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BEGIN:VEVENT
SUMMARY:Dennis Tseng (MIT)
DTSTART;VALUE=DATE-TIME:20200926T140000Z
DTEND;VALUE=DATE-TIME:20200926T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/1
DESCRIPTION:Title: Algebraic Geometry and the Log-Concavity of Matroid Invariants\
nby Dennis Tseng (MIT) as part of Moduli Across the Pandemic (MAP)\n\n\nAb
stract\nIn their celebrated paper\, Adiprasito\, Huh\, and Katz showed the
coefficients of the characteristic polynomial of any matroid form a log-c
oncave sequence. In an effort to interest algebraic geometers\, we introdu
ce the geometric side of the story\, which applies when the matroid is rep
resentable. In this story\, we will encounter familiar spaces\, like Grass
mannians and toric varieties. We will also see variations on this geometri
c setup\, leading to joint work with Andrew Berget and Hunter Spink\, and
preliminary work with the aforementioned authors and Christopher Eur.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Larson (Stanford University)
DTSTART;VALUE=DATE-TIME:20200926T151500Z
DTEND;VALUE=DATE-TIME:20200926T161500Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
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\nAbs
tract\nLet C be a curve of genus g. A fundamental problem in the theory of
algebraic curves is to understand maps of C to projective space of dimens
ion r of degree d. When the curve C is general\, the moduli space of such
maps is well-understood by the main theorems of Brill--Noether theory. Ho
wever\, in nature\, curves C are often encountered already equipped with a
map to some projective space\, which may force them to be special in modu
li. The simplest case is when C is general among curves of fixed gonality
. Despite much study over the past three decades\, a similarly complete p
icture has proved elusive in this case. In this talk\, I will discuss rece
nt joint work with Eric Larson and Isabel Vogt that completes such a pictu
re\, by proving analogs of all of the main theorems of Brill--Noether theo
ry in this setting.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frederik Benirschke (Stony Brook University)
DTSTART;VALUE=DATE-TIME:20201031T140000Z
DTEND;VALUE=DATE-TIME:20201031T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/3
DESCRIPTION:Title: Compactification of linear subvarieties\nby Frederik Benirschke
(Stony Brook University) as part of Moduli Across the Pandemic (MAP)\n\n\
nAbstract\nThe moduli space of differential forms on Riemann surfaces\, al
so known as stratum of differentials\, has natural coordinates given by th
e periods of the differential. A very special class of subvarieties of str
ata is given by linear subvarieties. These are algebraic subvarieties of s
trata which are given locally by linear equations among the periods. Inter
esting examples of linear varieties arise from both algebraic geometry as
well as Teichmüller theory. Using the recent compactification of strata d
eveloped by Bainbridge-Chen-Gendron-Grushevsky-Möller we construct an alg
ebraic compactification of linear subvarieties and study its properties. O
ur main result is that the boundary of a linear subvariety is again given
by linear equations among periods. Time permitting\, we show how our resu
lts can be used to study Hurwitz spaces.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hülya Argüz (Université de Versailles\, Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20201031T151500Z
DTEND;VALUE=DATE-TIME:20201031T161500Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/4
DESCRIPTION:Title: Enumerating punctured log Gromov-Witten invariants from wall-crossi
ng\nby Hülya Argüz (Université de Versailles\, Paris-Saclay) as par
t of Moduli Across the Pandemic (MAP)\n\n\nAbstract\nLog Gromov-Witten the
ory developed by Abramovich-Chen and Gross-Siebert concerns counts of stab
le maps with prescribed tangency conditions relative to a (not necessarily
smooth) divisor. An extension of log Gromov-Witten theory to the case whe
re one allows negative tangencies is provided by punctured log Gromov-Witt
en theory of Abramovich-Chen-Gross-Siebert. In this talk we describe an al
gorithmic method to compute punctured log Gromov-Witten invariants of log
Calabi-Yau varieties obtained from blow-ups of toric varieties along hyper
surfaces on the toric boundary. This method uses tropical geometry and wal
l-crossing computations. This is joint work with Mark Gross.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Bozlee (Tufts University)
DTSTART;VALUE=DATE-TIME:20201121T150000Z
DTEND;VALUE=DATE-TIME:20201121T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/5
DESCRIPTION:Title: Contractions of logarithmic curves and alternate compactifications
of the space of pointed elliptic curves\nby Sebastian Bozlee (Tufts Un
iversity) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstract\nThere
are many ways to construct proper moduli spaces of pointed curves of genu
s 1\, among them the spaces of Deligne-Mumford stable curves\, pseudostabl
e curves\, and m-stable curves. These spaces are birational to each other\
, and earlier work by Ranganathan\, Santos-Parker\, and Wise has shown tha
t logarithmic geometry gives us a nice system for resolving the rational m
aps between them: first one performs some blowups\, then one applies a con
traction to a universal family. In my thesis\, I construct a contraction m
ap 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 space of p
ointed elliptic curves of genus 1.\n\nWe will start with a description of
the moduli spaces\, discuss some basics of log geometry\, then describe th
e contraction construction. Time permitting\, we will sketch the process o
f finding contractions of universal families permitted by the construction
.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Carocci (EPFL)
DTSTART;VALUE=DATE-TIME:20201121T161500Z
DTEND;VALUE=DATE-TIME:20201121T171500Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/6
DESCRIPTION:Title: A modular smooth compactification of genus 2 curves in projective s
paces\nby Francesca Carocci (EPFL) as part of Moduli Across the Pandem
ic (MAP)\n\n\nAbstract\nModuli spaces of stable maps in genus bigger than
zero include many components of different dimensions meeting each other in
complicated ways\, and the closure of the smooth locus is difficult to de
scribe modularly. \n\nAfter the work of Li--Vakil--Zinger and Ranganathan-
-Santos-Parker--Wise in genus one\, we know that points in the boundary o
f the main component correspond to maps that admit a factorisation through
some curve with Gorenstein singularities on which the map is less degener
ate. \n\nThe question becomes how to construct such a universal family of
Gorenstein curves to then single out the (resolution) of the main componen
t of maps imposing the factorization property. In joint work with L. Batti
stella\, we construct one such family in genus two over a logarithmic modi
fication of the space of admissible covers.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatemeh Rezaee (Loughborough University)
DTSTART;VALUE=DATE-TIME:20210123T150000Z
DTEND;VALUE=DATE-TIME:20210123T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/7
DESCRIPTION:Title: Minimal Model Program via wall-crossing in higher dimensions?\n
by Fatemeh Rezaee (Loughborough University) as part of Moduli Across the P
andemic (MAP)\n\n\nAbstract\nIn this talk\, I will explain a new wall-cros
sing phenomenon on P^3 that induces non-Q-factorial singularities and 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 giving a
review of Bridgeland stability conditions on derived categories.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michel van Garrel (Warwick University)
DTSTART;VALUE=DATE-TIME:20210123T161500Z
DTEND;VALUE=DATE-TIME:20210123T171500Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/8
DESCRIPTION:Title: Stable maps to Looijenga pairs\nby Michel van Garrel (Warwick U
niversity) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstract\nStar
t with a rational surface Y admitting a decomposition of its anticanonical
divisor into at least 2 smooth nef components. We associate 5 curve count
ing theories to this Looijenga pair: 1) all genus stable log maps with max
imal tangency to each boundary component\; 2) genus 0 stable maps to the l
ocal Calabi-Yau surface obtained by twisting Y by the sum of the line bund
les dual to the components of the boundary\; 3) the all genus open Gromov-
Witten theory of a toric Calabi-Yau threefold associated to the Looijenga
pair\; 4) the Donaldson-Thomas theory of a symmetric quiver specified by t
he Looijenga pair and 5) BPS invariants associated to the various curve co
unting theories. In this joint work with Pierrick Bousseau and Andrea Brin
i\, we provide closed-form solutions to essentially all of the associated
invariants and show that the theories are equivalent. I will start by desc
ribing the geometric transitions from one geometry to the other\, then giv
e an overview of the curve counting theories and their relations. I will e
nd by describing how the scattering diagrams of Gross and Siebert are a na
tural place to count stable log maps.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irene Schwarz (Humboldt University)
DTSTART;VALUE=DATE-TIME:20210227T150000Z
DTEND;VALUE=DATE-TIME:20210227T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/9
DESCRIPTION:Title: On the Kodaira dimension of the moduli space of hyperelliptic curve
s with marked points\nby Irene Schwarz (Humboldt University) as part o
f Moduli Across the Pandemic (MAP)\n\n\nAbstract\nIt is known that the mod
uli space Hg\,n of genus g stable hyperelliptic curves with n marked point
s is uniruled for n ≤ 4g + 5. We consider the complementary case and sho
w that Hg\,n has non-negative Kodaira dimension for n = 4g+6 and is of gen
eral type for n ≥ 4g+7. Important parts of our proof are the calculation
of the canonical divisor and establishing that the singularities of Hg\,n
do not impose adjunction conditions.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mandy Cheung (Harvard University)
DTSTART;VALUE=DATE-TIME:20210227T161500Z
DTEND;VALUE=DATE-TIME:20210227T171500Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/10
DESCRIPTION:Title: Compactifications of cluster varieties and convexity\nby Mandy
Cheung (Harvard University) as part of Moduli Across the Pandemic (MAP)\n
\n\nAbstract\nCluster varieties are log Calabi-Yau varieties which are uni
ons of algebraic tori glued by birational "mutation" maps. They can be se
en as a generalization of the toric varieties. In toric geometry\, project
ive toric varieties can be described by polytopes. We will see how to gene
ralize the polytope construction to cluster convexity which satisfies piec
ewise linear structure. As an application\, we will see the non-integral v
ertex in the Newton Okounkov body of Grassmannian comes from broken line c
onvexity. We will also see links to the symplectic geometry and applicatio
n to mirror symmetry. The talk will be based on a series of joint works wi
th Bossinger\, Lin\, Magee\, Najera-Chavez\, and Vianna.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rob Silversmith (Northeastern)
DTSTART;VALUE=DATE-TIME:20210327T140000Z
DTEND;VALUE=DATE-TIME:20210327T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/11
DESCRIPTION:Title: Stratifications of Hilbert schemes from tropical geometry\nby
Rob Silversmith (Northeastern) as part of Moduli Across the Pandemic (MAP)
\n\n\nAbstract\nOne may associate\, to any homogeneous ideal I in a polyno
mial ring\, a combinatorial shadow called the tropicalization of I. In any
Hilbert scheme\, one may consider the set of ideals with a given tropical
ization\; these are the strata of the “tropical stratification" of the H
ilbert scheme. I will discuss some of the many questions one can ask about
tropicalizations of ideals\, and how they are related to some classical q
uestions in combinatorial algebraic geometry\, such as the classification
of torus orbits on Hilbert schemes of points in C^2. Some unexpected combi
natorial objects appear: e.g. when studying tropicalizations of subschemes
of P^1\, one is led to Schur polynomials and binary necklaces. This talk
includes joint work with Diane Maclagan.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Molcho (ETH)
DTSTART;VALUE=DATE-TIME:20210327T151500Z
DTEND;VALUE=DATE-TIME:20210327T161500Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
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 c
onsisting 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 ring of X
\, called the logarithmic tautological ring\, generated by certain "tautol
ogical" classes obtained from the strata of D. I will explain the basic st
ructure of the logarithmic tautological ring: its behavior under blowups\,
its relation to combinatorics\, and some methods to compute it. I will co
nclude by relating the logarithmic tautological ring of the moduli space o
f curves with the double ramification cycle\, and explain how the structur
e of the logarithmic tautological ring implies that the double ramificatio
n cycle is a product of divisors in a blowup of \\bar{M}_{g\,n}.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shiyue Li (Brown University)
DTSTART;VALUE=DATE-TIME:20210424T143000Z
DTEND;VALUE=DATE-TIME:20210424T153000Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/13
DESCRIPTION:Title: Topology of tropical moduli spaces of weighted stable curves in hi
gher genus\nby Shiyue Li (Brown University) as part of Moduli Across t
he Pandemic (MAP)\n\n\nAbstract\nThe space of tropical weighted curves 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 de
rive plenty of topological properties of the Hassett spaces by studying th
e 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-connected
for all genus greater than zero and all rational weights\, under the frame
work of symmetric Delta-complexes and via a result by Allcock-Corey-Payne
19. We also calculate the Euler characteristics of these spaces and the to
p weight Euler characteristics of the classical Hassett spaces in terms of
the combinatorics of the weights. I will also discuss some work in progre
ss on a geometric group theoretic approach to the simple connectivity of t
hese spaces. This is joint work with Siddarth Kannan\, Stefano Serpente an
d Claudia Yun.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samir Canning (UC San Diego)
DTSTART;VALUE=DATE-TIME:20210424T154500Z
DTEND;VALUE=DATE-TIME:20210424T164500Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
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 Pandem
ic (MAP)\n\n\nAbstract\nThe rational Chow ring of the moduli space of smoo
th 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 i
s generated by the tautological classes. On the other hand\, van Zelm has
shown that the bielliptic locus is not tautological when g=12. In recent j
oint 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 the Chow
ring by work of Faber. I will explain an overview of the proof with an emp
hasis on the special geometry of curves of low genus and low gonality.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rohini Ramadas (Brown University)
DTSTART;VALUE=DATE-TIME:20210522T140000Z
DTEND;VALUE=DATE-TIME:20210522T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/15
DESCRIPTION:Title: Special loci in the moduli space of self-maps of projective space<
/a>\nby Rohini Ramadas (Brown University) as part of Moduli Across the Pan
demic (MAP)\n\n\nAbstract\nA self-map of P^n is called post critically fin
ite (PCF) if its critical hypersurface is pre-periodic. I’ll give a surv
ey 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 present a
result\, joint with Patrick Ingram and Joseph H. Silverman\, that suggest
s that for n≥2\, PCF maps are comparatively scarce in the space of self-
maps of P^n. I’ll also mention joint work with Rob Silversmith\, and wor
k-in-progress with Xavier Buff and Sarah Koch\, on loci of “almost PCF
” maps of P^1.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rosa Schwarz (Leiden University)
DTSTART;VALUE=DATE-TIME:20210522T151500Z
DTEND;VALUE=DATE-TIME:20210522T161500Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/16
DESCRIPTION:Title: The universal and log double ramification cycle\nby Rosa Schwa
rz (Leiden University) as part of Moduli Across the Pandemic (MAP)\n\n\nAb
stract\nThe double ramification cycle is a class most commonly studied on
the moduli space of marked curves. In joint work with Y. Bae\, D. Holmes\,
R. Pandharipande\, and J. Schmitt\, we define the universal double ramifi
cation cycle in the operational Chow group of the Picard stack (of Jacobia
n). Even though we name it the universal double ramification cycle\, I wou
ld like to define this cycle and then explain why this is not the final mo
st natural DR-cycle to consider. For example\, it does not satisfy some ba
sic properties about intersecting these cycles (the double double ramifica
tion cycle) that intuitively should hold. In fact\, we need to consider ce
rtain log-blowups of the Picard stack as well. This results in a log DR-cy
cle on a log Chow ring\, which does satisfy these nice intersection proper
ties. Moreover\, we can ask and answer questions such as whether this DR-c
ycle is log tautological. This talk is based on recent joint work with D.
Holmes. (Some of this talk wil be closely related to what Sam Molcho discu
ssed in his talk in this seminar\, but the general approach is quite diffe
rent).\n
LOCATION:https://researchseminars.org/talk/modulipandemic/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dori Bejleri (Harvard)
DTSTART;VALUE=DATE-TIME:20210918T140000Z
DTEND;VALUE=DATE-TIME:20210918T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/17
DESCRIPTION:Title: Wall crossing for moduli of stable log varieties\nby Dori Bejl
eri (Harvard) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstract\nS
table log varieties or stable pairs (X\,D) are the higher dimensional gene
ralization 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 paramete
rs\, namely the coefficients of the boundary divisor D. In this talk\, aft
er introducing the theory of stable log varieties\, I will explain the wal
l-crossing behavior that governs how these compactifications change as one
varies the coefficients. I will also discuss some examples and applicatio
ns. This is joint work with Ascher\, Inchiostro\, and Patakfalvi.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yixian Wu (UT Austin)
DTSTART;VALUE=DATE-TIME:20210918T151500Z
DTEND;VALUE=DATE-TIME:20210918T161500Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/18
DESCRIPTION:Title: Splitting of Gromov-Witten Invariants with Toric Gluing Strata
\nby Yixian Wu (UT Austin) as part of Moduli Across the Pandemic (MAP)\n\n
\nAbstract\nFor the past decades\, relative Gromow-Witten theory and the d
egeneration formula have been proved to be an important technique in compu
ting Gromov-Witten invariants. The recent development of logarithmic and p
unctured Gromov-Witten theory of Abramovich\, Chen\, Gross and Siebert gen
eralizes the theories to normal crossing varieties. The natural next step
is to obtain a degeneration formula under the normal crossing degeneration
. In this talk\, I will present a formula relating the Gromov-Witten invar
iants of general fibers to the strata of invariants of components of the c
entral fiber\, with the assumption that the gluing happens at toric variet
ies. I will explain how tropical geometry naturally arises and provides th
e key tool for the formula.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shengxuan Liu (University of Warwick)
DTSTART;VALUE=DATE-TIME:20211120T150000Z
DTEND;VALUE=DATE-TIME:20211120T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/19
DESCRIPTION:Title: Stability condition on Calabi-Yau threefold of complete intersecti
on of quadratic and quartic hypersurfaces\nby Shengxuan Liu (Universit
y of Warwick) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstract\nI
n this talk\, I will first introduce the background of Bridgeland stabilit
y condition. Then I will mention some existence result of Bridgeland stabi
lity. Next I will prove the Bogomolov-Gieseker type inequality of X_(2\,4)
\, Calabi-Yau threefold of complete intersection of quadratic and quartic
hypersufaces\, by proving the Clifford type inequality of the curve X_(2\,
2\,2\,4). This will provide the existence of Bridgeland stability conditio
n of X_(2\,4).\n
LOCATION:https://researchseminars.org/talk/modulipandemic/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Heather Lee
DTSTART;VALUE=DATE-TIME:20211120T161500Z
DTEND;VALUE=DATE-TIME:20211120T171500Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/20
DESCRIPTION:Title: Counting special Lagrangian classes and semistable Mukai vectors f
or K3 surfaces\nby Heather Lee as part of Moduli Across the Pandemic (
MAP)\n\n\nAbstract\nMotivated by the study of the growth rate of the numbe
r of geodesics in flat surfaces with bounded lengths\, we study generaliza
tions of such problems for K3 surfaces. In one generalization\, we give a
result regarding the upper bound on the asymptotics of the number of class
es of irreducible special Lagrangians in K3 surfaces with bounded period i
ntegrals. In another generalization\, we give the exact leading term in t
he asymptotics of the number of Mukai vectors of semistable coherent sheav
es on algebraic K3 surfaces with bounded central charges\, with respect to
generic Bridgeland stability conditions. (I will provide all the necessa
ry background for the terminologies that appear here during the talk\, so
it's not necessary for the audience to know them beforehand.) This talk i
s based on joint work with Jayadev Athreya and Yu-Wei Fan.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Angelina Zheng (University of Padova)
DTSTART;VALUE=DATE-TIME:20220129T150000Z
DTEND;VALUE=DATE-TIME:20220129T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/21
DESCRIPTION:Title: Stable cohomology of the moduli space of trigonal curves\nby A
ngelina Zheng (University of Padova) as part of Moduli Across the Pandemic
(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 present the
rational cohomology of $T_g$ for higher genera. Specifically\, we prove t
hat it is independent of $i$ for $g>4i+3$ and that it coincides with the t
autological ring in this range. This will be done by studying the embeddin
g of trigonal curves in Hirzebruch surfaces and using Gorinov-Vassiliev's
method.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raymond Cheng (Columbia University)
DTSTART;VALUE=DATE-TIME:20220129T161500Z
DTEND;VALUE=DATE-TIME:20220129T171500Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/22
DESCRIPTION:Title: Geometry of q-bic Hypersurfaces\nby Raymond Cheng (Columbia Un
iversity) as part of Moduli Across the Pandemic (MAP)\n\n\nAbstract\nLet
’s count: $1\, 2\, q+1$. The eponymous objects are special projective hy
persurfaces of degree $q+1$\, where $q$ is a power of the positive ground
field characteristic. In this talk\, I would like to sketch an analogy bet
ween the geometry of $q$-bic hypersurfaces and that of quadric and cubic h
ypersurfaces. For instance\, the moduli spaces of linear spaces in $q$-bic
s are smooth and themselves have rich geometry. In the case of $q$-bic thr
eefolds\, I will describe an analogue of result of Clemens and Griffiths\,
which relates the intermediate Jacobian of the $q$-bic with the Albanese
of its surface of lines.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Weinreich (Brown University)
DTSTART;VALUE=DATE-TIME:20220226T150000Z
DTEND;VALUE=DATE-TIME:20220226T160000Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/23
DESCRIPTION:Title: Moduli spaces of linear maps with marked points\nby Max Weinre
ich (Brown University) as part of Moduli Across the Pandemic (MAP)\n\n\nAb
stract\nModuli spaces of degree d dynamical systems on projective space ar
e fundamental in algebraic dynamics. When the degree d is at least 2\, the
se moduli spaces can be defined via geometric invariant theory (GIT). But
when d = 1\, there is a fundamental problem: there are no GIT stable linea
r maps. Inspired by the case of genus 0 curves\, we show how to recover a
nice moduli space by including marked points. We construct the moduli spac
e of linear maps with marked points\, prove its rationality\, and show tha
t GIT stability is characterized by subtle dynamical conditions on the mar
ked map. The proof is a combinatorial analysis of polytopes generated by r
oot vectors of the A_N lattice from Lie theory.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Song Yu (Columbia University)
DTSTART;VALUE=DATE-TIME:20220226T161500Z
DTEND;VALUE=DATE-TIME:20220226T171500Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/24
DESCRIPTION:Title: Open/closed correspondence via relative/local correspondence\n
by Song Yu (Columbia University) as part of Moduli Across the Pandemic (MA
P)\n\n\nAbstract\nWe discuss a mathematical approach to the open/closed co
rrespondence proposed by Mayr\, which is a correspondence between the disk
invariants of toric Calabi-Yau threefolds and genus-zero closed Gromov-Wi
tten invariants of toric Calabi-Yau fourfolds. We establish the correspond
ence in two steps: First\, a correspondence between the disk invariants an
d the genus-zero maximally-tangent relative Gromov-Witten invariants of re
lative Calabi-Yau threefolds\, which follows from the topological vertex (
Li-Liu-Liu-Zhou\, Fang-Liu). Second\, a correspondence between the maximal
ly-tangent relative invariants and the closed invariants\, which can be vi
ewed as an instantiation of the log-local principle of van Garrel-Graber-R
uddat in the non-compact setting. Our correspondences are based on localiz
ation. We also discuss generalizations and implications of our corresponde
nces. Joint work with Chiu-Chu Melissa Liu.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wern Yeen Yeong (Notre Dame)
DTSTART;VALUE=DATE-TIME:20220326T140000Z
DTEND;VALUE=DATE-TIME:20220326T151500Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/25
DESCRIPTION:Title: Algebraic hyperbolicity of very general hypersurfaces in products
of projective spaces\nby Wern Yeen Yeong (Notre Dame) as part of Modul
i Across the Pandemic (MAP)\n\n\nAbstract\nA complex algebraic variety is
said to be hyperbolic if it contains no entire curves\, which are non-cons
tant holomorphic images of the complex line. Demailly introduced algebraic
hyperbolicity as an algebraic version of this property\, and it has since
been well-studied as a means for understanding Kobayashi’s conjecture\,
which says that a generic hypersurface in projective space is hyperbolic
whenever its degree is large enough. In this talk\, we study the algebraic
hyperbolicity of very general hypersurfaces of high bi-degrees in Pm x Pn
and completely classify them by their bi-degrees\, except for a few cases
in P3 x P1. We present three techniques to do that\, which build on past
work by Ein\, Voisin\, Pacienza\, Coskun and Riedl\, and others. As anothe
r application of these techniques\, we improve the known result that very
general hypersurfaces in Pn of degree at least 2n − 2 are algebraically
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://researchseminars.org/talk/modulipandemic/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Lian (HU Berlin)
DTSTART;VALUE=DATE-TIME:20220423T140000Z
DTEND;VALUE=DATE-TIME:20220423T150000Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/26
DESCRIPTION:Title: Tevelev degrees of hypersurfaces\nby Carl Lian (HU Berlin) as
part of Moduli Across the Pandemic (MAP)\n\n\nAbstract\nWe consider the fo
llowing problem: let (C\,p_1\,…\,p_n) be a fixed general pointed curve o
f genus g\, let X be a smooth hypersurface\, and let x_1\,…\,x_n be gene
ral points on X. Then\, how many degree d morphisms f:C->X are there for w
hich f(p_i)=x_i? This problem has been (largely\, but not completely) solv
ed „virtually“ in Gromov-Witten theory by Buch-Pandharipande and Cela.
The virtual counts are expected to be enumerative if d is sufficiently la
rge\, but this is only known for hypersurfaces of very low degree (joint w
ith Pandharipande).\n\nI will describe a more recent elementary approach t
o the problem via projective geometry\, which recovers the virtual counts.
The main difficulty is to analyze the transversality of the intersection
in question\, analogously to the prior investigation with Pandharipande. T
his leads to questions on bounding excess dimensions of certain families o
f singular curves on hypersurfaces which remain open.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Jovinelly (Notre Dame)
DTSTART;VALUE=DATE-TIME:20220423T151500Z
DTEND;VALUE=DATE-TIME:20220423T161500Z
DTSTAMP;VALUE=DATE-TIME:20240715T164335Z
UID:modulipandemic/27
DESCRIPTION:Title: Extreme Divisors on M_{0\,7} and Differences over Characteristic 2
\nby Eric Jovinelly (Notre Dame) as part of Moduli Across the Pandemic
(MAP)\n\n\nAbstract\nThe cone of effective divisors controls the rational
maps from a variety. We study this important object for M_{0\,n}\, the mo
duli space of stable rational curves with n markings. Fulton once conjectu
red the effective cones for each n would follow a certain combinatorial pa
ttern. However\, this pattern holds true only for n < 6. Despite many subs
equent attempts to describe the effective cones for all n\, we still lack
even a conjectural description. We study the simplest open case\, n=7\, an
d identify the first known difference between characteristic 0 and charact
eristic p. Although a full description of the effective cone for n=7 remai
ns open\, our methods allowed us to compute the entire effective cones of
spaces associated with other stability conditions.\n
LOCATION:https://researchseminars.org/talk/modulipandemic/27/
END:VEVENT
END:VCALENDAR