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BEGIN:VEVENT
SUMMARY:Dennis Tseng (MIT)
DTSTART;VALUE=DATE-TIME:20200926T140000Z
DTEND;VALUE=DATE-TIME:20200926T150000Z
DTSTAMP;VALUE=DATE-TIME:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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:20210926T114620Z
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
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