BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander Kusnetsov (Russian Academy of Sciences) DTSTART:20201023T170000Z DTEND:20201023T183000Z DTSTAMP:20260404T094753Z UID:CAGS/1 DESCRIPTION:Title: Rationality of Fano threefolds over non-closed fields\nby Alexande r Kusnetsov (Russian Academy of Sciences) as part of Columbia algebraic ge ometry seminar\n\n\nAbstract\nIn the first part of the talk I will review\ nwhat is known about rationality of Fano threefolds over\nan algebraically closed field of zero characteristic.\n\nIn the second part I will switch to the case of non-closed\nfields (still of characteristic zero) and discu ss our recent\nresults with Yuri Prokhorov in this direction.\n LOCATION:https://stable.researchseminars.org/talk/CAGS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Susanna Zimmerman (Université d'Angers) DTSTART:20201106T180000Z DTEND:20201106T193000Z DTSTAMP:20260404T094753Z UID:CAGS/2 DESCRIPTION:Title: Signature morphisms of Cremona groups\nby Susanna Zimmerman (Unive rsité d'Angers) as part of Columbia algebraic geometry seminar\n\n\nAbstr act\nA Cremona group Cr(n) is the groupe of birational self-maps of a proj ective space of dimension n. It is an algebraic group if n=1 and it is not of finite dimension for n>1\, in fact\, it contains a polynomial ring in n- variables. We are interested in homomorphism from Cr(n) to a finite gro up. For n=2 and the base-field over complex numbers\, no such quotient can exist\, basically because birational maps only contract rational curves. Over non-closed fields and in higher dimension\, there are many birational maps contracting non-rational subvarieties\, and it turns out that there are many homomorphisms from Cr(n) to a finite group. In this talk I explai n and motivate this phenomenon in dimension 2 and in dimension 3.\n LOCATION:https://stable.researchseminars.org/talk/CAGS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Zsolt Patakfalvi (EPFL) DTSTART:20201204T180000Z DTEND:20201204T193000Z DTSTAMP:20260404T094753Z UID:CAGS/3 DESCRIPTION:Title: Generic vanishing in positive characteristic and applications\nby Zsolt Patakfalvi (EPFL) as part of Columbia algebraic geometry seminar\n\n \nAbstract\nI will present a joint work with Christopher Hacon about findi ng the correct framework for generic vanishing statements for varieties ov er fields of positive characteristic. This has been an ongoing project sin ce 2013 throughout multiple articles. I will also present geometric applic ations on the characterization of abelian varieties (also joint with Zhang ) and on the singularities of Theta divisors of abelian varieties.\n LOCATION:https://stable.researchseminars.org/talk/CAGS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Roya Beheshti (Washington University in St. Louis) DTSTART:20201120T180000Z DTEND:20201120T193000Z DTSTAMP:20260404T094753Z UID:CAGS/4 DESCRIPTION:Title: Spaces of rational curves on Fano threefolds\nby Roya Beheshti (Wa shington University in St. Louis) as part of Columbia algebraic geometry s eminar\n\n\nAbstract\nI will discuss several results on the geometry of mo duli spaces of rational curves on smooth Fano threefolds. The key question is: \nwhat can be said about the number of irreducible components of the moduli space as the anti-canonical degree of the curves\nincreases?\nThis is joint work with Brian Lehmann\, Eric Riedl\, and Sho Tanimoto.\n\nThe first half of the talk is targeted at graduate students.\n LOCATION:https://stable.researchseminars.org/talk/CAGS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuchen Liu (Yale University) DTSTART:20201218T180000Z DTEND:20201218T193000Z DTSTAMP:20260404T094753Z UID:CAGS/5 DESCRIPTION:Title: Explicit K-moduli spaces\nby Yuchen Liu (Yale University) as part of Columbia algebraic geometry seminar\n\n\nAbstract\nK-stability has beco me a central tool in contructing moduli spaces for Fano varieties\, called K-moduli spaces. In this talk I will discuss the recent progress on expli cit construction of these moduli spaces\, mainly focusing on cubic threefo lds and fourfolds whose K-moduli spaces coincide with GIT. An essential in gredient is the use of normalized volumes to control singularities at the boundary of K-moduli spaces. This talk is partly based on joint work with Chenyang Xu.\n LOCATION:https://stable.researchseminars.org/talk/CAGS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Gavril Farkas (Humboldt-Universität zu Berlin) DTSTART:20210226T180000Z DTEND:20210226T193000Z DTSTAMP:20260404T094753Z UID:CAGS/6 DESCRIPTION:Title: Green's Conjecture via Koszul modules\nby Gavril Farkas (Humboldt- Universität zu Berlin) as part of Columbia algebraic geometry seminar\n\n \nAbstract\nUsing ideas from geometric group theory we provide a novel\nap proach to Green's Conjecture on syzygies of canonical curves. Via a\nstron g vanishing result for Koszul modules we deduce that a general\ncanonical curve of genus g satisfies Green's Conjecture when the\ncharacteristic is zero or at least (g+2)/2. Our results are new in\npositive characteristic (and answer positively the Eisenbud-Schreyer Conjecture)\, whereas in char acteristic zero they provide a different\nproof for theorems first obtaine d by Voisin. Joint work with Aprodu\, Papadima\, Raicu and Weyman.\n LOCATION:https://stable.researchseminars.org/talk/CAGS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Johannes Nicaise (Imperial College London) DTSTART:20210312T180000Z DTEND:20210312T193000Z DTSTAMP:20260404T094753Z UID:CAGS/7 DESCRIPTION:Title: Tropical obstructions to stable rationality\nby Johannes Nicaise ( Imperial College London) as part of Columbia algebraic geometry seminar\n\ n\nAbstract\nIt is an old and thorny problem in algebraic geometry to dete rmine which projective hypersurfaces are rational\, or\, more generally\, stably rational\, meaning that they become rational when we take the produ ct with a projective space of sufficiently large dimension. I will explain how one can use degeneration techniques and tropical methods to find new classes of non-stably rational hypersurfaces and complete intersections. T his talk is based on joint work with John Christian Ottem.\n LOCATION:https://stable.researchseminars.org/talk/CAGS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Soheyla Feyzbaksh (Imperial College London) DTSTART:20210326T170000Z DTEND:20210326T183000Z DTSTAMP:20260404T094753Z UID:CAGS/8 DESCRIPTION:Title: Application of a Bogomolov-Gieseker type inequality to counting invari ants\nby Soheyla Feyzbaksh (Imperial College London) as part of Columb ia algebraic geometry seminar\n\n\nAbstract\nIn the preliminary talk\, I w ill first explain the notion of (weak) Bridgeland stability conditions on the bounded derived category of coherent sheaves on a smooth projective th reefold. Then I will discuss the Bogomolov-Gieseker conjecture of Bayer-Ma crì-Toda.\n\nIn the main talk: I will work on a smooth projective threefo ld $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macrì-T oda\, such as the projective space $\\mathbb P^3$ or the quintic threefold . I will show certain moduli spaces of 2-dimensional torsion sheaves on $X $ are smooth bundles over Hilbert schemes of ideal sheaves of curves and p oints in $X$. When $X$ is Calabi-Yau this gives a simple wall crossing for mula expressing curve counts (and so ultimately Gromov-Witten invariants) in terms of counts of D4-D2-D0 branes. In the end\, I will sketch how we c an generalise this method to higher ranks to express DT invariants countin g Gieseker semistable sheaves of any rank $> 1$ on $X$ in terms of those c ounting sheaves of rank 0 and pure dimension 2. This is joint work with Ri chard Thomas.\n LOCATION:https://stable.researchseminars.org/talk/CAGS/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Ariyan Javenpeykar (Johannes Gutenburg Universität) DTSTART:20210409T170000Z DTEND:20210409T183000Z DTSTAMP:20260404T094753Z UID:CAGS/9 DESCRIPTION:Title: On the conjectures of Campana\, Lang\, and Vojta\nby Ariyan Javenp eykar (Johannes Gutenburg Universität) as part of Columbia algebraic geom etry seminar\n\n\nAbstract\nWhy do some polynomial equations have only fin itely many solutions in the integers? Lang-Vojta's conjecture provides a c onjectural answer and relates this number-theoretic question to complex ge ometry. I will start out this talk explaining the Lang-Vojta conjectures a nd provide a survey of currently known results. I will then present two ne w results:\n\n1. If a projective variety has only finitely many rational p oints over every number field\, then it has only finitely many birational automorphisms. (Joint with Junyi Xie.)\n\n2. If a projective variety X is a ramified cover of an abelian variety A over a number field K with A(K) d ense\, then the complement of (the image of ) X(K) in A(K) is still dense. (Joint with Pietro Corvaja\, Julian Lawrence Demeio\, Davide Lombardo\, a nd Umberto Zannier.)\n\nThese results are motivated by the Lang-Vojta conj ectures (I will explain how)\, and also provide evidence for these conject ures.\n\nI will then move on to Lang-Vojta's conjectures over function fie lds in characteristic zero and explain how to verify a version of Lang-Voj ta's conjecture for the moduli space of canonically polarized varieties (j oint with Ruiran Sun and Kang Zuo). If time permits\, I will discuss the c onjecture "opposite" to Lang\, as formulated by Campana\, and some recent progress here (joint with Erwan Rousseau).\n LOCATION:https://stable.researchseminars.org/talk/CAGS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Tuomas Tajakka (University of Washington) DTSTART:20210212T180000Z DTEND:20210212T193000Z DTSTAMP:20260404T094753Z UID:CAGS/10 DESCRIPTION:Title: Uhlenbeck compactification as a Bridgeland moduli space\nby Tuoma s Tajakka (University of Washington) as part of Columbia algebraic geometr y seminar\n\n\nAbstract\nIn recent years\, Bridgeland stability conditions have become\na central tool in the study of moduli of sheaves and their b irational\ngeometry. However\, moduli spaces of Bridgeland semistable obje cts are\nknown to be projective only in a limited number of cases. After\n reviewing the classical moduli theory of sheaves on curves and\nsurfaces\, I will present a new projectivity result for a Bridgeland\nmoduli space o n an arbitrary smooth projective surface\, as well as\ndiscuss how to inte rpret the Uhlenbeck compactification of the moduli\nof slope stable vector bundles as a Bridgeland moduli space. The proof\nis based on studying a d eterminantal line bundle constructed by Bayer\nand Macrì. Time permitting \, I will mention some ongoing work on\nPT-stability on a 3-fold.\n LOCATION:https://stable.researchseminars.org/talk/CAGS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Guy Moshkovitz (CUNY) DTSTART:20210423T170000Z DTEND:20210423T183000Z DTSTAMP:20260404T094753Z UID:CAGS/11 DESCRIPTION:Title: An Optimal Inverse Theorem\nby Guy Moshkovitz (CUNY) as part of C olumbia algebraic geometry seminar\n\n\nAbstract\nThe geometric rank of a k-tensor\, or a (k-1)-linear map\, is the codimension of its kernel variet y\, which is the variety cut out by the (k-1)-linear forms (for k=2 this i s simply matrix rank).\nUsing a carefully chosen subvariety of the kernel that satisfies certain smoothness and F-rationality properties\, together with a new iterative process for decomposing successive derivatives of a t ensor on a variety\, we prove that the partition rank of Naslund and the a nalytic rank of Gowers and Wolf are equivalent\, up to a constant dependin g on k\, over any large enough finite field. Proving the equivalence betwe en these two quantities is the main question in the "bias implies low rank " line of work in higher-order Fourier analysis\, and was reiterated by mu ltiple authors.\n\nJoint work with Alex Cohen.\n LOCATION:https://stable.researchseminars.org/talk/CAGS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Sándor Kovács (University of Washington) DTSTART:20210521T190000Z DTEND:20210521T203000Z DTSTAMP:20260404T094753Z UID:CAGS/12 DESCRIPTION:Title: Hodge sheaves for singular families\nby Sándor Kovács (Universi ty of Washington) as part of Columbia algebraic geometry seminar\n\n\nAbst ract\nThis is a report on joint work with Behrouz Taji. Given a flat proje ctive morphism $f:X\\to B$ of complex varieties\, assuming that $B$ is smo oth\, we construct a functorial system of reflexive Hodge sheaves on $B$. If in addition\, $X$ is also smooth then this system gives an extension of the Hodge bundle underlying the VHS of the smooth locus of $f$. This in t urn provides a criterion that all VHSs of geometric origin must satisfy. A s an independent application we prove a singular version of Viehweg's conj ecture about base spaces of families of maximal variation.\n LOCATION:https://stable.researchseminars.org/talk/CAGS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Aline Zanardini (University of Pennsylvania) DTSTART:20210514T170000Z DTEND:20210514T183000Z DTSTAMP:20260404T094753Z UID:CAGS/13 DESCRIPTION:Title: Stability of pencils of plane curves\nby Aline Zanardini (Univers ity of Pennsylvania) as part of Columbia algebraic geometry seminar\n\n\nA bstract\nIn this talk I will discuss some recent results on the problem of classifying pencils of plane curves via geometric invariant theory. We wi ll see how the stability of a pencil is related to the stability of its ge nerators\, to the log canonical threshold\, and to the multiplicities of a base point. In particular\, I will present some results on the stability of certain pencils of plane sextics called Halphen pencils of index two.\n LOCATION:https://stable.researchseminars.org/talk/CAGS/13/ END:VEVENT END:VCALENDAR