BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dennis Tseng (MIT) DTSTART:20200926T140000Z DTEND:20200926T150000Z DTSTAMP:20260404T094915Z UID:modulipandemic/1 DESCRIPTION:Title: Algebraic Geometry and the Log-Concavity of Matroid Invarian ts\nby Dennis Tseng (MIT) as part of Moduli Across the Pandemic (MAP)\ n\n\nAbstract\nIn their celebrated paper\, Adiprasito\, Huh\, and Katz sho wed the coefficients of the characteristic polynomial of any matroid form a log-concave sequence. In an effort to interest algebraic geometers\, we introduce the geometric side of the story\, which applies when the matroid is representable. In this story\, we will encounter familiar spaces\, lik e Grassmannians and toric varieties. We will also see variations on this g eometric setup\, leading to joint work with Andrew Berget and Hunter Spink \, and preliminary work with the aforementioned authors and Christopher Eu r.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Hannah Larson (Stanford University) DTSTART:20200926T151500Z DTEND:20200926T161500Z DTSTAMP:20260404T094915Z UID:modulipandemic/2 DESCRIPTION:Title: Brill--Noether theory over the Hurwitz space\nby Hannah Larson (Stanford University) as part of Moduli Across the Pandemic (MAP)\n \n\nAbstract\nLet C be a curve of genus g. A fundamental problem in the th eory of algebraic curves is to understand maps of C to projective space of dimension r of degree d. When the curve C is general\, the moduli space o f such maps is well-understood by the main theorems of Brill--Noether theo ry. However\, in nature\, curves C are often encountered already equipped with a map to some projective space\, which may force them to be special in moduli. The simplest case is when C is general among curves of fixed g onality. Despite much study over the past three decades\, a similarly com plete picture has proved elusive in this case. In this talk\, I will discu ss recent joint work with Eric Larson and Isabel Vogt that completes such a picture\, by proving analogs of all of the main theorems of Brill--Noeth er theory in this setting.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Frederik Benirschke (Stony Brook University) DTSTART:20201031T140000Z DTEND:20201031T150000Z DTSTAMP:20260404T094915Z UID:modulipandemic/3 DESCRIPTION:Title: Compactification of linear subvarieties\nby Frederik Ben irschke (Stony Brook University) as part of Moduli Across the Pandemic (MA P)\n\n\nAbstract\nThe moduli space of differential forms on Riemann surfac es\, also known as stratum of differentials\, has natural coordinates give n by the periods of the differential. A very special class of subvarieties of strata is given by linear subvarieties. These are algebraic subvarieti es of strata which are given locally by linear equations among the periods . Interesting examples of linear varieties arise from both algebraic geome try as well as Teichmüller theory. Using the recent compactification of s trata developed by Bainbridge-Chen-Gendron-Grushevsky-Möller we construct an algebraic compactification of linear subvarieties and study its proper ties. Our main result is that the boundary of a linear subvariety is again given by linear equations among periods. Time permitting\, we show how o ur results can be used to study Hurwitz spaces.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Hülya Argüz (Université de Versailles\, Paris-Saclay) DTSTART:20201031T151500Z DTEND:20201031T161500Z DTSTAMP:20260404T094915Z UID:modulipandemic/4 DESCRIPTION:Title: Enumerating punctured log Gromov-Witten invariants from wall -crossing\nby Hülya Argüz (Université de Versailles\, Paris-Saclay) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstract\nLog Gromov-Wit ten theory developed by Abramovich-Chen and Gross-Siebert concerns counts of stable maps with prescribed tangency conditions relative to a (not nece ssarily smooth) divisor. An extension of log Gromov-Witten theory to the c ase where one allows negative tangencies is provided by punctured log Grom ov-Witten theory of Abramovich-Chen-Gross-Siebert. In this talk we describ e an algorithmic method to compute punctured log Gromov-Witten invariants of log Calabi-Yau varieties obtained from blow-ups of toric varieties alon g hypersurfaces on the toric boundary. This method uses tropical geometry and wall-crossing computations. This is joint work with Mark Gross.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Bozlee (Tufts University) DTSTART:20201121T150000Z DTEND:20201121T160000Z DTSTAMP:20260404T094915Z UID:modulipandemic/5 DESCRIPTION:Title: Contractions of logarithmic curves and alternate compactific ations of the space of pointed elliptic curves\nby Sebastian Bozlee (T ufts University) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstract \nThere are many ways to construct proper moduli spaces of pointed curves of genus 1\, among them the spaces of Deligne-Mumford stable curves\, pseu dostable curves\, and m-stable curves. These spaces are birational to each other\, and earlier work by Ranganathan\, Santos-Parker\, and Wise has sh own that logarithmic geometry gives us a nice system for resolving the rat ional maps between them: first one performs some blowups\, then one applie s a contraction to a universal family. In my thesis\, I construct a contra ction map for more general families of log curves. Systematic exploration of the possible contractions of universal families (joint with Bob Kuo and Adrian Neff) uncovers new semistable modular compactifications of the spa ce of pointed elliptic curves of genus 1.\n\nWe will start with a descript ion of the moduli spaces\, discuss some basics of log geometry\, then desc ribe the contraction construction. Time permitting\, we will sketch the pr ocess of finding contractions of universal families permitted by the const ruction.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesca Carocci (EPFL) DTSTART:20201121T161500Z DTEND:20201121T171500Z DTSTAMP:20260404T094915Z UID:modulipandemic/6 DESCRIPTION:Title: A modular smooth compactification of genus 2 curves in proje ctive spaces\nby Francesca Carocci (EPFL) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstract\nModuli spaces of stable maps in genus bigge r than zero include many components of different dimensions meeting each o ther in complicated ways\, and the closure of the smooth locus is difficul t to describe modularly. \n\nAfter the work of Li--Vakil--Zinger and Ranga nathan--Santos-Parker--Wise in genus one\, we know that points in the bou ndary of the main component correspond to maps that admit a factorisation through some curve with Gorenstein singularities on which the map is less degenerate. \n\nThe question becomes how to construct such a universal fam ily of Gorenstein curves to then single out the (resolution) of the main c omponent of maps imposing the factorization property. In joint work with L . Battistella\, we construct one such family in genus two over a logarithm ic modification of the space of admissible covers.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Fatemeh Rezaee (Loughborough University) DTSTART:20210123T150000Z DTEND:20210123T160000Z DTSTAMP:20260404T094915Z UID:modulipandemic/7 DESCRIPTION:Title: Minimal Model Program via wall-crossing in higher dimensions ?\nby Fatemeh Rezaee (Loughborough University) as part of Moduli Acros s the Pandemic (MAP)\n\n\nAbstract\nIn this talk\, I will explain a new wa ll-crossing phenomenon on P^3 that induces non-Q-factorial singularities a nd thus cannot be understood as an operation in the Minimal Model Program of the moduli space\, unlike the case for many surfaces. I will start by g iving a review of Bridgeland stability conditions on derived categories.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Michel van Garrel (Warwick University) DTSTART:20210123T161500Z DTEND:20210123T171500Z DTSTAMP:20260404T094915Z UID:modulipandemic/8 DESCRIPTION:Title: Stable maps to Looijenga pairs\nby Michel van Garrel (Wa rwick University) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstrac t\nStart with a rational surface Y admitting a decomposition of its antica nonical divisor into at least 2 smooth nef components. We associate 5 curv e counting theories to this Looijenga pair: 1) all genus stable log maps w ith maximal tangency to each boundary component\; 2) genus 0 stable maps t o the local Calabi-Yau surface obtained by twisting Y by the sum of the li ne bundles dual to the components of the boundary\; 3) the all genus open Gromov-Witten theory of a toric Calabi-Yau threefold associated to the Loo ijenga pair\; 4) the Donaldson-Thomas theory of a symmetric quiver specifi ed by the Looijenga pair and 5) BPS invariants associated to the various c urve counting theories. In this joint work with Pierrick Bousseau and Andr ea Brini\, we provide closed-form solutions to essentially all of the asso ciated invariants and show that the theories are equivalent. I will start by describing the geometric transitions from one geometry to the other\, t hen give an overview of the curve counting theories and their relations. I will end by describing how the scattering diagrams of Gross and Siebert a re a natural place to count stable log maps.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Irene Schwarz (Humboldt University) DTSTART:20210227T150000Z DTEND:20210227T160000Z DTSTAMP:20260404T094915Z UID:modulipandemic/9 DESCRIPTION:Title: On the Kodaira dimension of the moduli space of hyperellipti c curves with marked points\nby Irene Schwarz (Humboldt University) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstract\nIt is known that the moduli space Hg\,n of genus g stable hyperelliptic curves with n marke d points is uniruled for n ≤ 4g + 5. We consider the complementary case and show that Hg\,n has non-negative Kodaira dimension for n = 4g+6 and is of general type for n ≥ 4g+7. Important parts of our proof are the calc ulation of the canonical divisor and establishing that the singularities o f Hg\,n do not impose adjunction conditions.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Mandy Cheung (Harvard University) DTSTART:20210227T161500Z DTEND:20210227T171500Z DTSTAMP:20260404T094915Z UID:modulipandemic/10 DESCRIPTION:Title: Compactifications of cluster varieties and convexity\nb y Mandy Cheung (Harvard University) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstract\nCluster varieties are log Calabi-Yau varieties which are unions of algebraic tori glued by birational "mutation" maps. They ca n be seen as a generalization of the toric varieties. In toric geometry\, projective toric varieties can be described by polytopes. We will see how to generalize the polytope construction to cluster convexity which satisfi es piecewise linear structure. As an application\, we will see the non-int egral vertex in the Newton Okounkov body of Grassmannian comes from broken line convexity. We will also see links to the symplectic geometry and app lication to mirror symmetry. The talk will be based on a series of joint w orks with Bossinger\, Lin\, Magee\, Najera-Chavez\, and Vianna.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Rob Silversmith (Northeastern) DTSTART:20210327T140000Z DTEND:20210327T150000Z DTSTAMP:20260404T094915Z UID:modulipandemic/11 DESCRIPTION:Title: Stratifications of Hilbert schemes from tropical geometry\nby Rob Silversmith (Northeastern) as part of Moduli Across the Pandemi c (MAP)\n\n\nAbstract\nOne may associate\, to any homogeneous ideal I in a polynomial ring\, a combinatorial shadow called the tropicalization of I. In any Hilbert scheme\, one may consider the set of ideals with a given t ropicalization\; these are the strata of the “tropical stratification" o f the Hilbert scheme. I will discuss some of the many questions one can as k about tropicalizations of ideals\, and how they are related to some clas sical questions in combinatorial algebraic geometry\, such as the classifi cation of torus orbits on Hilbert schemes of points in C^2. Some unexpecte d combinatorial objects appear: e.g. when studying tropicalizations of sub schemes of P^1\, one is led to Schur polynomials and binary necklaces. Thi s talk includes joint work with Diane Maclagan.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Molcho (ETH) DTSTART:20210327T151500Z DTEND:20210327T161500Z DTSTAMP:20260404T094915Z UID:modulipandemic/12 DESCRIPTION:Title: The logarithmic tautological ring\nby Sam Molcho (ETH) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstract\nLet (X\,D) be a pair consisting of a smooth variety X with a normal crossings divisor D. In this talk\, I will discuss the construction of a subring of the Chow ri ng of X\, called the logarithmic tautological ring\, generated by certain "tautological" classes obtained from the strata of D. I will explain the b asic structure of the logarithmic tautological ring: its behavior under bl owups\, its relation to combinatorics\, and some methods to compute it. I will conclude by relating the logarithmic tautological ring of the moduli space of curves with the double ramification cycle\, and explain how the s tructure of the logarithmic tautological ring implies that the double rami fication cycle is a product of divisors in a blowup of \\bar{M}_{g\,n}.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Shiyue Li (Brown University) DTSTART:20210424T143000Z DTEND:20210424T153000Z DTSTAMP:20260404T094915Z UID:modulipandemic/13 DESCRIPTION:Title: Topology of tropical moduli spaces of weighted stable curve s in higher genus\nby Shiyue Li (Brown University) as part of Moduli A cross the Pandemic (MAP)\n\n\nAbstract\nThe space of tropical weighted cur ves of genus g and volume 1 is the dual complex of the divisor of singular curves in Hassett’s moduli space of weighted stable genus g curves. One can derive plenty of topological properties of the Hassett spaces by stud ying the topology of these dual complexes. In this talk\, we show that the spaces of tropical weighted curves of genus g and volume 1 are simply-con nected for all genus greater than zero and all rational weights\, under th e framework of symmetric Delta-complexes and via a result by Allcock-Corey -Payne 19. We also calculate the Euler characteristics of these spaces and the top weight Euler characteristics of the classical Hassett spaces in t erms of the combinatorics of the weights. I will also discuss some work in progress on a geometric group theoretic approach to the simple connectivi ty of these spaces. This is joint work with Siddarth Kannan\, Stefano Serp ente and Claudia Yun.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Samir Canning (UC San Diego) DTSTART:20210424T154500Z DTEND:20210424T164500Z DTSTAMP:20260404T094915Z UID:modulipandemic/14 DESCRIPTION:Title: The Chow rings of the moduli space of curves of genus 7\, 8 \, and 9\nby Samir Canning (UC San Diego) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstract\nThe rational Chow ring of the moduli space of smooth curves is known when the genus is at most 6 by work of Mumford ( g=2)\, Faber (g=3\, 4)\, Izadi (g=5)\, and Penev-Vakil (g=6). In each case \, it is generated by the tautological classes. On the other hand\, van Ze lm has shown that the bielliptic locus is not tautological when g=12. In r ecent joint work with Hannah Larson\, we show that the Chow rings of M_7\, M_8\, and M_9 are generated by tautological classes\, which determines th e Chow ring by work of Faber. I will explain an overview of the proof with an emphasis on the special geometry of curves of low genus and low gonali ty.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Rohini Ramadas (Brown University) DTSTART:20210522T140000Z DTEND:20210522T150000Z DTSTAMP:20260404T094915Z UID:modulipandemic/15 DESCRIPTION:Title: Special loci in the moduli space of self-maps of projective space\nby Rohini Ramadas (Brown University) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstract\nA self-map of P^n is called post critica lly finite (PCF) if its critical hypersurface is pre-periodic. I’ll give a survey of many known results and some conjectures having to do with the locus of PCF maps in the moduli space of self-maps of P^1. I’ll then pr esent a result\, joint with Patrick Ingram and Joseph H. Silverman\, that suggests that for n≥2\, PCF maps are comparatively scarce in the space o f self-maps of P^n. I’ll also mention joint work with Rob Silversmith\, and work-in-progress with Xavier Buff and Sarah Koch\, on loci of “almos t PCF” maps of P^1.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Rosa Schwarz (Leiden University) DTSTART:20210522T151500Z DTEND:20210522T161500Z DTSTAMP:20260404T094915Z UID:modulipandemic/16 DESCRIPTION:Title: The universal and log double ramification cycle\nby Ros a Schwarz (Leiden University) as part of Moduli Across the Pandemic (MAP)\ n\n\nAbstract\nThe double ramification cycle is a class most commonly stud ied on the moduli space of marked curves. In joint work with Y. Bae\, D. H olmes\, R. Pandharipande\, and J. Schmitt\, we define the universal double ramification cycle in the operational Chow group of the Picard stack (of Jacobian). Even though we name it the universal double ramification cycle\ , I would like to define this cycle and then explain why this is not the f inal most natural DR-cycle to consider. For example\, it does not satisfy some basic properties about intersecting these cycles (the double double r amification cycle) that intuitively should hold. In fact\, we need to cons ider certain log-blowups of the Picard stack as well. This results in a lo g DR-cycle on a log Chow ring\, which does satisfy these nice intersection properties. Moreover\, we can ask and answer questions such as whether th is DR-cycle is log tautological. This talk is based on recent joint work w ith D. Holmes. (Some of this talk wil be closely related to what Sam Molch o discussed in his talk in this seminar\, but the general approach is quit e different).\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Dori Bejleri (Harvard) DTSTART:20210918T140000Z DTEND:20210918T150000Z DTSTAMP:20260404T094915Z UID:modulipandemic/17 DESCRIPTION:Title: Wall crossing for moduli of stable log varieties\nby Do ri Bejleri (Harvard) as part of Moduli Across the Pandemic (MAP)\n\n\nAbst ract\nStable log varieties or stable pairs (X\,D) are the higher dimension al generalization of pointed stable curves. They form proper moduli spaces which compactify the moduli space of normal crossings\, or more generally klt\, pairs. These stable pairs compactifications depend on a choice of p arameters\, namely the coefficients of the boundary divisor D. In this tal k\, after introducing the theory of stable log varieties\, I will explain the wall-crossing behavior that governs how these compactifications change as one varies the coefficients. I will also discuss some examples and app lications. This is joint work with Ascher\, Inchiostro\, and Patakfalvi.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Yixian Wu (UT Austin) DTSTART:20210918T151500Z DTEND:20210918T161500Z DTSTAMP:20260404T094915Z UID:modulipandemic/18 DESCRIPTION:Title: Splitting of Gromov-Witten Invariants with Toric Gluing Str ata\nby Yixian Wu (UT Austin) as part of Moduli Across the Pandemic (M AP)\n\n\nAbstract\nFor the past decades\, relative Gromow-Witten theory an d the degeneration formula have been proved to be an important technique i n computing Gromov-Witten invariants. The recent development of logarithmi c and punctured Gromov-Witten theory of Abramovich\, Chen\, Gross and Sieb ert generalizes the theories to normal crossing varieties. The natural nex t step is to obtain a degeneration formula under the normal crossing degen eration. In this talk\, I will present a formula relating the Gromov-Witte n invariants of general fibers to the strata of invariants of components o f the central fiber\, with the assumption that the gluing happens at toric varieties. I will explain how tropical geometry naturally arises and prov ides the key tool for the formula.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Shengxuan Liu (University of Warwick) DTSTART:20211120T150000Z DTEND:20211120T160000Z DTSTAMP:20260404T094915Z UID:modulipandemic/19 DESCRIPTION:Title: Stability condition on Calabi-Yau threefold of complete int ersection of quadratic and quartic hypersurfaces\nby Shengxuan Liu (Un iversity of Warwick) as part of Moduli Across the Pandemic (MAP)\n\n\nAbst ract\nIn this talk\, I will first introduce the background of Bridgeland s tability condition. Then I will mention some existence result of Bridgelan d stability. Next I will prove the Bogomolov-Gieseker type inequality of X _(2\,4)\, Calabi-Yau threefold of complete intersection of quadratic and q uartic hypersufaces\, by proving the Clifford type inequality of the curve X_(2\,2\,2\,4). This will provide the existence of Bridgeland stability c ondition of X_(2\,4).\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Heather Lee DTSTART:20211120T161500Z DTEND:20211120T171500Z DTSTAMP:20260404T094915Z UID:modulipandemic/20 DESCRIPTION:Title: Counting special Lagrangian classes and semistable Mukai ve ctors for K3 surfaces\nby Heather Lee as part of Moduli Across the Pan demic (MAP)\n\n\nAbstract\nMotivated by the study of the growth rate of th e number of geodesics in flat surfaces with bounded lengths\, we study gen eralizations of such problems for K3 surfaces. In one generalization\, we give a result regarding the upper bound on the asymptotics of the number o f classes of irreducible special Lagrangians in K3 surfaces with bounded p eriod integrals. In another generalization\, we give the exact leading te rm in the asymptotics of the number of Mukai vectors of semistable coheren t sheaves on algebraic K3 surfaces with bounded central charges\, with res pect to generic Bridgeland stability conditions. (I will provide all the necessary background for the terminologies that appear here during the tal k\, so it's not necessary for the audience to know them beforehand.) This talk is based on joint work with Jayadev Athreya and Yu-Wei Fan.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Angelina Zheng (University of Padova) DTSTART:20220129T150000Z DTEND:20220129T160000Z DTSTAMP:20260404T094915Z UID:modulipandemic/21 DESCRIPTION:Title: Stable cohomology of the moduli space of trigonal curves\nby Angelina Zheng (University of Padova) as part of Moduli Across the P andemic (MAP)\n\n\nAbstract\nThe rational cohomology of the moduli space $ T_g$ of trigonal curves of genus g has been computed by Looijenga for $g=3 $\, by Tommasi for $g=4$ and by myself for $g=5$. In this talk I will pres ent the rational cohomology of $T_g$ for higher genera. Specifically\, we prove that it is independent of $i$ for $g>4i+3$ and that it coincides wit h the tautological ring in this range. This will be done by studying the e mbedding of trigonal curves in Hirzebruch surfaces and using Gorinov-Vassi liev's method.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Raymond Cheng (Columbia University) DTSTART:20220129T161500Z DTEND:20220129T171500Z DTSTAMP:20260404T094915Z UID:modulipandemic/22 DESCRIPTION:Title: Geometry of q-bic Hypersurfaces\nby Raymond Cheng (Colu mbia University) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstract \nLet’s count: $1\, 2\, q+1$. The eponymous objects are special projecti ve hypersurfaces of degree $q+1$\, where $q$ is a power of the positive gr ound field characteristic. In this talk\, I would like to sketch an analog y between the geometry of $q$-bic hypersurfaces and that of quadric and cu bic hypersurfaces. For instance\, the moduli spaces of linear spaces in $q $-bics are smooth and themselves have rich geometry. In the case of $q$-bi c threefolds\, I will describe an analogue of result of Clemens and Griffi ths\, which relates the intermediate Jacobian of the $q$-bic with the Alba nese of its surface of lines.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Max Weinreich (Brown University) DTSTART:20220226T150000Z DTEND:20220226T160000Z DTSTAMP:20260404T094915Z UID:modulipandemic/23 DESCRIPTION:Title: Moduli spaces of linear maps with marked points\nby Max Weinreich (Brown University) as part of Moduli Across the Pandemic (MAP)\ n\n\nAbstract\nModuli spaces of degree d dynamical systems on projective s pace are fundamental in algebraic dynamics. When the degree d is at least 2\, these moduli spaces can be defined via geometric invariant theory (GIT ). But when d = 1\, there is a fundamental problem: there are no GIT stabl e linear maps. Inspired by the case of genus 0 curves\, we show how to rec over a nice moduli space by including marked points. We construct the modu li space of linear maps with marked points\, prove its rationality\, and s how that GIT stability is characterized by subtle dynamical conditions on the marked map. The proof is a combinatorial analysis of polytopes generat ed by root vectors of the A_N lattice from Lie theory.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Song Yu (Columbia University) DTSTART:20220226T161500Z DTEND:20220226T171500Z DTSTAMP:20260404T094915Z UID:modulipandemic/24 DESCRIPTION:Title: Open/closed correspondence via relative/local correspondenc e\nby Song Yu (Columbia University) as part of Moduli Across the Pande mic (MAP)\n\n\nAbstract\nWe discuss a mathematical approach to the open/cl osed correspondence proposed by Mayr\, which is a correspondence between t he disk invariants of toric Calabi-Yau threefolds and genus-zero closed Gr omov-Witten invariants of toric Calabi-Yau fourfolds. We establish the cor respondence in two steps: First\, a correspondence between the disk invari ants and the genus-zero maximally-tangent relative Gromov-Witten invariant s of relative Calabi-Yau threefolds\, which follows from the topological v ertex (Li-Liu-Liu-Zhou\, Fang-Liu). Second\, a correspondence between the maximally-tangent relative invariants and the closed invariants\, which ca n be viewed as an instantiation of the log-local principle of van Garrel-G raber-Ruddat in the non-compact setting. Our correspondences are based on localization. We also discuss generalizations and implications of our corr espondences. Joint work with Chiu-Chu Melissa Liu.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Wern Yeen Yeong (Notre Dame) DTSTART:20220326T140000Z DTEND:20220326T151500Z DTSTAMP:20260404T094915Z UID:modulipandemic/25 DESCRIPTION:Title: Algebraic hyperbolicity of very general hypersurfaces in pr oducts of projective spaces\nby Wern Yeen Yeong (Notre Dame) as part o f Moduli Across the Pandemic (MAP)\n\n\nAbstract\nA complex algebraic vari ety is said to be hyperbolic if it contains no entire curves\, which are n on-constant holomorphic images of the complex line. Demailly introduced al gebraic hyperbolicity as an algebraic version of this property\, and it ha s since been well-studied as a means for understanding Kobayashi’s conje cture\, which says that a generic hypersurface in projective space is hype rbolic whenever its degree is large enough. In this talk\, we study the al gebraic hyperbolicity of very general hypersurfaces of high bi-degrees in Pm x Pn and completely classify them by their bi-degrees\, except for a fe w cases in P3 x P1. We present three techniques to do that\, which build o n past work by Ein\, Voisin\, Pacienza\, Coskun and Riedl\, and others. As another application of these techniques\, we improve the known result tha t very general hypersurfaces in Pn of degree at least 2n − 2 are algebra ically hyperbolic when n is at least 6 to when n is at least 5\, leaving n = 4 as the only open case.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Carl Lian (HU Berlin) DTSTART:20220423T140000Z DTEND:20220423T150000Z DTSTAMP:20260404T094915Z UID:modulipandemic/26 DESCRIPTION:Title: Tevelev degrees of hypersurfaces\nby Carl Lian (HU Berl in) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstract\nWe consider the following problem: let (C\,p_1\,…\,p_n) be a fixed general pointed curve of genus g\, let X be a smooth hypersurface\, and let x_1\,…\,x_n be general points on X. Then\, how many degree d morphisms f:C->X are ther e for which f(p_i)=x_i? This problem has been (largely\, but not completel y) solved „virtually“ in Gromov-Witten theory by Buch-Pandharipande an d Cela. The virtual counts are expected to be enumerative if d is sufficie ntly large\, but this is only known for hypersurfaces of very low degree ( joint with Pandharipande).\n\nI will describe a more recent elementary app roach to the problem via projective geometry\, which recovers the virtual counts. The main difficulty is to analyze the transversality of the inters ection in question\, analogously to the prior investigation with Pandharip ande. This leads to questions on bounding excess dimensions of certain fam ilies of singular curves on hypersurfaces which remain open.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Eric Jovinelly (Notre Dame) DTSTART:20220423T151500Z DTEND:20220423T161500Z DTSTAMP:20260404T094915Z UID:modulipandemic/27 DESCRIPTION:Title: Extreme Divisors on M_{0\,7} and Differences over Character istic 2\nby Eric Jovinelly (Notre Dame) as part of Moduli Across the P andemic (MAP)\n\n\nAbstract\nThe cone of effective divisors controls the r ational maps from a variety. We study this important object for M_{0\,n}\, the moduli space of stable rational curves with n markings. Fulton once c onjectured the effective cones for each n would follow a certain combinato rial pattern. However\, this pattern holds true only for n < 6. Despite ma ny subsequent attempts to describe the effective cones for all n\, we stil l lack even a conjectural description. We study the simplest open case\, n =7\, and identify the first known difference between characteristic 0 and characteristic p. Although a full description of the effective cone for n= 7 remains open\, our methods allowed us to compute the entire effective co nes of spaces associated with other stability conditions.\n LOCATION:https://stable.researchseminars.org/talk/modulipandemic/27/ END:VEVENT END:VCALENDAR