 1) as part of ODTU-Bilkent Alg ebraic Geometry Seminars\n\n\nAbstract\nI will estimate the asymptotic beh avior of the expected measure of the amoeba of complex plane curves. Given a collection of complex bidisks of size inverse to the square root of the degree\, it involves a lower estimate of the probability that one of thes e bidisk be a submanifold chart of a complex plane curve. This is a joint work with Ali Ulaş Özgür Kişisel.\n LOCATION:https://researchseminars.org/talk/OBAGS/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Hasan Suluyer (METU) DTSTART:20250425T124000Z DTEND:20250425T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/67 DESCRIPTION:Title: P encils of Conic-Line Curves\nby Hasan Suluyer (METU) as part of ODTU-B ilkent Algebraic Geometry Seminars\n\n\nAbstract\nA pencil is a line in th e projective space of complex homogeneous polynomials of some degree d > 2 . The number m of curves whose irreducible components are only lines in so me pencils of degree d curves plays an important role for the existence of special line arrangements\, which are called (m\,d)-nets. It was proved t hat the number m\, independent of d\, cannot exceed 4 for an (m\,d)-net. W hen the degree of each irreducible component of a curve is at most 2\, thi s curve is called a conic-line curve and it is a union of lines or irreduc ible conics in the complex projective plane. Our main goal is to find an u pper bound on the number m of such curves in pencils in CP^2 with the numb er of concurrent lines in these pencils.\n\nIn this talk\, we study the re strictions on the number m of conic-line curves in special pencils. The mo st general result we obtain is the relation between upper bounds on m and the number of concurrent lines in these pencils. We construct a one-parame ter family of pencils such that each pencil in the family contains exactly 4 conic-line curves.\n LOCATION:https://researchseminars.org/talk/OBAGS/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Ratko Darda (Sabancı) DTSTART:20250509T124000Z DTEND:20250509T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/68 DESCRIPTION:Title: M anin's Conjecture and stacks\nby Ratko Darda (Sabancı) as part of ODT U-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nGiven a system of pol ynomial equations\, one may ask how many solutions it has in the rational numbers. If there are infinitely many\, we further ask about the number of solutions of bounded "size." The answer depends heavily on the geometry o f the variety defined by the system. When the variety is Fano—meaning th at the top wedge power of the tangent bundle is ample—the "correct" math ematical framework is provided by Manin's conjecture\, which predicts the asymptotic number of rational points of bounded height.\n\nAnother importa nt conjecture in a similar spirit is Malle's conjecture\, which predicts t he number of Galois extensions of the rational numbers with bounded discri minant.\n\nWe explain how both conjectures can be viewed as special cases of a single conjecture concerning the number of rational points of bounded height on stacks. We then discuss some recent advances\, including the po sitive characteristic. This talk is based on joint work with Takehiko Yasu da.\n LOCATION:https://researchseminars.org/talk/OBAGS/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Bayram Tekin (Bilkent) DTSTART:20251017T124000Z DTEND:20251017T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/69 DESCRIPTION:Title: A rank-4 tensor Riemann would have loved plus spinor-techniques in differen tial geometry\nby Bayram Tekin (Bilkent) as part of ODTU-Bilkent Algeb raic Geometry Seminars\n\n\nAbstract\nI would like to discuss two topics t hat have proved very useful in the parts of differential geometry used in General Relativity and other theories of gravity. The first one is the int roduction of a divergence-free rank 4 tensor which was hiding in plain sig ht up until our paper ( Phys. Rev. D 99 (2019) 4\, 044026). The second top ic will include formulating differential geometry in terms of Weyl spinors which are fundamental representations of SL(2\,C).\n LOCATION:https://researchseminars.org/talk/OBAGS/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Türkü Özlüm Çelik (Max Planck Institute of Molecular Cell Bio logy and Genetics) DTSTART:20251024T124000Z DTEND:20251024T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/70 DESCRIPTION:Title: I nteraction Networks via Grassmannians\nby Türkü Özlüm Çelik (Max Planck Institute of Molecular Cell Biology and Genetics) as part of ODTU-B ilkent Algebraic Geometry Seminars\n\n\nAbstract\nWhen can a network of mu tually reinforcing N components remain stable? To approach such questions\ , we describe the interactions through generalized Lotka–Volterra equati ons—a broad class of dynamical systems modeling how components influence one another over time. This formulation leads to a family of semi-algebra ic sets determined by the sign pattern of the parameters. These sets encod e positivity conditions defining regions of potential coexistence\, with p olynomial degrees growing exponentially in N. Embedding the parameter spac e into the real Grassmannian Gr(N\,2N) transforms these conditions into si gn relations governed by the Grassmann–Plücker equations and oriented m atroids. This geometric reformulation yields a realization problem through which we detect impossible interaction networks and study the algebraic s tructure underlying stability. If time permits\, we will also touch on how these structures connect to algebraic curves. This talk is based on our r ecent work arXiv:2509.00165.\n LOCATION:https://researchseminars.org/talk/OBAGS/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Farbod Shokrieh (Washington) DTSTART:20251031T134000Z DTEND:20251031T144000Z DTSTAMP:20260422T225757Z UID:OBAGS/71 DESCRIPTION:Title: G raphs in algebraic and arithmetic geometry\nby Farbod Shokrieh (Washin gton) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nG raphs can be viewed as (non-archimedean) analogs of Riemann surfaces. For example\, there is a notion of Jacobians for graphs. More classically\, gr aphs can be viewed as electrical networks. I will explain the interplay be tween these points of view and some applications in arithmetic geometry.\n \nNotice that this talk starts at 16:40 Türkiye time (+3GMT)\n LOCATION:https://researchseminars.org/talk/OBAGS/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Halil İbrahim Karakaş (Başkent) DTSTART:20251107T124000Z DTEND:20251107T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/72 DESCRIPTION:Title: O n the enumeration of Arf numerical semigroups with given multiplicity and conductor\nby Halil İbrahim Karakaş (Başkent) as part of ODTU-Bilke nt Algebraic Geometry Seminars\n\n\nAbstract\nThe number of numerical semi groups with given Frobenious number (or conductor\, or genus) is one of th e topics that is studied by many researchers. In our previous works\, we h ave given parametrizations of Arf numerical semigroups of small multiplici ty and obtained formulas for the number of Arf numerical semigroups with m ultiplicity less than 14 and arbitrary conductor. I presented part of thes e results in ODTÜ-Bikent AG seminars 6 years ago. We noticed that the num ber of Arf numerical semigroups with multiplicity $m$ and conductor $c$ is (eventually) constant for some $m$ (especially for prime $m$) when rest ricted to some congruence classes of $c$ modulo $m$. In a recent work with N. Tutaş\, we have characterized those multiplicities $m$ and congruence classes of $c$ modulo $m$ for which the above property holds. This talk w ill be based on [Karakaş H İ and Tutaş N\, (2025)\, On the enumeration of Arf numerical semigroups with given multiplicity and conductor\, Semigr oup Forum 110\, 308-316.] where the above characterization is given.\n LOCATION:https://researchseminars.org/talk/OBAGS/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Slawomir Rams (Jagiellonian) DTSTART:20251114T124000Z DTEND:20251114T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/73 DESCRIPTION:Title: M aximal configurations of rational curves on K3-surfaces of high degrees\nby Slawomir Rams (Jagiellonian) as part of ODTU-Bilkent Algebraic Geom etry Seminars\n\n\nAbstract\nOne of unexpected consequences of the orbibun dle Miyaoka-Yau-Sakai inequality is a bound on the maximal number of rat ional degree-d curves on smooth complex K3-surfaces of given degree obtai ned by Miyaoka in 2009. After recalling the necessary notions\, in my tal k I will present various results concerning the question whether the abov e bound is sharp for rational (resp. smooth rational) curves on K3-surfa ces of high degree. \n\nBased on joint work with M. Schuett (Hannover) an d A. Degtyarev (Ankara).\n LOCATION:https://researchseminars.org/talk/OBAGS/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Mohammed Sadek (Sabancı) DTSTART:20251121T124000Z DTEND:20251121T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/74 DESCRIPTION:Title: T orsion Subgroups of Hyperelliptic Jacobian Varieties\nby Mohammed Sade k (Sabancı) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbst ract\nIn this talk\, we explore some number theoretic aspects of hyperelli ptic curves. It is known that the number of isomorphism classes of hyperel liptic curves with the same discriminant over a fixed number field is fini te. A more challenging task is to count\, if not list\, all such isomorphi sm classes. We also present explicit constructions of hyperelliptic Jacobi an varieties with rational torsion points of prescribed order.\n LOCATION:https://researchseminars.org/talk/OBAGS/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Syed Waqar Ali Shah (Bilkent) DTSTART:20251128T124000Z DTEND:20251128T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/75 DESCRIPTION:Title: E uler systems for exterior square motives\nby Syed Waqar Ali Shah (Bilk ent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nTh e Birch–Swinnerton-Dyer conjecture relates the behavior of the L-functio n of an elliptic curve at its central point to the rank of its group of ra tional points. The Bloch–Kato conjecture generalizes this principle to a broad family of motivic Galois representations\, predicting a precise rel ationship between the order of vanishing of motivic L-functions at integer values and the structure of the associated Selmer groups. Since the found ational work of Kolyvagin in the nineties\, Euler systems have played a ce ntral role in approaching these conjectures\, and in recent years their sc ope has expanded significantly within the automorphic setting of Shimura v arieties.\n\nIn this talk\, I will focus on unitary Shimura varieties GU(2 \,2)\, whose middle-degree cohomology realizes the exterior square of the four-dimensional Galois representations attached to certain automorphic re presentations of GL_4. The period integral formula of Pollack–Shah for e xterior square L-functions has a natural motivic interpretation\, suggesti ng the feasibility of constructing a nontrivial Euler system. A key obstac le to this construction is the failure of a suitable multiplicity-one prop erty\, which has long prevented the verification of the certain norm relat ions required for Euler system methods. I will present a new approach that overcomes this difficulty. The resulting Euler system in the middle-degre e cohomology of GU(2\,2) provides the first nontrivial evidence toward the Bloch–Kato conjecture for exterior square motives and opens several pro mising avenues for further arithmetic applications. This is joint work wit h Andrew Graham and Antonio Cauchi.\n LOCATION:https://researchseminars.org/talk/OBAGS/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Nil Şahin (Bilkent) DTSTART:20251205T124000Z DTEND:20251205T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/76 DESCRIPTION:Title: N umerical semigroups with multiplicity one more than its width\nby Nil Şahin (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\n Abstract\nA numerical semigroup S is called Sally type if its multiplicity is one more than its width. In this talk\, we will analyze the properties of numerical semigroups of Sally type with embedding dimension $e-1$ and $e-2$ where $e$ denotes the multiplicity. We compute the minimal number of generators of the defining ideal using Hochster's Formula then we deter mine the minimal generators.\n\nJoint work with Dubey\, Goel\, Singh and S rinivasan\n LOCATION:https://researchseminars.org/talk/OBAGS/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Degtyarev (Bilkent) DTSTART:20251212T124000Z DTEND:20251212T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/77 DESCRIPTION:Title: A utomorphisms of sextic $K3$-surfaces\nby Alexander Degtyarev (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\n$K3$-s urfaces play the role of elliptic curves in the realm of algebraic surface s. They are sophisticated enough to produce interesting and meaningful res ults that may hint possible generalizations\, yet simple enough to make th eir study feasible. One remarkable feature of $K3$-surfaces is that\, amon g all complete intersections of dimension at least two\, they are the only ones whose group of projective automorphisms may (and typically is) much smaller than their group of birational automorphisms.\n\nI will discuss a particular example of sextic $K3$-surfaces and a particular construction o f non-projective automorphisms\, related to lines. In particular\, it will be shown that\, whenever a sextic has at least two lines\, its group of b irational automorphisms is infinite.\n\nThis is a joint work with Igor Dol gachev\, Shigeyuki Kondo\, and Slawomir Rams.\n LOCATION:https://researchseminars.org/talk/OBAGS/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Öznur Turhan (Galatasaray & Polish Academy) DTSTART:20260220T124000Z DTEND:20260220T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/78 DESCRIPTION:Title: N ewton-nondegenerate line singularities\, Lê numbers and Bekka (c)-regular ity\nby Öznur Turhan (Galatasaray & Polish Academy) as part of ODTU-B ilkent Algebraic Geometry Seminars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/OBAGS/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Meral Tosun (Galatasaray) DTSTART:20260227T124000Z DTEND:20260227T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/79 DESCRIPTION:Title: M cKay quivers Beyond ADE\nby Meral Tosun (Galatasaray) as part of ODTU- Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nThe classical McKay cor respondence relates finite subgroups of SL(2\,C) to affine ADE Dynkin diag rams and Du Val surface singularities. In this talk\, we extend this persp ective to small finite subgroups of GL(2\,C) whose quotients produce isola ted surface singularities. Using character theory and a product formula fo r McKay quivers\, we give an explicit description of the quivers associate d with the natural two-dimensional representation.\n LOCATION:https://researchseminars.org/talk/OBAGS/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierrick Bousseau (Oxford) DTSTART:20260306T124000Z DTEND:20260306T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/80 DESCRIPTION:Title: B PS polynomials and Welschinger invariants\nby Pierrick Bousseau (Oxfor d) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nUsin g tropical geometry\, Block-Göttsche defined polynomials with the remarka ble property to interpolate between Gromov-Witten counts of complex curves and Welschinger counts of real curves in toric del Pezzo surfaces. I will describe a generalization of Block-Göttsche polynomials to arbitrary\, n ot-necessarily toric\, rational surfaces and propose a conjectural relatio n with refined Donaldson-Thomas invariants. This is joint work with Hulya Arguz.\n LOCATION:https://researchseminars.org/talk/OBAGS/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Michele Ancona (Côte d'Azur) DTSTART:20260313T124000Z DTEND:20260313T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/81 DESCRIPTION:Title: H arnack manifolds\nby Michele Ancona (Côte d'Azur) as part of ODTU-Bil kent Algebraic Geometry Seminars\n\n\nAbstract\nIn 1876\, Axel Harnack pro ved in a foundational article that\n\n1) every real algebraic curve of deg ree d in RP^2 has at most (d-1)(d-2)/2 + 1 connected components\;\n\n2) fo r every d there exists a curve of degree d with exactly this number of con nected components.\n\n\nOver the past 150 years\, these results have playe d a central role in the study of the topology of real algebraic varieties. The first part of Harnack’s theorem generalizes to the so-called Smith –Floyd inequality for arbitrary real algebraic varieties: the sum of the Betti numbers of the real part is at most the corresponding sum for the c omplex part. Despite spectacular advances\, the generalization of the seco nd part of Harnack’s theorem remains open in the case of projective hype rsurfaces.\n\nFor these\, however\, Ilia Itenberg and Oleg Viro showed tha t the Smith–Floyd inequality is asymptotically optimal by using the comb inatorial patchworking technique. In joint work with Erwan Brugallé and J ean-Yves Welschinger\, we show that an elementary generalization of Harnac k’s original construction method in dimension 2 yields this asymptotic o ptimality for any ample line bundle on a real algebraic variety. Beyond Be tti numbers\, we also describe the diffeomorphism type of an open subset o f these topologically rich varieties.\n LOCATION:https://researchseminars.org/talk/OBAGS/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Mesut Şahin (Hacettepe) DTSTART:20260327T124000Z DTEND:20260327T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/82 DESCRIPTION:Title: G robner Bases and Linear Codes on Weighted Projective Planes\nby Mesut Şahin (Hacettepe) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n \nAbstract\nLet $F$ be the finite field with $q$ elements and $K$ be its a lgebraic closure. The ring $S=F[x_0\,x_1\,x_2]$ is graded via $\\deg(x_i)= w_i$\, for $i=0\,1\,2$\, where $w_0\, w_1$ and $w_2$ generate a numerical semigroup! We study some linear codes obtained from the weighted projectiv e plane $P(w_0\,w_1\,w_2)$ over $K$.\n\nWe get a linear code by evaluating homogeneous polynomials of degree $d$ at the subset $Y\\{ P_1\,...\,P_N\ \}$ of $F$-rational points\, which defines the evaluation map: $f \\mapsto (f(P_1)\,...f(P_N))$. The image is a subspace of $F^N$\, which is called a weighted projective Reed-Muller (WPRM) code. Its length is $|Y|=N=q^2+q+ 1$. In the present talk\, we discuss how Grobner theory is used for studyi ng the other two parameters: the dimension and the minimum distance extend ing and generalizing the results scattered throughout the literature. We a lso determine the regularity set which helps eliminating the trivial codes as well as giving a lower bound for the minimum distance.\n\nThis is a jo int work with Yağmur Çakıroğlu (Hacettepe University) and Jade Nardi ( Université de Rennes 1).\n LOCATION:https://researchseminars.org/talk/OBAGS/82/ END:VEVENT BEGIN:VEVENT SUMMARY:Roberto Villaflor Loyola (Universidad Técnica Federico Santa Mar ía) DTSTART:20260403T124000Z DTEND:20260403T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/83 DESCRIPTION:Title: O n the linear cycles conjecture\nby Roberto Villaflor Loyola (Universid ad Técnica Federico Santa María) as part of ODTU-Bilkent Algebraic Geome try Seminars\n\n\nAbstract\nThe classical Noether-Lefschetz theorem claims that a very general degree $d>3$ surface in $\\mathbb{P}^3$ has Picard nu mber one. The locus of surfaces with higher Picard rank is known as the No ether-Lefschetz locus\, which is known to have a countable number of irred ucible components. For $d>4$\, it is classical result due independently to Green and Voisin\, that the unique component of highest codimension corre sponds to the locus of surfaces which contain lines. \n\nThe natural gener alization of this question to higher dimensional hypersurfaces of the proj ective space is known as the "linear cycles conjecture"\, and rem ains open even for fourfolds. For surfaces\, the proof is based in the fac t that locally (analytically) one can parametrize each component by a Hodg e locus\, and then use the Infinitesimal Variation of Hodge Structure to c ompute (and bound) the dimension of its Zariski tangent space. \n\nA natur al stronger version of the linear cycles conjecture is that the Hodge loci with maximal tangent space are those corresponding to linear cycles. \n\n In this talk I will report on recent results disproving this conjecture fo r all degrees and dimensions. \n\nThis is a joint work with Jorge Duque Fr anco.\n LOCATION:https://researchseminars.org/talk/OBAGS/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Degtyarev (Bilkent) DTSTART:20260417T124000Z DTEND:20260417T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/84 DESCRIPTION:Title: A decade of line counting: an overview\nby Alexander Degtyarev (Bilkent ) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nI wil l give a brief overview of a long project that started a decade ago (in\nc ollaboration with Ilia Itenberg and Sinan Sert\\"oz and in parallel with\n S{\\l}awomir Rams and Matthias Sch\\"utt) and originally intended to bridg e a minor\ngap in the proof of Segre's celebrated theorem on 64 lines on a smooth\nquartic surface. Confining ourselves to polarized K3-surfaces\, n ow we manage\nto answer questions that no one even dared to ask\, mostly b ecause of lack of\ntools. For example\, we \n\n$\\bullet$\nobtained sharp upper bounds on the possible number of lines on a smooth polarized\nK3-sur face of any degree\,\n\n$\\bullet$ obtained similar bounds for quartics\, sextics\, and octics with singularities\,\n\n$\\bullet$ advanced in the un derstanding of conics on K3-surfaces\,\n\n\n$\\bullet$ started the study o f twisted cubics.\n \n\nI will try to discuss both classical (more than 5 years old) results\nand recent advances\; if time permits\, I will also tr y to outline the\ntechniques used.\n LOCATION:https://researchseminars.org/talk/OBAGS/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Andreas Leopold Knutsen (Bergen) DTSTART:20260424T124000Z DTEND:20260424T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/85 DESCRIPTION:Title: D istinguishing Brill-Noether loci\nby Andreas Leopold Knutsen (Bergen) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nBrill-N oether theory has since the end of the 19th century studied linear systems on smooth projective curves (or\, equivalently\, compact Riemann surfaces ). A degree $d$ linear system\nof dimension $r$ on a curve $C$\, called a $g^r_d$\, roughly corresponds to a non-degenerate morphism $C \\to \\mathb b{P}^r$ of degree $d$. In the moduli space $\\mathcal{M}_g$ of curves of g enus $g$ one can define the Brill-Noether loci\n\\[ \\mathcal{M}^r_{g\,d}: = \\{ C \\in \\mathcal{M}_g \\\; : \\\; C \\\; {\\rm has~a} \\\; g^r_d \\} \, \\]\nwhich are closed subvarieties.\n\nThe classical Brill-Noether-Pe tri theorem\, proved first by D. Gieseker in 1982\,\nstates that a general smooth curve $C$ of genus $g$ admits a linear system of dimension $r$ and degree $d$\nif and only if the Brill–Noether number\n\\[ \\rho(g\, r\, d): = g - (r+ 1)(g-d+r) \\geq 0.\\]\nThis can be restated as $\\mathcal{M} ^r_{g\,d}=\\mathcal{M}_g$ if and only if $\\rho(g\, r\, d) \\geq 0$. When $\\rho(g\, r\, d) < 0$ it is known that the codimension of any component of $\\mathcal{M}^r_{g\,d}$ is at most $-\\rho(g\, r\, d)$.\nIn general sur prisingly little is known about the geometry of Brill–Noether loci\nwhen $\\rho(g\, r\, d) < 0$\, in particular about the containments between the m.\n\nI will describe results from a joint work with Asher Auel and Richar d Haburcak (arXiv:2406.19993)\, where we determine all the maximal Brill- Noether loci (wrt containment) in terms of numerical conditions on $g\,r\, d$ and show that they are all distinct.\n LOCATION:https://researchseminars.org/talk/OBAGS/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Chitayat (Padova) DTSTART:20260410T124000Z DTEND:20260410T134000Z DTSTAMP:20260422T225757Z UID:OBAGS/86 DESCRIPTION:Title: B orel subgroups of $\\rm{Aut}(\\mathbb{A}^n)$\nby Michael Chitayat (Pad ova) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nLe t $X$ be an affine variety. It was recently proved that a connected solvab le $G\\subseteq \\rm{Aut}(X)$ can be decomposed as a semi-direct product $ G=T\\ltimes U$ where $T$ is an algebraic torus and $U$ is a nested unipote nt subgroup. A $\\textit{Borel Subgroup of}$ $\\rm{Aut}(X)$ is a maximal e lement of the set of connected solvable subgroups of $\\rm{Aut}(X)$. In th is talk I will discuss Borel subgroups of $\\rm{Aut}(X)$ with a focus on t he special case where $X=\\mathbb{A}^n$.\n\nThis is joint work with Andriy Regeta and Daniel Daigle.\n LOCATION:https://researchseminars.org/talk/OBAGS/86/ END:VEVENT END:VCALENDAR