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:20260422T212746Z UID:CAGS/1 DESCRIPTION:Title: Rat ionality of Fano threefolds over non-closed fields\nby Alexander Kusne tsov (Russian Academy of Sciences) as part of Columbia algebraic geometry seminar\n\n\nAbstract\nIn the first part of the talk I will review\nwhat i s 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 discuss our recent\nresults with Yuri Prokhorov in this direction.\n LOCATION:https://researchseminars.org/talk/CAGS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Susanna Zimmerman (Université d'Angers) DTSTART:20201106T180000Z DTEND:20201106T193000Z DTSTAMP:20260422T212746Z UID:CAGS/2 DESCRIPTION:Title: Sig nature morphisms of Cremona groups\nby Susanna Zimmerman (Université d'Angers) as part of Columbia algebraic geometry seminar\n\n\nAbstract\nA Cremona group Cr(n) is the groupe of birational self-maps of a projective space of dimension n. It is an algebraic group if n=1 and it is not of fin ite dimension for n>1\, in fact\, it contains a polynomial ring in n- vari ables. We are interested in homomorphism from Cr(n) to a finite group. For n=2 and the base-field over complex numbers\, no such quotient can exist\ , basically because birational maps only contract rational curves. Over no n-closed fields and in higher dimension\, there are many birational maps c ontracting non-rational subvarieties\, and it turns out that there are man y homomorphisms from Cr(n) to a finite group. In this talk I explain and m otivate this phenomenon in dimension 2 and in dimension 3.\n LOCATION:https://researchseminars.org/talk/CAGS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Zsolt Patakfalvi (EPFL) DTSTART:20201204T180000Z DTEND:20201204T193000Z DTSTAMP:20260422T212746Z UID:CAGS/3 DESCRIPTION:Title: Gen eric vanishing in positive characteristic and applications\nby Zsolt P atakfalvi (EPFL) as part of Columbia algebraic geometry seminar\n\n\nAbstr act\nI will present a joint work with Christopher Hacon about finding the correct framework for generic vanishing statements for varieties over fiel ds of positive characteristic. This has been an ongoing project since 2013 throughout multiple articles. I will also present geometric applications on the characterization of abelian varieties (also joint with Zhang) and o n the singularities of Theta divisors of abelian varieties.\n LOCATION:https://researchseminars.org/talk/CAGS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Roya Beheshti (Washington University in St. Louis) DTSTART:20201120T180000Z DTEND:20201120T193000Z DTSTAMP:20260422T212746Z UID:CAGS/4 DESCRIPTION:Title: Spa ces of rational curves on Fano threefolds\nby Roya Beheshti (Washingto n University in St. Louis) as part of Columbia algebraic geometry seminar\ n\n\nAbstract\nI will discuss several results on the geometry of moduli sp aces 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 joi nt work with Brian Lehmann\, Eric Riedl\, and Sho Tanimoto.\n\nThe first h alf of the talk is targeted at graduate students.\n LOCATION:https://researchseminars.org/talk/CAGS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuchen Liu (Yale University) DTSTART:20201218T180000Z DTEND:20201218T193000Z DTSTAMP:20260422T212746Z UID:CAGS/5 DESCRIPTION:Title: Exp licit K-moduli spaces\nby Yuchen Liu (Yale University) as part of Colu mbia algebraic geometry seminar\n\n\nAbstract\nK-stability has become a ce ntral tool in contructing moduli spaces for Fano varieties\, called K-modu li spaces. In this talk I will discuss the recent progress on explicit con struction of these moduli spaces\, mainly focusing on cubic threefolds and fourfolds whose K-moduli spaces coincide with GIT. An essential ingredien t is the use of normalized volumes to control singularities at the boundar y of K-moduli spaces. This talk is partly based on joint work with Chenyan g Xu.\n LOCATION:https://researchseminars.org/talk/CAGS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Gavril Farkas (Humboldt-Universität zu Berlin) DTSTART:20210226T180000Z DTEND:20210226T193000Z DTSTAMP:20260422T212746Z UID:CAGS/6 DESCRIPTION:Title: Gre en's Conjecture via Koszul modules\nby Gavril Farkas (Humboldt-Univers ität zu Berlin) as part of Columbia algebraic geometry seminar\n\n\nAbstr act\nUsing ideas from geometric group theory we provide a novel\napproach to Green's Conjecture on syzygies of canonical curves. Via a\nstrong vanis hing result for Koszul modules we deduce that a general\ncanonical curve o f 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 an swer positively the Eisenbud-Schreyer Conjecture)\, whereas in characteris tic zero they provide a different\nproof for theorems first obtained by Vo isin. Joint work with Aprodu\, Papadima\, Raicu and Weyman.\n LOCATION:https://researchseminars.org/talk/CAGS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Johannes Nicaise (Imperial College London) DTSTART:20210312T180000Z DTEND:20210312T193000Z DTSTAMP:20260422T212746Z UID:CAGS/7 DESCRIPTION:Title: Tro pical obstructions to stable rationality\nby Johannes Nicaise (Imperia l College London) as part of Columbia algebraic geometry seminar\n\n\nAbst ract\nIt is an old and thorny problem in algebraic geometry to determine w hich projective hypersurfaces are rational\, or\, more generally\, stably rational\, meaning that they become rational when we take the product with a projective space of sufficiently large dimension. I will explain how on e can use degeneration techniques and tropical methods to find new classes of non-stably rational hypersurfaces and complete intersections. This tal k is based on joint work with John Christian Ottem.\n LOCATION:https://researchseminars.org/talk/CAGS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Soheyla Feyzbaksh (Imperial College London) DTSTART:20210326T170000Z DTEND:20210326T183000Z DTSTAMP:20260422T212746Z UID:CAGS/8 DESCRIPTION:Title: App lication of a Bogomolov-Gieseker type inequality to counting invariants\nby Soheyla Feyzbaksh (Imperial College London) as part of Columbia alge braic geometry seminar\n\n\nAbstract\nIn the preliminary talk\, I will fir st explain the notion of (weak) Bridgeland stability conditions on the bou nded derived category of coherent sheaves on a smooth projective threefold . Then I will discuss the Bogomolov-Gieseker conjecture of Bayer-Macrì-To da.\n\nIn the main talk: I will work on a smooth projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda\, s uch as the projective space $\\mathbb P^3$ or the quintic threefold. I wil l show certain moduli spaces of 2-dimensional torsion sheaves on $X$ are s mooth bundles over Hilbert schemes of ideal sheaves of curves and points i n $X$. When $X$ is Calabi-Yau this gives a simple wall crossing formula ex pressing curve counts (and so ultimately Gromov-Witten invariants) in term s of counts of D4-D2-D0 branes. In the end\, I will sketch how we can gene ralise this method to higher ranks to express DT invariants counting Giese ker semistable sheaves of any rank $> 1$ on $X$ in terms of those counting sheaves of rank 0 and pure dimension 2. This is joint work with Richard T homas.\n LOCATION:https://researchseminars.org/talk/CAGS/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Ariyan Javenpeykar (Johannes Gutenburg Universität) DTSTART:20210409T170000Z DTEND:20210409T183000Z DTSTAMP:20260422T212746Z UID:CAGS/9 DESCRIPTION:Title: On the conjectures of Campana\, Lang\, and Vojta\nby Ariyan Javenpeykar ( Johannes Gutenburg Universität) as part of Columbia algebraic geometry se minar\n\n\nAbstract\nWhy do some polynomial equations have only finitely m any solutions in the integers? Lang-Vojta's conjecture provides a conjectu ral answer and relates this number-theoretic question to complex geometry. I will start out this talk explaining the Lang-Vojta conjectures and prov ide a survey of currently known results. I will then present two new resul ts:\n\n1. If a projective variety has only finitely many rational points o ver every number field\, then it has only finitely many birational automor phisms. (Joint with Junyi Xie.)\n\n2. If a projective variety X is a ramif ied cover of an abelian variety A over a number field K with A(K) dense\, then the complement of (the image of ) X(K) in A(K) is still dense. (Joint with Pietro Corvaja\, Julian Lawrence Demeio\, Davide Lombardo\, and Umbe rto Zannier.)\n\nThese results are motivated by the Lang-Vojta conjectures (I will explain how)\, and also provide evidence for these conjectures.\n \nI will then move on to Lang-Vojta's conjectures over function fields in characteristic zero and explain how to verify a version of Lang-Vojta's co njecture for the moduli space of canonically polarized varieties (joint wi th Ruiran Sun and Kang Zuo). If time permits\, I will discuss the conjectu re "opposite" to Lang\, as formulated by Campana\, and some recent progres s here (joint with Erwan Rousseau).\n LOCATION:https://researchseminars.org/talk/CAGS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Tuomas Tajakka (University of Washington) DTSTART:20210212T180000Z DTEND:20210212T193000Z DTSTAMP:20260422T212746Z UID:CAGS/10 DESCRIPTION:Title: Uh lenbeck compactification as a Bridgeland moduli space\nby Tuomas Tajak ka (University of Washington) as part of Columbia algebraic geometry semin ar\n\n\nAbstract\nIn recent years\, Bridgeland stability conditions have b ecome\na central tool in the study of moduli of sheaves and their biration al\ngeometry. However\, moduli spaces of Bridgeland semistable objects are \nknown to be projective only in a limited number of cases. After\nreviewi ng the classical moduli theory of sheaves on curves and\nsurfaces\, I will present a new projectivity result for a Bridgeland\nmoduli space on an ar bitrary smooth projective surface\, as well as\ndiscuss how to interpret t he Uhlenbeck compactification of the moduli\nof slope stable vector bundle s as a Bridgeland moduli space. The proof\nis based on studying a determin antal line bundle constructed by Bayer\nand Macrì. Time permitting\, I wi ll mention some ongoing work on\nPT-stability on a 3-fold.\n LOCATION:https://researchseminars.org/talk/CAGS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Guy Moshkovitz (CUNY) DTSTART:20210423T170000Z DTEND:20210423T183000Z DTSTAMP:20260422T212746Z UID:CAGS/11 DESCRIPTION:Title: An Optimal Inverse Theorem\nby Guy Moshkovitz (CUNY) as part of Columbia algebraic geometry seminar\n\n\nAbstract\nThe geometric rank of a k-tenso r\, or a (k-1)-linear map\, is the codimension of its kernel variety\, whi ch is the variety cut out by the (k-1)-linear forms (for k=2 this is simpl y matrix rank).\nUsing a carefully chosen subvariety of the kernel that sa tisfies certain smoothness and F-rationality properties\, together with a new iterative process for decomposing successive derivatives of a tensor o n a variety\, we prove that the partition rank of Naslund and the analytic rank of Gowers and Wolf are equivalent\, up to a constant depending on k\ , over any large enough finite field. Proving the equivalence between thes e two quantities is the main question in the "bias implies low rank" line of work in higher-order Fourier analysis\, and was reiterated by multiple authors.\n\nJoint work with Alex Cohen.\n LOCATION:https://researchseminars.org/talk/CAGS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Sándor Kovács (University of Washington) DTSTART:20210521T190000Z DTEND:20210521T203000Z DTSTAMP:20260422T212746Z UID:CAGS/12 DESCRIPTION:Title: Ho dge sheaves for singular families\nby Sándor Kovács (University of W ashington) as part of Columbia algebraic geometry seminar\n\n\nAbstract\nT his is a report on joint work with Behrouz Taji. Given a flat projective m orphism $f:X\\to B$ of complex varieties\, assuming that $B$ is smooth\, w e construct a functorial system of reflexive Hodge sheaves on $B$. If in a ddition\, $X$ is also smooth then this system gives an extension of the Ho dge bundle underlying the VHS of the smooth locus of $f$. This in turn pro vides a criterion that all VHSs of geometric origin must satisfy. As an in dependent application we prove a singular version of Viehweg's conjecture about base spaces of families of maximal variation.\n LOCATION:https://researchseminars.org/talk/CAGS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Aline Zanardini (University of Pennsylvania) DTSTART:20210514T170000Z DTEND:20210514T183000Z DTSTAMP:20260422T212746Z UID:CAGS/13 DESCRIPTION:Title: St ability of pencils of plane curves\nby Aline Zanardini (University of Pennsylvania) as part of Columbia algebraic geometry seminar\n\n\nAbstract \nIn this talk I will discuss some recent results on the problem of classi fying pencils of plane curves via geometric invariant theory. We will see how the stability of a pencil is related to the stability of its generator s\, to the log canonical threshold\, and to the multiplicities of a base p oint. In particular\, I will present some results on the stability of cert ain pencils of plane sextics called Halphen pencils of index two.\n LOCATION:https://researchseminars.org/talk/CAGS/13/ END:VEVENT END:VCALENDAR