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BEGIN:VEVENT
SUMMARY:Juliette Bruce (Brown University)
DTSTART:20221129T200000Z
DTEND:20221129T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/1
DESCRIPTION:Title: Top weight cohomology of A_g\nby Juliette Bruce (Brown
University) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture h
eld in Harvard Science Center 507.\n\nAbstract\nI will discuss recent work
calculating the top weight cohomology of the moduli space A_g of principa
lly polarized abelian varieties of dimension g for small values of g. The
key idea is that this piece of cohomology is encoded combinatorially via t
he relationship between the boundary complex of a compactification of A_g
and the moduli space of tropical abelian varieties. This is joint work wit
h Madeline Brandt\, Melody Chan\, Margarida Melo\, Gwyneth Moreland\, and
Corey Wolfe.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tasuki Kinjo (University of Tokyo)
DTSTART:20221206T213000Z
DTEND:20221206T223000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/2
DESCRIPTION:Title: Cohomological Donaldson-Thomas theory for 2-Calabi--Yau cat
egories\nby Tasuki Kinjo (University of Tokyo) as part of Harvard MIT
Algebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nCoho
mological Donaldson-Thomas (CoDT) invariants were introduced by Kontsevich
-Soibelman and Brav-Bussi-Dupont-Joyce-Szendroi as categorifications of th
e Donaldson-Thomas invariants counting objects in 3-Calabi-Yau categories.
In this talk\, I will explain applications of the CoDT theory to the coho
mological study of the moduli of objects in 2-Calabi-Yau categories. Among
other things\, I will construct a coproduct on the Borel-Moore homology o
f the moduli stack of objects in these categories and establish a PBW-type
statement for the Kapranov-Vasserot cohomological Hall algebras. This tal
k is based on a joint work in progress with Ben Davison.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Padmavathi Srinivasan (ICERM)
DTSTART:20230418T190000Z
DTEND:20230418T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/3
DESCRIPTION:Title: A canonical algebraic cycle associated to a curve in its Ja
cobian\nby Padmavathi Srinivasan (ICERM) as part of Harvard MIT Algebr
aic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbs
tract\nWe will talk about the Ceresa class\, which is the image under a cy
cle class map of a canonical homologically trivial algebraic cycle associa
ted to a curve in its Jacobian. In his 1983 thesis\, Ceresa showed that th
e generic curve of genus at least 3 has nonvanishing Ceresa cycle modulo a
lgebraic equivalence. Strategies for proving Fermat curves have infinite o
rder Ceresa cycles due to B. Harris\, Bloch\, Bertolini-Darmon-Prasanna\,
Eskandari-Murty use a variety of ideas ranging from computation of explici
t iterated period integrals\, special values of p-adic L functions and poi
nts of infinite order on the Jacobian of Fermat curves. In fact\, Bloch's
results about the Ceresa cycle of Fermat quartics provided the first concr
ete evidence for the generalization of the BSD conjecture to the Bloch-Bei
linson conjectures.\n\nWe will survey several recent results about the Cer
esa cycle and the Ceresa class. The Ceresa class vanishes for all hyperell
iptic curves and was expected to be nonvanishing for non-hyperelliptic cur
ves. We will present joint work with Dean Bisogno\, Wanlin Li and Daniel L
itt\, where we construct a non-hyperelliptic genus 3 quotient of the Frick
e--Macbeath curve with torsion Ceresa class\, using the character theory o
f the automorphism group of the curve\, namely\, PSL2(F8).\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi Lombardi (University of Milan)
DTSTART:20230131T200000Z
DTEND:20230131T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/4
DESCRIPTION:Title: On the invariance of Hodge numbers under derived equivalenc
e\nby Luigi Lombardi (University of Milan) as part of Harvard MIT Alge
braic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nA
bstract\nA conjecture of Orlov predicts the invariance of the Hodge number
s of a smooth projective complex variety under derived equivalence. For in
stance this has been verified in the case of varieties of general type. In
this talk\, I will examine the case of varieties that are fibered by vari
eties of general type through the Albanese map. For this class of varietie
s I will prove the derived invariance of Hodge numbers of type $h^{0\,p}$\
, together with a few other invariants arising from the Albanese map. This
talk is based on a joint work with F. Caucci and G. Pareschi.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Küronya (Goethe-Universität Frankfurt)
DTSTART:20230214T200000Z
DTEND:20230214T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/5
DESCRIPTION:Title: Newton-Okounkov bodies and local positivity\nby Alex K
üronya (Goethe-Universität Frankfurt) as part of Harvard MIT Algebraic G
eometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract
\nThe purpose of this talk is to discuss Newton-Okounkov bodies\, \na conv
ex geometric construction associated to divisors on projective \nvarieties
. We will touch on their relationship with local positivity\, \nmultiplica
tive filtrations on section rings\, and applications.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Marian (Northeastern University)
DTSTART:20221206T200000Z
DTEND:20221206T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/6
DESCRIPTION:Title: On quot schemes of rank zero quotients over a curve\nby
Alina Marian (Northeastern University) as part of Harvard MIT Algebraic G
eometry Seminar\n\nLecture held in MIT 2-132.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samir Canning (ETH Zurich)
DTSTART:20221212T200000Z
DTEND:20221212T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/7
DESCRIPTION:Title: The Chow ring of the moduli space of degree 2 K3 surfaces\nby Samir Canning (ETH Zurich) as part of Harvard MIT Algebraic Geometr
y Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nThe
intersection theory of the moduli space of K3 surfaces polarized by a latt
ice is a subject of recent interest because of its deep connections with a
wide variety of mathematics\, including the intersection theory of moduli
spaces of curves and the study of modular forms. Oprea and Pandharipande
conjectured that the tautological rings of these moduli spaces of K3 surfa
ces are highly structured in a way that mirrors the picture for the moduli
space of curves. I will discuss the proof of this conjecture in the case
of K3 surfaces polarized by a degree 2 line bundle. This is joint work wit
h Dragos Oprea and Rahul Pandharipande.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sung Gi Park (Harvard University)
DTSTART:20230207T200000Z
DTEND:20230207T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/8
DESCRIPTION:Title: Kodaira dimension and hyperbolicity for smooth families of
varieties\nby Sung Gi Park (Harvard University) as part of Harvard MIT
Algebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nIn
this talk\, I will discuss the behavior of positivity\, hyperbolicity\, an
d Kodaira dimension under smooth morphisms of complex quasi-projective man
ifolds. This includes a vast generalization of a classical result: a fibra
tion from a projective surface of non-negative Kodaira dimension to a proj
ective line has at least three singular fibers. Furthermore\, I will expla
in a proof of Popa's conjecture on the superadditivity of the log Kodaira
dimension over bases of dimension at most three. These theorems are applic
ations of the main technical result\, namely the logarithmic base change t
heorem.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Hotchkiss (University of Michigan)
DTSTART:20230221T200000Z
DTEND:20230221T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/9
DESCRIPTION:Title: The period-index problem over the complex numbers\nby J
ames Hotchkiss (University of Michigan) as part of Harvard MIT Algebraic G
eometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract
\nThe period-index problem is a longstanding question about the complexity
of Brauer classes over a field. I will discuss some Hodge-theoretic aspec
ts of the problem for complex function fields\, and give some applications
to Brauer groups and the integral Hodge conjecture.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asher Auel (Dartmouth)
DTSTART:20230228T200000Z
DTEND:20230228T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/10
DESCRIPTION:Title: Maximal Brill-Noether loci\nby Asher Auel (Dartmouth)
as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Harva
rd Science Center 507.\n\nAbstract\nBrill-Noether theory answers the quest
ion of whether a general curve of genus $g$ admits $g^r_d$\, a linear syst
em of rank $r$ and degree $d$. A refined Brill-Noether theory hopes to an
swer the question of whether a "general curve with a $g^r_d$" admits a $g^
{r'}_{d'}$. In other words\, we want to know about the relative position
between Brill-Noether loci in the moduli space of curves of genus $g$. I'
ll explain a strategy for distinguishing Brill-Noether loci by studying th
e lifting of linear systems on curves in polarized K3 surfaces\, which mot
ivates a conjecture identifying the maximal Brill-Noether loci with respec
t to containment. Via an analysis of the stability of Lazarsfeld-Mukai bun
dles\, we obtain new lifting results for linear systems of rank 3 which su
ffice to prove the maximal Brill-Noether loci conjecture in genus 9-19\, 2
2\, and 23. This is joint work with Richard Haburcak.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Lacini (University of Kansas)
DTSTART:20230307T200000Z
DTEND:20230307T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/11
DESCRIPTION:Title: Syzygies of adjoint linear series on projective varieties<
/a>\nby Justin Lacini (University of Kansas) as part of Harvard MIT Algebr
aic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbs
tract\nSyzygies of algebraic varieties have long been a topic of intense i
nterest among algebraists and geometers alike. Starting with the pioneerin
g work of Mark Green on curves\, numerous attempts have been made to exten
d these results to higher dimensions. Ein and Lazarsfeld proved that if A
is a very ample line bundle\, then K_X + mA satisfies property N_p for any
m>=n+1+p. It has ever since been an open question if the same holds true
for A ample and basepoint free. In joint work with Purnaprajna Bangere we
give a positive answer to this question.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomer Schlank (MIT)
DTSTART:20230314T190000Z
DTEND:20230314T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/12
DESCRIPTION:Title: Higher Tsen Theorem\nby Tomer Schlank (MIT) as part of
Harvard MIT Algebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nA
bstract\nTsen's Theorem gives a simple sufficient criterion for an algebr
aic variety to have a point over a complex function field.\nIn the talk we
shall discuss a way to define on the collection of such points a structur
e of a stack and show that this stack is homologically contractible.\nWe s
hall explain a variant of this phenomenon that can be employed for the stu
dy of Beilinson-Drinfeld Opers for reductive groups.\nThis is joint work w
ith D. Beraldo and D. Kazhdan.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (Yale University)
DTSTART:20230321T190000Z
DTEND:20230321T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/13
DESCRIPTION:Title: Non-abelian Hodge theory and the P=W conjecture\nby Ju
nliang Shen (Yale University) as part of Harvard MIT Algebraic Geometry Se
minar\n\nLecture held in MIT 2-132.\n\nAbstract\nIn the first part of my t
alk\, I will introduce the P=W conjecture by de Cataldo\, Hausel\, and Mig
liorini (2010)\, predicting that the perverse filtration associated with t
he Hitchin system is identified with the weight filtration associated with
the corresponding character variety\, via non-abelian Hodge theory. Then
I will discuss a proof of the conjecture in joint work with Davesh Maulik\
, where we combine some ideas from enumerative geometry and representation
theory.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melody Chan (Brown University)
DTSTART:20230328T190000Z
DTEND:20230328T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/14
DESCRIPTION:Title: The weight 0 compactly supported Euler characteristic of m
oduli spaces of marked hyperelliptic curves\nby Melody Chan (Brown Uni
versity) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held
in Harvard Science Center 507.\n\nAbstract\nJoint work with Madeline Bran
dt and Siddarth Kannan. We use moduli\nspaces of G-admissible covers and
tropical geometry to give a\nsum-over-graphs formula for the weight-0 comp
actly supported Euler\ncharacteristic of the moduli spaces H_{g\,n} of n-m
arked hyperelliptic\ncurves of genus g\, as a virtual representation of S_
n. Computer\ncalculations then enable fully explicit formulas for the abo
ve in\nsmall genus. My aim is to make this talk accessible to anyone with
\npassing familiarity with M_g and its Deligne-Mumford compactification.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gavril Farkas (Humboldt University Berlin)
DTSTART:20230404T190000Z
DTEND:20230404T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/15
DESCRIPTION:Title: Resonance and Koszul modules in algebraic geometry\nby
Gavril Farkas (Humboldt University Berlin) as part of Harvard MIT Algebra
ic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbst
ract\nInspired from ideas in topology\, Koszul modules and the associated
resonance varieties turned out to have important algebro-geometric applica
tions for instance to (i) Green's Conjecture on syzygies of canonical curv
es\, (ii) stabilization of cohomology of projective varieties in arbitrary
characteristics and (iii) Chen invariants of hyperplane arrangements. I w
ill discuss new developments related to this circle of ideas obtained in j
oint work with Aprodu\, Raicu and Suciu.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Collins (MIT)
DTSTART:20230411T190000Z
DTEND:20230411T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/16
DESCRIPTION:Title: Mirror symmetry\, stability conditions and geometric invar
iant theory\nby Tristan Collins (MIT) as part of Harvard MIT Algebraic
Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nBridgeland st
ability conditions were originally motivated by the concept of Pi stabilit
y in theoretical physics\, as introduced in work of M. Douglas. Pi stabil
ity is an attempt to describe BPS states in string theory compactification
s. Alternatively\, BPS states in string theory can often be described by
solutions of certain nonlinear partial differential equations. In this ta
lk I will explain how\, starting from nonlinear PDEs\, ideas in GIT lead t
o a version of algebraic stability which is similar to Bridgeland stabilit
y. In particular\, I will explain how in several examples in dimension 2\
, GIT stability for line bundles implies Bridgeland stability\, but not co
nversely. In particular\, this yields effective tests for Bridgeland stab
ility in many examples.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dawei Chen (Boston College)
DTSTART:20230425T190000Z
DTEND:20230425T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/17
DESCRIPTION:Title: Counting differentials with fixed residues\nby Dawei C
hen (Boston College) as part of Harvard MIT Algebraic Geometry Seminar\n\n
Lecture held in Harvard Science Center 507.\n\nAbstract\nIn this talk\, we
investigate meromorphic differentials on the Riemann sphere with a single
zero and several poles of predetermined orders. Our aim is to determine t
he number of such differentials that satisfy the condition where the resid
ue at each pole is fixed. This question was previously explored by Gendron
and Tahar\, who employed graph counting techniques derived from the flat
geometry of differentials. We introduce a new approach using intersection
theory on moduli spaces of differentials. This is joint work with Miguel P
rado Godoy.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Casalaina-Martin (University of Colorado)
DTSTART:20230502T190000Z
DTEND:20230502T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/18
DESCRIPTION:Title: Moduli spaces of cubic hypersurfaces\nby Sebastian Cas
alaina-Martin (University of Colorado) as part of Harvard MIT Algebraic Ge
ometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\
nIn this talk I will give an overview of some recent work\, joint with Sam
uel Grushevsky\, Klaus Hulek\, and Radu Laza\, on the geometry and topolog
y of compactifications of the moduli spaces of cubic threefolds and cubic
surfaces. A focus of the talk will be on some results regarding non-isomor
phic smooth compactifications of the moduli space of cubic surfaces\, show
ing that two natural desingularizations of the moduli space have the same
cohomology\, and are both blow-ups of the moduli space at the same point\,
but are nevertheless\, not isomorphic\, and in fact\, not even K-equivale
nt.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Bitoun (University of Calgary)
DTSTART:20230509T190000Z
DTEND:20230509T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/19
DESCRIPTION:Title: On the D-module of an isolated singularity.\nby Thomas
Bitoun (University of Calgary) as part of Harvard MIT Algebraic Geometry
Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nLet Z be the germ of a
complex hypersurface isolated singularity of equation f. We consider the f
amily of analytic D-modules generated by the powers of 1/f and relate it t
o the pole order filtration on the de Rham cohomology of the complement of
\\{f=0\\}. This work builds on Vilonen’s characterization of the inters
ection homology D-module.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No seminar
DTSTART:20230516T190000Z
DTEND:20230516T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/20
DESCRIPTION:by No seminar as part of Harvard MIT Algebraic Geometry Semina
r\n\nLecture held in Harvard Science Center 507 or MIT 2-132.\nAbstract: T
BA\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Schnell (SUNY Stony Brook)
DTSTART:20230315T190000Z
DTEND:20230315T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/21
DESCRIPTION:Title: Hodge theory and Lagrangian fibrations (special time/locat
ion: 2-255)\nby Christian Schnell (SUNY Stony Brook) as part of Harva
rd MIT Algebraic Geometry Seminar\n\nLecture held in special location: 2-
255.\n\nAbstract\nThis is a talk about Lagrangian fibrations on holomorphi
c symplectic manifolds\, for example the Hitchin fibration (on the moduli
space of Higgs bundles over a curve). The general fiber of such a Lagrangi
an fibration is an abelian variety\, but the singular fibers are rather my
sterious. There were several beautiful conjectures about the Hodge theory
of Lagrangian fibrations\, proposed by Junliang Shen\, Qizheng Yin\, and D
avesh Maulik. I will try to introduce the conjectures and give an idea of
the proof.\n\nThis talk will be in 2-255 at MIT.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Tholozan (École Normale Supérieure)
DTSTART:20230523T190000Z
DTEND:20230523T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/22
DESCRIPTION:Title: Complex variations of Hodge structures of rank 2 over curv
es\nby Nicolas Tholozan (École Normale Supérieure) as part of Harvar
d MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center
507.\n\nAbstract\nThrough the work of Simpson\, complex variations of hod
ge structures (C-VHS) play a central role in the study of the moduli space
of local systems over a complex algebraic variety. In this talk I will co
nsider one of the simplest examples\, namely C-VHS of rank 2 over curves.
These objects are known to hyperbolic geometers as « branched hyperbolic
surfaces ».\n\nI will review what is known about their monodromy\, and di
scuss in particular a joint result with Bertrand Deroin: every PSL(2\,R)-l
ocal system of Euler class 2g-3 over a curve of genus g admits an isomonod
romic deformation that supports a C-VHS.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jun-Yong Park (University of Melbourne)
DTSTART:20230426T173000Z
DTEND:20230426T183000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/23
DESCRIPTION:Title: Height moduli on algebraic stacks and counting families of
varieties (special time and location SC 221)\nby Jun-Yong Park (Unive
rsity of Melbourne) as part of Harvard MIT Algebraic Geometry Seminar\n\nL
ecture held in Harvard Science Center 221 (special location).\n\nAbstract\
nI will begin by reviewing the classical algorithm of Tate with some expli
cit polynomial calculations. Combining this with twisted stable maps theor
y leads us to the height moduli of rational points of fixed stacky height
on the fine modular curve Mbar_{1\,1} over global function fields. We will
then compute arithmetic invariants of elliptic surfaces moduli via topolo
gical methods and give applications to counting elliptic curves over Fq(t)
.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miguel Moreira (MIT)
DTSTART:20230912T190000Z
DTEND:20230912T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/25
DESCRIPTION:Title: Enumerative geometry\, wall-crossing and Virasoro constrai
nts\nby Miguel Moreira (MIT) as part of Harvard MIT Algebraic Geometry
Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nGiven a moduli space o
f either sheaves on a smooth projective variety or a moduli space of repre
sentations of a quiver\, there are several invariants that we can extract.
One of the ways to get numbers out of a moduli space is to integrate (pos
sibly against a virtual fundamental class) certain tautological classes. S
uch numbers often have interesting structures behind\, and I will talk abo
ut two: how they change when one changes a stability condition (wall-cross
ing formulas) and some universal and explicit linear relations that those
invariants always seem to satisfy (Virasoro constraints). Both of these ph
enomena are related to a vertex algebra found by D. Joyce. For simplicity
I will mostly focus on the case of representations of a quiver. The talk i
s based on joint work with A. Bojko and W. Lim.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elden Elmanto (University of Toronto)
DTSTART:20230919T190000Z
DTEND:20230919T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/26
DESCRIPTION:Title: Cycling in Cambridge\nby Elden Elmanto (University of
Toronto) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held
in MIT 2-132.\n\nAbstract\nI spent most of my time here cycling (or is it
biking?) and thinking about algebraic cycles from a homotopical viewpoint
. I will speak about the latter. In joint work with Matthew Morrow\, we de
veloped a theory of motivic cohomology of schemes beyond the case of smoot
h schemes over a field. I will explain the cycle-theoretic aspects of this
construction\, focusing on the case of surfaces\, revisiting older result
s of Krishna and Srinivas.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Satriano (University of Waterloo)
DTSTART:20230926T190000Z
DTEND:20230926T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/27
DESCRIPTION:Title: Beyond twisted maps: crepant resolutions of log terminal s
ingularities and a motivic McKay correspondence\nby Matthew Satriano (
University of Waterloo) as part of Harvard MIT Algebraic Geometry Seminar\
n\nLecture held in Harvard Science Center 507.\n\nAbstract\nCrepant resolu
tions have inspired connections between birational geometry\, derived cate
gories\, representation theory\, and motivic integration. In this talk\, w
e prove that every variety with log-terminal singularities admits a crepan
t resolution by a smooth stack. We additionally prove a motivic McKay corr
espondence for stack-theoretic resolutions. Finally\, we show how our work
naturally leads to a generalization of twisted mapping spaces. No prior k
nowledge of stacks will be assumed. This is joint work with Jeremy Usatine
.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brad Dirks (Stony Brook)
DTSTART:20231003T190000Z
DTEND:20231003T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/28
DESCRIPTION:Title: The minimal exponent of LCI subvarieties\nby Brad Dirk
s (Stony Brook) as part of Harvard MIT Algebraic Geometry Seminar\n\nLectu
re held in Harvard Science Center 507.\n\nAbstract\nClassification of sing
ularities is an interesting problem in many areas of algebraic geometry\,
like the minimal model program. One classical approach is to assign to a v
ariety a rational number\, its log canonical threshold. For complex hypers
urface singularities\, this invariant has been refined by M. Saito to the
minimal exponent. This invariant is related to Bernstein-Sato polynomials\
, Hodge ideals and higher du Bois and higher rational singularities.\n\nIn
joint work with Qianyu Chen\, Mircea Mustață and Sebastián Olano\, we
defined the minimal exponent for LCI subvarieties of smooth complex variet
ies. We relate it to local cohomology\, higher du Bois and higher rational
singularities. I will describe what was done in the hypersurface case\, g
ive our definition in the LCI case and explain the relation to local cohom
ology modules and the classification of singularities.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Pieloch (MIT)
DTSTART:20231010T190000Z
DTEND:20231010T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/29
DESCRIPTION:Title: Uniruling projective families over $\\mathbb{CP}^1$ with r
ational (multi)sections\nby Alex Pieloch (MIT) as part of Harvard MIT
Algebraic Geometry Seminar\n\nLecture held in MIT 2-131.\n\nAbstract\nWe w
ill discuss a result which states that every projective family over $\\mat
hbb{CP}^1$ with at most two singular fibres is uniruled by rational (multi
)sections. We obtain these rational curves by using techniques from sympl
ectic geometry. In this talk\, we will focus on (1) discussing the motiva
tion for this work from Hodge theory and (2) presenting the geometric cons
tructions and ideas involved in our proofs. No knowledge of symplectic ge
ometry is required.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Dinkins (MIT)
DTSTART:20231017T190000Z
DTEND:20231017T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/30
DESCRIPTION:Title: Generalized quantum difference equations for quiver variet
ies\nby Hunter Dinkins (MIT) as part of Harvard MIT Algebraic Geometry
Seminar\n\nLecture held in MIT 2-143.\n\nAbstract\nCurve counts inside ce
rtain varieties are constrained by an equation called the quantum differen
ce equation. Okounkov and Smirnov described the quantum difference equatio
n for Nakajima quiver varieties in terms of a quantum group. There is a na
tural modification of their description\, which leads to a collection of "
exotic" quantum difference equations\, one for each alcove in a certain hy
perplane arrangement. Our main result is an enumerative-geometric descript
ion of the fundamental solution of these exotic equations. I will give an
overview of these ideas\, illustrating the results for the example of the
Hilbert scheme of points in the complex plane.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Gross (Cambridge)
DTSTART:20231024T190000Z
DTEND:20231024T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/31
DESCRIPTION:Title: Mirror symmetry and partial compactifications of K3 moduli
\nby Mark Gross (Cambridge) as part of Harvard MIT Algebraic Geometry
Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nI will
talk about work with Hacking\, Keel and Siebert on using mirror construct
ions to provide partial compactifications of the moduli of K3 surfaces. St
arting with a one-parameter maximally\nunipotent degeneration of Picard ra
nk 19 K3 surfaces\, we construct\, using methods of myself and Siebert\, a
mirror family which is defined in a formal neighbourhood of a union of st
rata of a toric variety whose fan is defined\, to first approximation\, as
the Mori fan of the original degeneration. This\nformal family may then b
e glued in to the moduli space of polarized K3 surfaces to obtain a partia
l compactification. Perhaps the most significant by-product of this constr
uction is the existence of theta functions in this formal neighbourhood\,
certain canonical bases for sections of powers of the\npolarizing line bun
dle.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakub Witaszek (Princeton)
DTSTART:20231031T190000Z
DTEND:20231031T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/32
DESCRIPTION:Title: Singularities in mixed characteristic via the Riemann-Hilb
ert correspondence\nby Jakub Witaszek (Princeton) as part of Harvard M
IT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center 50
7.\n\nAbstract\nIn my talk\, I will start by reviewing how various propert
ies of characteristic zero singularities can be understood topologically b
y ways of the Riemann-Hilbert correspondence. After that\, I will explain
how similar ideas can be applied in the study of mixed characteristic sing
ularities. This is based on a joint work (in progress) with Bhargav Bhatt\
, Linquan Ma\, Zsolt Patakfalvi\, Karl Schwede\, Kevin Tucker\, and Joe Wa
ldron.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Talk Cancelled (Talk Cancelled)
DTSTART:20231107T200000Z
DTEND:20231107T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/33
DESCRIPTION:Title: Talk Cancelled\nby Talk Cancelled (Talk Cancelled) as
part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard
Science Center 507.\n\nAbstract\nI will discuss an elementary notion -- th
e angle rank of a polynomial -- and an application to the Tate conjecture
for Abelian varieties over finite fields.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iacopo Brivio (Harvard University (CMSA))
DTSTART:20231114T200000Z
DTEND:20231114T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/34
DESCRIPTION:Title: Superadditivity of anticanonical Iitaka dimension in posit
ive characteristic\nby Iacopo Brivio (Harvard University (CMSA)) as pa
rt of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Sc
ience Center 507.\n\nAbstract\nGiven a fibration $f\\colon X\\to Y$ of smo
oth complex projective with general fiber $F$\, the celebrated Iitaka conj
ecture predicts the inequality $\\kappa(K_X)\\geq \\kappa(K_F)+\\kappa(K_Y
)$. Recently Chang showed that\, under some natural conditions\, the inequ
ality $\\kappa(-K_X)\\leq \\kappa(-K_F)+\\kappa(-K_Y)$ holds.\n\nIn this t
alk I will show that\, despite the failure in positive characteristic of b
oth the Iitaka conjecture and Chang's theorem\, it is possible to recover
the latter for "tame" positive characteristic fibrations. This is based on
joint work with M. Benozzo and C.-K. Chang.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:César Lozano Huerta (Universidad Nacional Autónoma de México)
DTSTART:20231121T200000Z
DTEND:20231121T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/35
DESCRIPTION:Title: The Noether-Lefschetz loci formed by determinantal surface
s in projective 3-space.\nby César Lozano Huerta (Universidad Naciona
l Autónoma de México) as part of Harvard MIT Algebraic Geometry Seminar\
n\nLecture held in Harvard Science Center 507.\n\nAbstract\nSolomon Lefsch
etz showed that the Picard group of a general surface in P3 of degree grea
ter than three is ZZ. That is\, the vast majority of surfaces in P3 have t
he smallest possible Picard group. The set of surfaces of degree greater t
han 3 on which this theorem fails is called the Noether-Lefschetz locus. T
his locus has infinite components and their dimensions are somehow mysteri
ous.\n\nIn this talk\, I will calculate the dimension of infinite Noether-
Lefschetz components that are simple in a sense\, but still give us an ide
a of the complexity of the entire Noether-Lefschetz locus. This is joint w
ork with Montserrat Vite and Manuel Leal.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emelie Arvidsson (University of Utah)
DTSTART:20231128T200000Z
DTEND:20231128T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/36
DESCRIPTION:Title: Properties of log canonical singularities in positive char
acteristic\nby Emelie Arvidsson (University of Utah) as part of Harvar
d MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center
507.\n\nAbstract\nWe will investigate if some well known properties of lo
g canonical singularities over the complex numbers still hold true over pe
rfect fields of positive characteristic and over excellent rings with perf
ect residue fields. We will discuss both pathological behavior in characte
ristic p as well as some positive results for threefolds. We will see that
the pathological behavior of these singularities in positive characterist
ic is closely linked to the failure of certain vanishing theorems in posit
ive characteristic. Additionally\, we will explore how these questions are
related to the moduli theory of varieties of general type.\n\nThis is bas
ed on joint work with F. Bernasconi and Zs. Patakfalvi\, as well as joint
work with Q. Posva.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Baudin (EPFL Lausanne)
DTSTART:20231205T200000Z
DTEND:20231205T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/37
DESCRIPTION:Title: On Ueno's conjecture in positive characteristics\nby J
eff Baudin (EPFL Lausanne) as part of Harvard MIT Algebraic Geometry Semin
ar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nIn characte
ristic zero\, Ueno's conjecture states that if X is a smooth projective va
riety with Kodaira dimension zero\, then its Albanese morphism in an algeb
raic fiber space and the Kodaira dimension of the general fiber is again z
ero. This was proven by Cao and Păun in 2016. \n\nBuilding on the generic
vanishing techniques of Hacon and Patakfalvi\, we prove a positive charac
teristic version of this result. We use it to deduce new cases of Iitaka's
subadditivity conjecture in positive characteristics. The goal of this ta
lk is to explain how these techniques work\, and how we can use them to pr
ove such results.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Perry (University of Michigan)
DTSTART:20231212T200000Z
DTEND:20231212T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/38
DESCRIPTION:Title: The period-index conjecture for abelian threefolds\nby
Alex Perry (University of Michigan) as part of Harvard MIT Algebraic Geom
etry Seminar\n\nLecture held in MIT 2-131.\n\nAbstract\nThe period-index c
onjecture asks for a precise bound on one measure of complexity of a Braue
r class (its index) in terms of another (its period). I will discuss joint
work with James Hotchkiss which proves this conjecture for Brauer classes
on abelian threefolds.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Lian (Tufts University)
DTSTART:20240206T200000Z
DTEND:20240206T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/39
DESCRIPTION:Title: Enumerativity of fixed-domain Gromov-Witten invariants
\nby Carl Lian (Tufts University) as part of Harvard MIT Algebraic Geometr
y Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nIt is well-understood
that Gromov-Witten (GW) invariants often fail to be enumerative. For exam
ple\, when r is at least 3\, the higher-genus GW invariants of P^r fail to
count smooth curves in projective space in any transparent sense. The sit
uation seems to be better when one fixes the complex structure of the doma
in curve. It was originally speculated that if X is a Fano variety\, then
the "fixed-domain" GW count of curves of sufficiently large degree passing
through the maximal number of general points is enumerative. I will discu
ss some positive and negative results in this direction\, focusing on the
case of hypersurfaces. The most recent results are joint with Roya Behesht
i\, Brian Lehmann\, Eric Riedl\, Jason Starr\, and Sho Tanimoto\, and buil
d on earlier work with Rahul Pandharipande and Alessio Cela.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Canceled
DTSTART:20240213T200000Z
DTEND:20240213T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/40
DESCRIPTION:Title: Canceled\nby Canceled as part of Harvard MIT Algebraic
Geometry Seminar\n\nLecture held in MIT 2-132.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Montserrat Teixidor (Tufts University)
DTSTART:20240220T200000Z
DTEND:20240220T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/41
DESCRIPTION:Title: Brill-Noether loci\nby Montserrat Teixidor (Tufts Univ
ersity) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held
in Harvard Science Center 507.\n\nAbstract\nBrill-Noether loci are defined
as the set of curves of genus g that have an unexpected linear series of
degree d and dimension r.\n\nPflueger showed that these loci are non-empty
when the expected codimension is at most g-3. By studying linear series o
n chains of elliptic curves\, we give a new proof of a slightly refined ve
rsion of this result. We can also look at the behavior of the generic curv
e in the locus.\n\nAn interesting conjecture of Auel and Haburcak states
that these loci are distinct and not contained in each other\, unless they
come from adding or removing fixed points. Their proof made use of curves
contained in K3 surfaces and was sufficient to prove the result in small
genus. Using chains of elliptic curves\, we can obtain additional informat
ion.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maksym Fedorchuk (Boston College)
DTSTART:20240227T200000Z
DTEND:20240227T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/42
DESCRIPTION:Title: CM-minimizers and standard models of Fano fibrations over
curves\nby Maksym Fedorchuk (Boston College) as part of Harvard MIT Al
gebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nA rece
nt achievement in K-stability of Fano varieties is an\nalgebro-geometric c
onstruction of a projective moduli space of\nK-polystable Fanos. The ample
line bundle on this moduli space is the\nCM line bundle of Tian. One of t
he consequences of the general theory\nis that given a family of K-stable
Fanos over a punctured curve\, the\npolystable filling is the one that min
imizes the degree of the CM line\nbundle after every finite base change
. A natural question is to\nask what are the CM-minimizers without<
/i> base change. In\nanswering this question\, we arrive at a theory of Ko
llár stability\nfor fibrations over one-dimensional bases\, and standard
models of Fano\nfibrations. After explaining the general theory\, I will s
ketch work in\nprogress on standard models of quartic threefold hypersurfa
ces. This\ntalk is based on joint work with Hamid Abban and Igor Krylov.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marta Benozzo (Imperial College)
DTSTART:20240305T200000Z
DTEND:20240305T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/43
DESCRIPTION:Title: On the canonical bundle formula in positive characteristic
\nby Marta Benozzo (Imperial College) as part of Harvard MIT Algebraic
Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstra
ct\nAn important problem in birational geometry is trying to relate in a m
eaningful way the canonical bundles of the source and the base of a fibrat
ion. The first instance of such a formula is Kodaira’s canonical bundle
formula for surfaces which admit a fibration with elliptic fibres. It desc
ribes the relation between the canonical bundles in terms of the singulari
ties of the fibres and their j-invariants.\nIn higher dimension\, we do no
t have an equivalent of the j-invariant\, but we can still define a moduli
part. Over fields of characteristic 0\, positivity properties of the modu
li part have been studied using variations of Hodge structures. Recently\,
the problem has been approached with techniques from the minimal model pr
ogram. These methods can be used to prove a canonical bundle formula resul
t in positive characteristic.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Marquand (NYU)
DTSTART:20240312T190000Z
DTEND:20240312T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/44
DESCRIPTION:Title: The defect of a cubic threefold\nby Lisa Marquand (NYU
) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Har
vard Science Center 507.\n\nAbstract\nThe defect of a cubic threefold with
isolated singularities is a measure of the failure of Poincare duality\,
and also the failure to be Q-factorial. From the work of Cheltsov\, a cubi
c threefold with only nodal singularities is Q factorial if and only if th
ere are at most 5 nodes. We investigate the defect of cubic threefolds wit
h worse than nodal isolated singularities\, and provide a geometric method
to compute this global invariant. One can then compute the Mixed Hodge st
ructure on the middle cohomology of the cubic threefold\, in terms of the
defect (a global invariant) and local invariants (Du Bois and Link invaria
nts) determined by the singularity types. We then relate the defect to geo
metric properties of the cubic threefold\, showing it is positive if and o
nly if the cubic contains a plane or a rational normal cubic scroll. The f
ocus of this work is to provide more insight into the existence of reducib
le fibers for compactified intermediate jacobian fibrations associated to
a smooth (not necessarily general) cubic fourfold. This is joint work with
Sasha Viktorova.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changho Han (Waterloo)
DTSTART:20240319T190000Z
DTEND:20240319T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/45
DESCRIPTION:Title: Extending the torelli map to alternative compactifications
of the moduli space of curves\nby Changho Han (Waterloo) as part of H
arvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science C
enter 507.\n\nAbstract\nIt is well-known that the Torelli map\, that turns
a smooth curve of genus g into its Jacobian (a principally polarized abel
ian variety of dimension g)\, extends to a map from the Deligne—Mumford
moduli of stable curves to the moduli of semi-abelic varieties by Alexeev.
Moreover\, it is also known that the Torelli map does not extend over the
alternative compactifications of the moduli of curves as described by the
Hassett—Keel program\, including the moduli of pseudostable curves (can
have nodes and cusps but not elliptic tails). But it is not yet known whe
ther the Torelli map extends over alternative compactifications of the mod
uli of curves described by Smyth\; what about the moduli of curves of genu
s g with rational m-fold singularities\, where m is a positive integer bou
nded above? As a joint work in progress with Jesse Kass and Matthew Satria
no\, I will describe moduli spaces of curves with m-fold singularities (wi
th topological constraints) and describe how far the Torelli map extends o
ver such spaces into the Alexeev compactifications.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dhruv Ranganathan (Cambridge)
DTSTART:20240326T190000Z
DTEND:20240326T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/46
DESCRIPTION:Title: A degeneration of the Hilbert scheme\nby Dhruv Rangana
than (Cambridge) as part of Harvard MIT Algebraic Geometry Seminar\n\nLect
ure held in MIT 2-449 (note special room!).\n\nAbstract\nSpecial Room: 2-
449\n\nGrothendieck's Hilbert scheme is a compact parameter space for subs
chemes of a projective scheme X. It is one of the basic moduli spaces in a
lgebraic geometry\, in the sense that it is the starting point for the con
struction of many others. One simple question about the Hilbert scheme is
the following: as X undergoes a nice degeneration\, what is the right way
to degenerate the Hilbert scheme of X along with it? One possible answer\,
proposed in the PhD thesis of Kennedy-Hunt\, comes from an object called
the logarithmic Hilbert scheme. I will give an introduction to this circle
of these ideas\, explain the basic geometric properties of the logarithmi
c Hilbert scheme\, and sketch connections with certain moduli spaces of hi
gher dimensional varieties. The talk reports on work of Kennedy-Hunt\, joi
nt work with Kennedy-Hunt\, and joint work with Maulik.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julianna Tymoczko (Smith College)
DTSTART:20240402T190000Z
DTEND:20240402T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/47
DESCRIPTION:Title: Webs and Schubert calculus for Springer fibers\nby Jul
ianna Tymoczko (Smith College) as part of Harvard MIT Algebraic Geometry S
eminar\n\nLecture held in MIT 2-132.\n\nAbstract\nClassical Schubert calcu
lus analyzes the geometry of the flag variety\, namely the space of nested
subspaces $V_1 \\subseteq V_2 \\subseteq \\cdots \\subseteq \\mathbb{C}^n
$\, asking enumerative questions about intersections of linear spaces that
turn out to be equivalent to deep problems in combinatorics and represent
ation theory. In this talk\, we'll describe some recent results in the Sc
hubert calculus of Springer fibers. Given a nilpotent linear operator $X$
\, the Springer fiber of $X$ is the subvariety of flags that are fixed by
$X$ in the sense that $XV_i \\subseteq V_i$ for all $i$. The top-dimensio
nal cohomology of Springer fibers admits a representation of the symmetric
group first discovered by Tonny Springer as the seminal example of a geom
etric representation. Where classical Schubert calculus describes geometr
y governed by permutations\, that of Springer fibers incorporates the comb
inatorics both of permutations and of partitions. We'll describe new resu
lts about this geometry in more detail\, including evidence that from a ge
ometric and topological perspective\, the best combinatorial model for Spr
inger fibers comes from representation-theoretic objects called webs.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Esser (Princeton)
DTSTART:20240409T190000Z
DTEND:20240409T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/48
DESCRIPTION:Title: The Dual Complex of a G-variety\nby Louis Esser (Princ
eton) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in
Harvard Science Center 507.\n\nAbstract\nWe introduce a new invariant of
G-varieties\, the dual complex\, which roughly measures how divisors in th
e complement of the free locus intersect. We show that the top homology gr
oup of this complex is an equivariant birational invariant of G-varieties.
As an application\, we demonstrate the non-linearizability of certain lar
ge abelian group actions on smooth hypersurfaces in projective space of an
y dimension and degree at least 3.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Han-Bom Moon (Fordham University)
DTSTART:20240416T190000Z
DTEND:20240416T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/49
DESCRIPTION:Title: Derived category of moduli space of vector bundles on a cu
rve\nby Han-Bom Moon (Fordham University) as part of Harvard MIT Algeb
raic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nThe deriv
ed category of moduli spaces of vector bundles on a curve is expected to b
e decomposed into the derived categories of symmetric products of the base
curve. I will briefly explain the expectation and known results\, and som
e consequences. This is joint work in progress with Kyoung-Seog Lee.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Larson (UC Berkeley)
DTSTART:20240423T190000Z
DTEND:20240423T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/50
DESCRIPTION:Title: The Chow ring of the universal Picard stack over the hyper
elliptic locus\nby Hannah Larson (UC Berkeley) as part of Harvard MIT
Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\
n\nAbstract\nUnderstanding the line bundles on curves are essential to und
erstanding the curves themselves. As such\, the universal Picard stack J^d
_g --> M_g parametrizing degree d line bundles on genus g curves is an imp
ortant object of study. Recently\, progress has been made on the intersect
ion theory of M_g in low genus by stratifying the moduli space by gonality
. The smallest piece in this stratification is the hyperelliptic locus. Mo
tivated by this\, I'll present several results about the restriction of J^
d_g to the hyperelliptic locus\, denoted J^d_{2\,g}. These include a prese
ntation of the rational Chow ring of J^d_{2\,g}. I also determine the inte
gral Picard group of J^d_{2\,g}\, completing (and extending to the PGL_2-e
quivariant case) prior work of Erman and Wood.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qile Chen (Boston College)
DTSTART:20240430T190000Z
DTEND:20240430T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/51
DESCRIPTION:Title: Campana rational connectedness\nby Qile Chen (Boston C
ollege) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held
in MIT 2-132.\n\nAbstract\nThe notion of Campana points were introduced by
Campana and Abramovich\, which interpolate between rational points and in
tegral points. In this talk\, we will focus on the geometric side and intr
oduce Campana rational connectedness --- a version of rational connectedne
ss for varieties with simple normal crossings boundaries. We further prove
that over function fields\, weak approximations by Campana points at good
places hold assuming Campana rational connectedness of fibers\, generaliz
ing a theorem of Hassett and Tschinkel. We further verify Campana rational
connectedness for many basic examples. Our approach relies on the theory
of stable log maps and their moduli. This is a joint work in progress with
Brian Lehmann and Sho Tanimoto.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Harris (Harvard University)
DTSTART:20240507T190000Z
DTEND:20240507T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/52
DESCRIPTION:Title: The Enriques Conjectures\nby Joe Harris (Harvard Unive
rsity) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held i
n Harvard Science Center 507.\n\nAbstract\nTwo fundamental facts about the
moduli space M_g of smooth curves of genus g are what are called Harer's
theorems: that the Picard group of M_g is of rank one\, generated (over th
e rational numbers) by the Hodge class\; and that the relative Picard grou
p of the universal curve over M_g is also of rank one\, generated by the r
elative dualizing sheaf. We can make analogous statements about the Severi
variety of plane curves and the Hurwitz space parametrizing branched cove
rs\, which are still open\; in fact\, the former was conjectured by Enriqu
es more than a century ago and remains open.\n\nIn this talk I'd like to d
escribe all of these theorems/conjectures\, and the implications among the
m\, including Isabel Vogt's recent work on Severi varieties. I'll be worki
ng entirely with rational coefficients\, so torsion classes\, which are fa
r more mysterious\, will not enter into it.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Borys Kadets (Hebrew University of Jerusalem)
DTSTART:20240402T203000Z
DTEND:20240402T213000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/56
DESCRIPTION:Title: Curves with many degree $d$ points (Joint with the MIT num
ber theory seminar\, note the special time and location)\nby Borys Kad
ets (Hebrew University of Jerusalem) as part of Harvard MIT Algebraic Geom
etry Seminar\n\nLecture held in MIT 2-449.\n\nAbstract\nWhen does a nice c
urve $X$ over a number field $k$ have infinitely many closed points of deg
ree $d$?\nFaltings' theorem allows us to rephrase this problem in purely a
lgebro-geometric terms\, though the resulting geometric question is far fr
om being fully solved. Previous work gave easy to state answers to the pro
blem for degrees $2$ (Harris-Silverman) and $3$ (Abramovich-Harris)\, but
also uncovered exotic constructions of such curves in all degrees $d \\geq
slant 4$ (Debarre-Fahlaoui). I will describe recent progress on the proble
m\, which answers the question in the large genus case. Along the way we u
ncover systematic explanations for the Debarre-Fahlaoui counstructions and
provide a complete geometric answer for $d \\leqslant 5$. The talk is bas
ed on joint work with Isabel Vogt.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Hase-Liu (Columbia University)
DTSTART:20241001T190000Z
DTEND:20241001T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/57
DESCRIPTION:Title: A circle method for algebraic geometers\nby Matthew Ha
se-Liu (Columbia University) as part of Harvard MIT Algebraic Geometry Sem
inar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nBrowning
and Vishe studied the moduli space of smooth genus zero curves of fixed de
gree on a smooth low-degree hypersurface using the circle method\, a techn
ique from analytic number theory. I'll explain how their strategy can be i
nterpreted completely algebro-geometrically\, and then use this perspectiv
e to generalize their results to the higher genus setting. Time permitting
\, I'll also discuss some applications to Geometric Manin's conjecture and
terminal singularities of these moduli spaces\, the latter of which is jo
int work with Jakob Glas.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:César Lozano Huerta (Universidad Nacional Autónoma de México)
DTSTART:20240625T190000Z
DTEND:20240625T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/58
DESCRIPTION:Title: Geometry of syzygies of sheaves on P2 via interpolation an
d Bridgeland stability.\nby César Lozano Huerta (Universidad Nacional
Autónoma de México) as part of Harvard MIT Algebraic Geometry Seminar\n
\nLecture held in Harvard Science Center 232.\n\nAbstract\nThe minimal fre
e resolution of a sheaf on P2\, such as a vector bundle or the ideal sheaf
of points\, carries important information about its moduli space. However
\, how it may do so has remained unclear.\n\nThis talk aims to clarify the
previous situation and\, I will compute the cone of effective divisors of
moduli spaces of sheaves using syzygies.\n\nNote the special room on the
second floor\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yajnaseni Dutta (Leiden University)
DTSTART:20240924T190000Z
DTEND:20240924T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/59
DESCRIPTION:Title: Twisted Intermediate Jacobian Fibrations\nby Yajnaseni
Dutta (Leiden University) as part of Harvard MIT Algebraic Geometry Semin
ar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nIn this tal
k\, I will report on a joint work in progress with D. Mattei and E. Shinde
r\, where we construct\, using Hodge modules\, a group scheme that can be
thought of as the intermediate Jacobian of a certain complete family of cu
bic threefolds. We show that the group scheme acts on a well-known abelian
fibration. The action gives rise to twisted versions of the abelian fibra
tion. This is similar to twisting genus 1 fibrations with irreducible fibr
es via its Tate-Shafarevich group.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andres Fernandez Herrero (University of Pennsylvania)
DTSTART:20240910T190000Z
DTEND:20240910T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/60
DESCRIPTION:Title: Decomposition theorem for the logarithmic Hitchin fibratio
n\nby Andres Fernandez Herrero (University of Pennsylvania) as part of
Harvard MIT Algebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nA
bstract\nThe focus of this talk will be the moduli space of logarithmic G-
Higgs bundles on a smooth projective curve\, where G is a reductive group.
I will explain some recent progress towards understanding the intersecti
on cohomology of this moduli space: a description of the decomposition the
orem for the corresponding Hitchin fibration. This is based on work in pr
ogress joint with Mark de Cataldo\, Roberto Fringuelli and Mirko Mauri.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusuf Mustopa (University of Massachusetts)
DTSTART:20241008T190000Z
DTEND:20241008T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/61
DESCRIPTION:Title: Convex Fujita Numbers and Projective Bundles\nby Yusuf
Mustopa (University of Massachusetts) as part of Harvard MIT Algebraic Ge
ometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nThe Fujita Freen
ess Conjecture predicts that for an ample line bundle $L$ on a smooth proj
ective variety $X$ of dimension $n\,$ the adjoint bundle $K \\otimes L^{\\
otimes m}$ is basepoint free for $m \\geq n+1\,$ and is currently open for
all $n \\geq 6.$ A numerical\n(and a priori stronger) form of this conje
cture\, whose hypothesis replaces the condition on $m$ with conditions on
intersection numbers involving $L\,$ was proposed by Helmke in 1997. As a
n interpolation between these two forms\, one can ask whether $K \\otimes
L_{1} \\otimes \\cdots \\otimes L_{m}$ is globally generated if $m \\geq n
+1$ and $L_{1}\, \\cdots \,L_{m}$ are arbitrary ample line bundles on $X.$
This leads naturally to the notion of the convex\nFujita number ${\\rm F
u}(X)$ of $X\,$ which measures "how soon" the global generation takes effe
ct. In this talk\, I will discuss ongoing joint work with Jiaming Chen\,
Alex Kuronya\, and Jakob Stix on the possible values of ${\\rm Fu}(X)\,$ w
ith emphasis on the case where $X$ is a projectivized vector bundle.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Paul Brasselet (CNRS)
DTSTART:20241112T190000Z
DTEND:20241112T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/62
DESCRIPTION:Title: Characteristic classes of singular varieties\nby Jean-
Paul Brasselet (CNRS) as part of Harvard MIT Algebraic Geometry Seminar\n\
nLecture held in Harvard Science Center Hall A.\n\nAbstract\nIn the case o
f manifolds\, Hirzebruch showed how to unify the theories of characteristi
c classes of Chern\, Todd and Thom-Hirzebruch. These three theories have b
een generalized to the case of singular complex algebraic varieties as nat
ural transformations of functors. We show how motivic theory allows these
natural transformations to be unified and what the underlying problems are
.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kendric Schefers (Stony Brook University)
DTSTART:20241210T200000Z
DTEND:20241210T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/63
DESCRIPTION:Title: Microlocal perspective on homology\nby Kendric Schefer
s (Stony Brook University) as part of Harvard MIT Algebraic Geometry Semin
ar\n\nLecture held in MIT 2-132.\n\nAbstract\nThe difference between the h
omology and cohomology of a space can be seen as a measure of the singular
ity of that space. This measure can be made precise for special fibers of
maps between smooth varieties by introducing the so-called "microlocal hom
ology" of such a map\, an object which records the singularities of the sp
ecial fiber as well as the codirections in which those singularities arise
.\n\nIn this talk\, we show that the microlocal homology is in fact intrin
sic to the special fiber—independent of its particular presentation—by
relating it to an object of (-1)-shifted symplectic geometry: the canonic
al perverse sheaf categorifying Donaldson-Thomas invariants introduced by
Joyce et al. Time permitting\, we will relate the microlocal homology to t
he singular support theory of coherent sheave\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Church (Stanford University)
DTSTART:20240917T190000Z
DTEND:20240917T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/64
DESCRIPTION:Title: Curves on complete intersections and measures of irrationa
lity\nby Benjamin Church (Stanford University) as part of Harvard MIT
Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\
n\nAbstract\nGiven a projective variety $X$\, it is always covered by curv
es obtained by taking the intersection with a linear subspace. We study wh
ether there exist curves on $X$ that have smaller numerical invariants tha
n those of the linear slices. If $X$ is a general complete intersection of
large degrees\, we show that there are no curves on $X$ of smaller degree
\, nor are there curves of asymptotically smaller gonality. This verifies
a folklore conjecture on the degrees of subvarieties of complete intersect
ions as well as a conjecture of Bastianelli--De Poi--Ein--Lazarsfeld--Ulle
ry on measures of irrationality for complete intersections. This is joint
work with Nathan Chen and Junyan Zhao.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Brazelton (Harvard University)
DTSTART:20241015T190000Z
DTEND:20241015T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/65
DESCRIPTION:Title: Symmetry in classical enumerative geometry\nby Thomas
Brazelton (Harvard University) as part of Harvard MIT Algebraic Geometry S
eminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nIn this
talk we'll discuss an equivariant principle of conservation of number\, p
roven using methods from equivariant homotopy theory. It roughly states th
at in the presence of symmetry\, not only the number of solutions is conse
rved\, but their symmetries are as well. For instance when a cubic surface
is defined by a symmetric polynomial\, its 27 lines always carry the same
S4 action. We apply this idea in joint work with C. Bethea to compute bit
angents to smooth plane quartics with nontrivial automorphism groups\, whe
re we see that homotopical techniques directly reveal patterns which are n
ot obvious from a classical moduli perspective. We will also discuss work
with S. Raman\, in which we initiate a study of Galois groups of symmetric
enumerative problems\, leveraging tools from Hodge theory and computation
al numerical analysis.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anh Đức Võ (Harvard University)
DTSTART:20241022T190000Z
DTEND:20241022T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/66
DESCRIPTION:Title: Du Bois complexes and singularities\nby Anh Đức Võ
(Harvard University) as part of Harvard MIT Algebraic Geometry Seminar\n\
nLecture held in Harvard Science Center 507.\n\nAbstract\nIn this talk\, I
will discuss the notion of Du Bois complexes and provide an overview of c
lassical notions: rational and Du Bois singularities. I will then discuss
their recent extensions to k-rational and k-Du Bois singularities\, both f
or local complete intersections (LCIs) and non-LCI varieties. Additionally
\, I will discuss results on the injectivity and vanishing properties of D
u Bois complexes in the context of these generalizations. This talk is bas
ed on joint works with Mihnea Popa\, Wanchun Shen\, and Sridhar Venkatesh.
\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Botta (Columbia University)
DTSTART:20241029T190000Z
DTEND:20241029T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/67
DESCRIPTION:Title: Maulik-Okounkov Lie algebras and BPS Lie algebras\nby
Tommaso Botta (Columbia University) as part of Harvard MIT Algebraic Geome
try Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nThe Maulik-Okounkov
Lie algebra associated to a quiver Q controls the R-matrix formalism deve
loped by Maulik and Okounkov in the context of quantum cohomology of Nakaj
ima quiver varieties. On the other hand\, the BPS Lie algebra originates f
rom cohomological DT theory\, particularly from the theory of cohomologica
l Hall algebras associated with 3 Calabi-Yau categories. In this talk\, I
will explain how to identify the MO Lie algebra of an arbitrary quiver wit
h the (appropriate) BPS Lie algebra. The bridge to compare these seemingly
diverse words is the theory of non-abelian stable envelopes\, which is ex
ploited to relate representations of the MO Lie algebra to representations
of the BPS Lie algebra. In conclusion\, I will apply this result to deduc
e Okounkov's conjecture\, equating the graded dimensions of the MO Lie alg
ebra with the coefficients of Kac polynomials. This is joint work with Ben
Davison.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Younghan Bae (University of Michigan)
DTSTART:20241105T200000Z
DTEND:20241105T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/68
DESCRIPTION:Title: Fourier transformation and the Abel-Jacobi section\nby
Younghan Bae (University of Michigan) as part of Harvard MIT Algebraic Ge
ometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nLet v1\, ... \,
vn be a vector of integers that sum to zero. On the relative Jacobian over
the moduli space of smooth genus g curves with n sections\, the Abel-Jaco
bi section maps a marked curve (C\, x1\, ...\, xn) to a line bundle O(v1.x
1+ ... + vn.xn). Using the Fourier-Mukai transform\, this locus can be exp
ressed as a power of twisted theta divisor. When the curve acquires nodal
singularities\, the relative Jacobian can be compactified via stable rank
1 torsion-free sheaves. After blowing up the base\, the Abel-Jacobi sectio
n extends and its class can be computed using Pixton's formula on the univ
ersal double ramification cycle formula.\n\nIn this talk\, we propose a co
njectural closed formula for the pushforward of monomials of divisor class
es on compactified Jacobians. This conjecture is motivated by an explicit
computation of Fourier transform on the compactified Jacobian and combinat
orial properties of the Pixton's formula. We verify the conjecture over va
rious open loci of the base. This is joint work in progress with Samouil M
olcho and Aaron Pixton.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hélène Esnault (Harvard University)
DTSTART:20241119T200000Z
DTEND:20241119T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/69
DESCRIPTION:Title: A non-abelian version of Deligne's Fixed Part Theorem\
nby Hélène Esnault (Harvard University) as part of Harvard MIT Algebraic
Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstra
ct\nWe prove a non-abelian version of Deligne’s Fix Part Theorem. It\nis
a statement which is purely anchored in complex geometry. The\nreason for
the consideration is a vaster program which aims at\nunderstanding some a
spects of the monodromy-weight conjecture\nin unequal characteristic by
’tilting it’ to a complex situation for\nwhich we have the tools devel
oped notably by Morihiko Saito and\nTakuro Mochizuki. This lecture focuses
on a small part of it.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Petrov (MIT)
DTSTART:20241126T200000Z
DTEND:20241126T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/70
DESCRIPTION:Title: De Rham cohomology of varieties in positive characteristic
\nby Alexander Petrov (MIT) as part of Harvard MIT Algebraic Geometry
Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nHodge
theory provides an additional structure of Hodge decomposition on the coho
mology of a smooth proper variety over complex numbers\, and implies cohom
ology vanishing results such as Kodaira vanishing. For varieties in positi
ve characteristic Hodge decomposition in general fails to exist\, but Deli
gne and Illusie found a very satisfactory substitute for Hodge theory that
applies to smooth proper varieties over $\\mathbf{F}_p$ that lift to $\\m
athbf{Z}/p^2$ and have dimension $\\leq p$. They proved that in this case
the algebraic de Rham complex is quasi-isomorphic to the direct sum of its
cohomology sheaves\, which induces a decomposition of de Rham cohomology
into the direct sum of Hodge cohomology groups\, and implies Kodaira vanis
hing.\n\nFor liftable varieties of larger dimension Hodge decomposition mi
ght still fail to exist\, but there are more narrow classes of varieties o
f arbitrary dimension\, such as Frobenius-split and quasi-Frobenius-split
ones\, for which the de Rham complex decomposes. I will discuss the proof
of these decomposition results which relies on interpreting de Rham cohomo
logy via the de Rham stack\, introduced in positive characteristic by Drin
feld and Bhatt-Lurie.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Halpern-Leistner (Cornell University)
DTSTART:20241203T200000Z
DTEND:20241203T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/71
DESCRIPTION:Title: Dispatches from the ends of the stability manifold\nby
Daniel Halpern-Leistner (Cornell University) as part of Harvard MIT Algeb
raic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nThe manif
old of Bridgeland stability conditions parameterizes a homological structu
re on a triangulated category that is analogous to a Kaehler structure on
a projective variety. Recently\, I have introduced a noncommutative minima
l model program\, which proposes to identify canonical (semiorthogonal)dec
ompositions of derived categories of coherent sheaves by studying paths in
the stability manifold converging to certain points at infinity. I will d
iscuss a partial compactification of the stability manifold\, the space of
augmented stability conditions\, which makes this picture more precise. T
o do this\, I will introduce a structure on a triangulated category that w
e call a multi-scale decomposition\, which generalizes a semiorthogonal de
composition\, and a new moduli space of genus zero curves equipped with me
romorphic differentials. The main conjecture about the space of augmented
stability conditions is that it is a manifold with corners (in a specific
way that I will explain). One consequence: If this conjecture holds for an
y smooth and proper dg-category\, then any stability condition on a smooth
and proper dg-category admits proper moduli spaces of semistable objects.
\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Doran (University of Alberta\, Bard College\, and CMSA)
DTSTART:20241217T200000Z
DTEND:20241217T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/72
DESCRIPTION:Title: Bounding the Complexity of Feynman Integrals with Hodge Th
eory\nby Charles Doran (University of Alberta\, Bard College\, and CMS
A) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Ha
rvard Science Center 507.\n\nAbstract\nTwenty years ago\, Bloch\, Esnault\
, and Kreimer introduced an algebro-geometric formulation of Feynman integ
ration\, building on Griffiths' theory of variation of mixed Hodge structu
re. Explicit computation for specific Feynman graphs with all parameters
has proved an elusive goal. With Andrew Harder and Pierre Vanhove\, we us
e quadric bundles to establish a complexity bound on the motives underlyin
g an infinite collection of two-loop Feynman integrals. For another famil
y of graphs with unbounded loop order\, we describe the geometry and Hodge
theory of the Feynman motives of Calabi-Yau type.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashvin Swaminathan (Harvard University)
DTSTART:20250304T200000Z
DTEND:20250304T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/75
DESCRIPTION:Title: A positive proportion of hyperelliptic curves have no unex
pected quadratic points\nby Ashvin Swaminathan (Harvard University) as
part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard
Science Center 507.\n\nAbstract\nWe prove that when even-degree hyperelli
ptic curves are ordered by the sizes of their coefficients\, a positive pr
oportion of them have no unexpected quadratic points --- i.e.\, no points
defined over quadratic fields except for those that arise by pulling back
rational points from P^1. To obtain this result\, we combine a generalizat
ion of Selmer-group Chabauty (due to Poonen-Stoll) with new results on the
average size of the 2-Selmer groups of Jacobians of even-degree hyperelli
ptic curves. This is joint work with Manjul Bhargava\, Jef Laga\, and Arul
Shankar.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sándor Kovács (University of Washington)
DTSTART:20250124T200000Z
DTEND:20250124T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/76
DESCRIPTION:Title: KSB stability is automatic in codimension 3\nby Sándo
r Kovács (University of Washington) as part of Harvard MIT Algebraic Geom
etry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nI
will start with a review of KSB/A stability\, especially their local vers
ion and then discuss joint work with János Kollár\, showing that it is e
nough to check these conditions\, including flatness\, up to codimension 2
. This implies that we have a very good understanding of this stability co
ndition in general\, because local KSB-stability is trivial at codimension
1 points\, and quite well understood at codimension 2 points\, since we h
ave a complete classification of 2-dimensional slc singularities.\n\nNote
the special date. The time and location are the usual.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:SPRING BREAK
DTSTART:20250318T190000Z
DTEND:20250318T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/77
DESCRIPTION:by SPRING BREAK as part of Harvard MIT Algebraic Geometry Semi
nar\n\nLecture held in Harvard Science Center 507 or MIT 2-132.\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoon-Joo Kim (Columbia University)
DTSTART:20250204T200000Z
DTEND:20250204T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/78
DESCRIPTION:Title: The Néron model of a Lagrangian fibration\nby Yoon-Jo
o Kim (Columbia University) as part of Harvard MIT Algebraic Geometry Semi
nar\n\nLecture held in Harvard Science Center 507 or MIT 2-132.\n\nAbstrac
t\nSingular fibers in minimal elliptic fibrations were classified by Kodai
ra and Néron in the 1960s. In his proof\, Néron constructed and systemat
ically used a special group scheme acting on an elliptic fibration. This g
roup scheme is now called the Néron model.\nA Lagrangian fibration is a h
igher-dimensional generalization of an elliptic fibration. Néron’s theo
ry is restricted to 1-dimensional bases\, so one cannot use Néron’s ori
ginal approach to study higher-dimensional Lagrangian fibrations. The high
er-dimensional analog of Néron’s definition was recently proposed by Da
vid Holmes. Quite unfortunately\, Holmes also showed that such a generaliz
ed Néron model often fails to exist\, even in simple cases.\nIn this talk
\, we show that Holmes’s generalized Néron model does exist for an arbi
trary projective Lagrangian fibration of a smooth symplectic variety\, und
er a single assumption that the Lagrangian fibration has no fully-nonreduc
ed fibers. This generalizes Néron’s result to many higher-dimensional L
agrangian fibrations. Such a construction has several applications. First\
, it extends Ngô's results on Hitchin fibrations to many Lagrangian fibra
tions. Second\, it allows Lagrangian fibrations to be considered as a mini
mal model-compactification of a smooth commutative group scheme-torsor. Th
ird\, it provides a tool to study birational behaviors of Lagrangian fibra
tions. Finally\, the notion of a Tate-Shafarevich twist can be understood
via the Néron model.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Ibáñez Núñez (Columbia University)
DTSTART:20250401T190000Z
DTEND:20250401T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/79
DESCRIPTION:Title: Euler characteristic of Artin stacks and intrinsic Donalds
on-Thomas theory\nby Andrés Ibáñez Núñez (Columbia University) as
part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in MIT 2-1
31.\n\nAbstract\nThe Euler characteristic of an Artin stack over the compl
ex numbers is not a priori well-defined\, due to the presence of non-zero
cohomology in infinitely many degrees. We will show how to fix the definit
ion by introducing a combinatorial gadget that we call the component latti
ce of the stack. This will allow us to define a certain algebraic structur
e on the ring of naive motives over the stack\, akin to a Hall algebra. Th
is Hall structure produces a motivic invariant of the stack for which the
Euler characteristic is well-defined\, a fact that we call the no-pole the
orem.\n\nIn the case of (-1)-shifted symplectic stacks\, our machinery pro
duces generalized Donaldson-Thomas invariants. When the stack parametrizes
objects in an abelian category\, one recovers Joyce-Song invariants. Thus
our work is a generalization of Donaldson-Thomas theory to abstract stack
s. We will explain how the intrinsic set-up also allows to simplify the fo
undations of (usual) motivic Donaldson-Thomas theory considerably.\n\nThis
is joint work with Chenjing Bu and Tasuki Kinjo.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lenny Taelman (University of Amsterdam)
DTSTART:20250128T200000Z
DTEND:20250128T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/80
DESCRIPTION:Title: Deformations of Calabi—Yau varieties in characteristic p
\nby Lenny Taelman (University of Amsterdam) as part of Harvard MIT Al
gebraic Geometry Seminar\n\nLecture held in MIT 2-361.\n\nAbstract\nA smoo
th projective variety X is said to be Calabi-Yau if its canonical bundle i
s trivial. I will discuss joint work with Lukas Brantner\, in which we use
derived algebraic geometry to study deformations of Calabi-Yau varieties
in characteristic p. We prove a positive characteristic analogue of the Bo
gomolov-Tian-Todorov theorem (which states that deformations of Calabi-Yau
varieties in characteristic 0 are unobstructed)\, and show that 'ordinary
' Calabi-Yau varieties admit canonical lifts to characteristic zero (gener
alising earlier results of Serre-Tate for abelian varieties\, and Deligne
and Nygaard for K3 surfaces). In this talk\, no prior knowledge of derived
algebraic geometry will be assumed.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan Zavyalov (Princeton University)
DTSTART:20250408T190000Z
DTEND:20250408T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/81
DESCRIPTION:Title: The trace morphism and Poincaré duality in p-adic non-arc
himedean geometry\nby Bogdan Zavyalov (Princeton University) as part o
f Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Scienc
e Center 507.\n\nAbstract\nI will explain a construction of the trace morp
hism for smooth morphism \nof analytic adic spaces. Then I will explain ho
w one can use this trace to prove various \nPoincare Duality type results.
In particular\, I will discuss a new easy proof of Poincare Duality \nfor
F_p-cohomology groups of smooth proper p-adic rigid-analytic spaces and a
n appropriate\ngeneralization of this result to arbitrary proper morphisms
.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Bakker (UIC)
DTSTART:20250506T190000Z
DTEND:20250506T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/82
DESCRIPTION:Title: The linear Shafarevich conjecture for quasiprojective vari
eties (part 2)\nby Ben Bakker (UIC) as part of Harvard MIT Algebraic G
eometry Seminar\n\nLecture held in MIT 2-131.\n\nAbstract\nShafarevich ask
ed whether the universal cover of a smooth projective variety X is always
holomorphically convex\, meaning it admits a proper map to a Stein space.
This was proven in the linear case---namely when X admits an almost faith
ful representation of its fundamental group---by Eyssidieux--Katzarkov--Pa
ntev--Ramachandran using techniques from non-abelian Hodge theory. In joi
nt work with Y. Brunebarbe and J. Tsimerman\, we prove a version of the li
near Shafarevich conjecture for quasiprojective varieties. The proof reli
es on a number of recent advances in non-abelian Hodge theory in the non-p
roper case.\n\nIn the first talk I will outline the general strategy and e
xplain why non-abelian Hodge theory naturally shows up in the context of S
hafarevich's question. In the second talk I will provide some details of
the proof\, including the role played by the twistor geometry of the stack
of local systems and the algebraic integrability of Katzarkov--Zuo foliat
ions. As a bonus\, I will also explain how these techniques prove the alg
ebraicity of Shafarevich morphisms\, which generalizes Griffiths' conjectu
re on the algebraicity of the images of period maps to arbitrary local sys
tems.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillermo Peñafort Sanchis (University of Valencia)
DTSTART:20250211T200000Z
DTEND:20250211T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/83
DESCRIPTION:Title: Open problems about deformations of singular holomorphic m
ap germs\nby Guillermo Peñafort Sanchis (University of Valencia) as p
art of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard S
cience Center 507.\n\nAbstract\nThe theory of deformations of germs of hol
omorphic mappings and the theory of deformations of germs of complex hyper
surfaces share many features\, which become apparent once one knows how to
translate from one to the other. But\, for any result about hypersurfaces
\, the corresponding result about mappings tends to be much harder to prov
e. In this talk we will discuss open problems about singular mappings\, ba
sed on the following known results about isolated hypersurface singulariti
es:\n \n\n· The Milnor number is greater than or equal to the Tjurina num
ber and their quotient cannot exceed the dimension of the ambie
nt space.\n\n \n· If two hypersurfaces have the same topological type\, t
hen their Milnor numbers are equal.\n \n\n· Singularities cannot be split
in two without giving rise to non-trivial homology.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasudevan Srinivas (Tata and Univ. of Buffalo)
DTSTART:20250415T190000Z
DTEND:20250415T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/84
DESCRIPTION:Title: Some finiteness results for the etale fundamental group in
positive characteristics\nby Vasudevan Srinivas (Tata and Univ. of Bu
ffalo) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held i
n Harvard Science Center 507.\n\nAbstract\nThis talk will discuss some res
ults on etale fundamental groups of varieties over an algebraically closed
field of characteristic p > 0\, based on joint work with Hélène Esnault
and other coauthors. One result\, along with Mark Shusterman\, is that th
e tame fundamental group is finitely presented for such a variety which is
the complement of an SNC divisor in a smooth projective variety. A second
\, along with Jakob Stix\, is to give an obstruction for a smooth projecti
ve variety to admit a lifting to characteristic 0\, in terms of the struct
ure of its etale fundamental group as a profinite group. We will finally t
ouch on some open questions.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sameera Vemulapalli (Harvard University)
DTSTART:20250218T200000Z
DTEND:20250218T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/85
DESCRIPTION:Title: Brill--Noether theory of smooth plane curves\nby Samee
ra Vemulapalli (Harvard University) as part of Harvard MIT Algebraic Geome
try Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nGi
ven a smooth curve C\, it is natural to ask: what are all the degree $d$ m
aps from $C$ into a projective space $\\mathbb{P}^r$? The study of this qu
estion is called Brill-Noether theory. Given a curve $C$\, the data of a d
egree d map $C \\rightarrow \\mathbb{P}^r$ is equivalent to the data of a
degree $d$ line bundle on $C$ together with a choice of $r + 1$ global sec
tions having no common zeros. As such\, a central object of study is the B
rill–Noether locus $W^r_d(C)$\, which is defined to be the space of degr
ee $d$ line bundles on $C$ with at least $r+1$ global sections.\n\nThe fam
ous Brill-Noether theorem gives a nice description of $W^r_d(C)$ when $C$
is a general curve of genus $g$. However\, curves we come across in nature
(such as curves in the plane) are not general\, and may fail the Brill-No
ether theorem! In this talk\, I'll describe joint work with Hannah Larson
\, in which we describe the Brill-Noether theory of smooth plane curves (a
nd more generally\, curves on Hirzebruch surfaces)\, using tools from arit
hmetic statistics.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Lehmann (Boston College)
DTSTART:20250325T190000Z
DTEND:20250325T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/86
DESCRIPTION:Title: Homological stability for rational curves on quartic del P
ezzo surfaces\nby Brian Lehmann (Boston College) as part of Harvard MI
T Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center 507
.\n\nAbstract\nThe moduli space of rational curves on a Fano variety is ex
pected to exhibit "motivic" stability. Both Manin's conjecture (over a fi
nite field) and the Cohen-Jones-Segal conjecture (over the complex numbers
) are instances of this meta-conjecture.\n\nI will discuss ongoing joint w
ork with Ronno Das\, Sho Tanimoto\, and Philip Tosteson in which we prove
versions of these two conjectures for degree 4 del Pezzo surfaces. The pr
oofs share a common method\, demonstrating the compatibility of these conj
ectures in this special case. Our work builds upon a new technique develo
ped previously by Das-Tosteson using additional arguments from algebraic g
eometry\, topology\, and number theory.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Izzet Coskun (UIC)
DTSTART:20250422T190000Z
DTEND:20250422T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/87
DESCRIPTION:Title: Brill-Noether for moduli spaces of sheaves on surfaces
\nby Izzet Coskun (UIC) as part of Harvard MIT Algebraic Geometry Seminar\
n\nLecture held in Harvard Science Center 507.\n\nAbstract\nIn this talk\,
I will discuss recent work on Brill-Noether theory for moduli spaces of s
heaves on surfaces. I will first discuss the cohomology of the general sta
ble sheaf on surfaces such as K3 and abelian surfaces. If time permits\,
I will describe some recent results on the cohomology jumping loci. This t
alk is based on joint work with Jack Huizenga\, Howard Nuer\, Neelarnab Ra
ha and Kota Yoshioka.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Wu (Zhejiang University)
DTSTART:20250429T190000Z
DTEND:20250429T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/88
DESCRIPTION:Title: Geometry of Bernstein-Sato ideals\nby Lei Wu (Zhejiang
University) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture
held in Harvard Science Center 507.\n\nAbstract\nIn studying Mellin transf
orms of multivariable polynomial functions\, Gelfand defined the so-called
Archimedean zeta function of a polynomial and conjectured that the archim
edean zeta function has a meromorphic continuation on the whole complex pl
ane in 1950s. Bernstein introduced the so-called Bernstein-Sato polynomial
(or b-function) and solved the conjecture in the 1970s. In this talk\, I
will discuss how we can generalize the construction of Bernstein for a fin
ite union of polynomial functions by defining Bernstein-Sato ideals follow
ing the ideas of Sabbah. Then I will discuss geometric properties of such
ideals and prove that the variety of the Bernstein-Sato ideal is defined o
ver Q and each of its irreducible components is a translated linear subspa
ce\, generalizing a classical result of Kashiwara for b-functions.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ishan Levy (University of Copenhagen)
DTSTART:20250513T190000Z
DTEND:20250513T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/89
DESCRIPTION:Title: Hurwitz spaces and the asymptotic Picard rank conjecture\nby Ishan Levy (University of Copenhagen) as part of Harvard MIT Algebr
aic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbs
tract\nI will explain work joint with Aaron Landesman where we prove that
for a finite group G and conjugacy invariant subset c\, Hurwitz spaces par
ameterizing connected G-covers of the complement of a configuration of poi
nts on a disk with monodromy in c satisfy homological stability. We use th
is to prove that the Hurwitz stack parameterizing simply branched degree d
covers of P^1 with n branch points has trivial rational Picard group when
n is much larger than d.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ajith Urundolil Kumaran (MIT)
DTSTART:20250225T200000Z
DTEND:20250225T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/90
DESCRIPTION:Title: Refined tropical curve counting with descendants\nby A
jith Urundolil Kumaran (MIT) as part of Harvard MIT Algebraic Geometry Sem
inar\n\nLecture held in MIT 2-131.\n\nAbstract\nWe introduce the enumerati
ve geometry of curves in the algebraic torus $(\\mathbb{C}^\\ast)^2$. We s
how that a certain class of invariants associated with moduli spaces of cu
rves in $(\\mathbb{C}^\\ast)^2$ can be calculated explicitly using a refin
ed tropical correspondence theorem. If time permits we will explain how th
e proof relies on higher double ramification cycles and work of Buryak-Ros
si on integrable systems on the moduli space of curves. This is joint work
with Patrick Kennedy-Hunt and Qaasim Shafi.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Jovinelly (Brown University)
DTSTART:20250311T190000Z
DTEND:20250311T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/91
DESCRIPTION:Title: Free Curves in Singular Varieties\nby Eric Jovinelly (
Brown University) as part of Harvard MIT Algebraic Geometry Seminar\n\nLec
ture held in MIT 2-131.\n\nAbstract\nRational curves are intricately linke
d to the birational geometry of varieties containing them. Certain curves
\, called free curves\, have the nicest deformation properties. However\,
it is unknown whether mildly singular Fano varieties contain free rationa
l curves in their smooth locus. In this talk\, we discuss free curves of
higher genus. Using recent results about tangent bundles\, we prove that
any klt Fano variety has higher genus free curves. We then use the existe
nce of such free curves to get some applications: we prove the existence o
f free rational curves in terminal Fano threefolds\; obtain an optimal upp
er bound on the length of extremal rays in the Kleiman-Mori cone of any kl
t pair\; and study the fundamental group of the smooth locus of a Fano var
iety. This is joint work with Brian Lehmann and Eric Riedl.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Klingler (Humboldt Univ.)
DTSTART:20251111T200000Z
DTEND:20251111T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/92
DESCRIPTION:Title: Special loci for local systems\nby Bruno Klingler (Hum
boldt Univ.) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture
held in Harvard Science Center 507.\n\nAbstract\nGiven a local system on a
complex algebraic variety\, what are the subvarieties on which the monodr
omy drops? The talk will discuss these monodromy special loci\, a natural
generalisation of (the positive period dimension components of) the Hodge
loci.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Bryan (University of British Columbia)
DTSTART:20250527T190000Z
DTEND:20250527T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/93
DESCRIPTION:Title: Genus zero maps\, quivers\, and Bott Periodicity.\nby
Jim Bryan (University of British Columbia) as part of Harvard MIT Algebrai
c Geometry Seminar\n\nLecture held in MIT 2-131.\n\nAbstract\nWe give a qu
iver description of the space of genus 0 parameterized maps to various Gen
eralized Flag Varieties. In the 90s it was proven that for maps of large d
egree\, these spaces are good homotopy approximations to the space of all
continuous maps — the double loops spaces that appear in the Bott Period
icity theorem (both the 2-fold and 8-fold periodicity theorems). Our quive
r description recovers Bott Periodicity in the large rank and degree limit
and can thus be regarded as a finite dimensional\, algebraic refinement o
f Bott Periodicity. This is joint work with Ravi Vakil.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Bakker (UIC)
DTSTART:20250505T190000Z
DTEND:20250505T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/95
DESCRIPTION:Title: The linear Shafarevich conjecture for quasiprojective vari
eties (part 1)\nby Ben Bakker (UIC) as part of Harvard MIT Algebraic G
eometry Seminar\n\nLecture held in MIT 2-449 (special date/time!).\n\nAbst
ract\nShafarevich asked whether the universal cover of a smooth projective
variety X is always holomorphically convex\, meaning it admits a proper m
ap to a Stein space. This was proven in the linear case---namely when X a
dmits an almost faithful representation of its fundamental group---by Eyss
idieux--Katzarkov--Pantev--Ramachandran using techniques from non-abelian
Hodge theory. In joint work with Y. Brunebarbe and J. Tsimerman\, we prov
e a version of the linear Shafarevich conjecture for quasiprojective varie
ties. The proof relies on a number of recent advances in non-abelian Hodg
e theory in the non-proper case.\n\nIn the first talk I will outline the g
eneral strategy and explain why non-abelian Hodge theory naturally shows u
p in the context of Shafarevich's question. In the second talk I will pro
vide some details of the proof\, including the role played by the twistor
geometry of the stack of local systems and the algebraic integrability of
Katzarkov--Zuo foliations. As a bonus\, I will also explain how these tec
hniques prove the algebraicity of Shafarevich morphisms\, which generalize
s Griffiths' conjecture on the algebraicity of the images of period maps t
o arbitrary local systems.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Hacon (University of Utah)
DTSTART:20251021T190000Z
DTEND:20251021T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/96
DESCRIPTION:Title: The cone theorem for Kähler varieties\nby Christopher
Hacon (University of Utah) as part of Harvard MIT Algebraic Geometry Semi
nar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nThere has
been substantial recent progress towards the minimal model program for Kä
hler varieties. In this talk I will discuss a recent proof of the Cone Th
eorem for Kähler varieties of arbitrary dimension and related results suc
h as the canonical bundle formula\, subadjunction and Wenhao Ou's recent b
reakthrough result on the characterization of uniruled compact Kähler man
ifolds.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Grushevsky (SUNY Stony Brook)
DTSTART:20250923T200000Z
DTEND:20250923T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/97
DESCRIPTION:Title: Maximal compact subvarieties of ${\\mathcal A}_g$\nby
Sam Grushevsky (SUNY Stony Brook) as part of Harvard MIT Algebraic Geometr
y Seminar\n\nLecture held in MIT 2-131.\n\nAbstract\nWe present results on
the maximal dimension of compact subvarieties of the moduli space of abel
ian varieties and of moduli of complex curves of compact type. Equivalentl
y\, this is the maximal dimension of a compact complex parameter space for
a maximally varying family of abelian varieties/curves\, etc. Based on jo
int work with Mondello\, Salvati Manni\, Tsimerman.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debaditya Raychadhury (University of Arizona)
DTSTART:20250909T190000Z
DTEND:20250909T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/98
DESCRIPTION:Title: Singularities of secant varieties\nby Debaditya Raycha
dhury (University of Arizona) as part of Harvard MIT Algebraic Geometry Se
minar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nSecant v
arieties are classical objects in algebraic geometry. Given a smooth proje
ctive variety inside a projective space\, its secant variety is by definit
ion the closure of the union of secant lines. It is almost always singular
and sits inside the same projective space by its construction. In this ta
lk\, we will discuss the singularities of secant varieties when the embedd
ing is sufficiently positive. In particular\, we will study the Du Bois co
mplex of secant varieties and will also discuss about its local cohomology
modules. The results are obtained in various collaborations with Q. Chen\
, B. Dirks\, S. Olano and L. Song.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yongnam Lee (IBS-Center for Complex Geometry)
DTSTART:20250930T190000Z
DTEND:20250930T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/99
DESCRIPTION:Title: Compact moduli of elliptic surfaces with a multiple fiber<
/a>\nby Yongnam Lee (IBS-Center for Complex Geometry) as part of Harvard M
IT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center 50
7.\n\nAbstract\nMotivated by Miranda and Ascher-Bejleri's works on compact
ifications of the moduli space of rational elliptic surfaces with a sectio
n\, we study constructions and boundaries of compact moduli spaces of elli
ptic surfaces with a multiple fiber.\n\nIn a joint work with Donggun Lee\,
we propose an approach to understanding the limit surfaces when a multipl
e fiber degenerates into an additive type singular fiber\, via Q-Gorenstei
n smoothings of slc surfaces. And in ongoing work with Dori Bejleri and D
onggun Lee\, we study compact moduli spaces of the rational elliptic surfa
ces of index 2 and of Enriques surfaces with bisections using the theory o
f twisted stable maps.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyunsuk Kim (University of Michigan)
DTSTART:20250916T190000Z
DTEND:20250916T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/100
DESCRIPTION:Title: Hodge theory of toric singularities\nby Hyunsuk Kim (
University of Michigan) as part of Harvard MIT Algebraic Geometry Seminar\
n\nLecture held in Harvard Science Center 507.\n\nAbstract\nA toric variet
y is a normal variety containing an algebraic torus as an open dense subse
t whose action on itself extends to the whole space. They provide a fruitf
ul interplay between algebraic geometry and convex geometry since properti
es on one side (e.g. smoothness\, compactness) can be translated into prop
erties involving discrete objects (e.g. cones\, fans\, polytopes). I will
talk about singularities of these varieties from a Hodge theoretic point o
f view\, with applications towards local cohomology and singular cohomolog
y\, based on joint works with Sridhar Venkatesh.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruijie Yang (University of Kansas)
DTSTART:20251014T190000Z
DTEND:20251014T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/101
DESCRIPTION:Title: p-adic zeta function\, Hodge theory and hyperplane arrang
ements\nby Ruijie Yang (University of Kansas) as part of Harvard MIT A
lgebraic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n
\nAbstract\nIn 1988\, Igusa observed a mysterious relationship between the
poles of the p-adic zeta function and the roots of the Bernstein-Sato pol
ynomial. This relationship was later formulated precisely by Denef and Loe
ser and is now known as the Strong Monodromy Conjecture. In the special ca
se of hyperplane arrangements\, Budur\, Mustațǎ and Teitler proposed the
n/d conjecture in 2009\, which asserts that if a polynomial defines a cen
tral\, essential\, and indecomposable hyperplane arrangement of degree d i
n C^n\, then -n/d must be a root of its b-function. They showed that the n
/d conjecture implies the Strong Monodromy Conjecture for hyperplane arran
gements. \n\nIn this talk\, I will discuss my recent joint work with Douga
l Davis on a proof of the n/d conjecture\, which draws on the theory of co
mplex mixed Hodge modules of Sabbah and Schnell\, as well as our new ''wal
l-crossing'' theory for V-filtrations of holonomic D-modules along local c
omplete intersections. The latter is inspired by the recent breakthrough b
y Davis-Vilonen on the Schmid-Vilonen conjecture\, which characterizes the
unitarity of a representation of a real Lie group via Hodge theory. Furth
ermore\, we also prove that the pole order of the Igusa zeta function is l
ess than or equal to the multiplicity of the b-function along the real par
t of the pole. If time permits\, I will discuss how to extend this idea to
prove the Strong Monodromy Conjecture for multi-arrangements\, as well as
the multivariate n/d conjecture\, both proposed by Budur in 2015.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Johnston (MIT)
DTSTART:20251104T210000Z
DTEND:20251104T220000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/102
DESCRIPTION:Title: Quantum periods\, toric degenerations and intrinsic mirro
r symmetry\nby Sam Johnston (MIT) as part of Harvard MIT Algebraic Geo
metry Seminar\n\nLecture held in MIT 2-131.\n\nAbstract\nMirror symmetry f
or Fano varieties predicts a relation between the enumerative geometry of
a Fano variety Y and the complex geometry of a Landau-Ginzburg model\, rea
lized as a pair (X\,W) with X a quasi-projective variety and W a regular f
unction on X. The pair (X\,W) itself is expected to reflect a pair on the
Fano side\, namely a decomposition of Y into a disjoint union of an affine
log Calabi-Yau and an anticanonical divisor D. We will discuss recent wor
k which shows how the intrinsic mirror construction of Gross and Siebert n
aturally produce LG models associated to a pair (Y\,D)\, assuming milder c
onditions on the singularities of D than typically required for the intrin
sic mirror construction. In particular\, we show that classical periods of
this LG model recover the quantum periods of Y\, and that these periods a
re equal to a certain naive curve count on Y. In the setting when Y\\D is
an affine cluster variety\, we will describe how these LG models naturally
give rise to Laurent polynomial mirrors and corresponding toric degenerat
ions. As an example\, we consider Y = Gr(n-k\,n)\, D a particular choice o
f anticanonical divisor with affine cluster variety complement and give an
explicit description of the intrinsic LG model in terms of Plücker coord
inates on Gr(k\,n)\, recovering mirrors constructed and investigated by Ma
rsh-Rietsch and Rietsch-Williams.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Svaldi (Università degli Studi di Milano)
DTSTART:20251007T190000Z
DTEND:20251007T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/103
DESCRIPTION:Title: Boundedness theorems for fibered varieties with trivial c
anonical bundle\nby Roberto Svaldi (Università degli Studi di Milano)
as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Harv
ard Science Center 507.\n\nAbstract\nI will explain ideas and techniques b
ehind recent new results showing that several classes of fibered varieties
with trivial canonical bundle are bounded\, that is\, they are parametris
ed by finitely many families of deformations.\nNamely\, I will show how ab
elian or K3 fibered Calabi—Yau varieties are bounded\, up to simple bira
tional equivalences\, in the algebraic category\, and how the same results
holds in the analytic category for Lagrangian holomorphic symplectic vari
eties.\nThis is joint work with Engel\, Filipazzi\, Greer\, Mauri.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Thimm (UBC)
DTSTART:20251202T210000Z
DTEND:20251202T220000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/105
DESCRIPTION:Title: Wall-Crossing and the DT/PT3 Descendant Correspondence\nby Felix Thimm (UBC) as part of Harvard MIT Algebraic Geometry Seminar\
n\nLecture held in MIT 2-131.\n\nAbstract\nDonaldson–Thomas and Pandhari
pande–Thomas invariants are two ways of counting curves in Calabi-Yau 3-
folds\, related by a change of stability conditions. Wall-crossing is a te
chnique that allows us to compare enumerative invariants under such a chan
ge in stability condition. It has emerged as a powerful tool for computati
ons and in the study of properties of generating series of various types o
f enumerative invariants. I will present joint work with N. Kuhn and H. Li
u on how to use localization of virtual classes to wall-cross more general
invariants with descendant insertions. In the process I will explain how
Juanolou's trick from more classical algebraic geometry comes in as a usef
ul and central ingredient.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daebeom Choi (UPenn)
DTSTART:20251216T210000Z
DTEND:20251216T220000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/106
DESCRIPTION:Title: Extremal effective curves and non-semiample line bundles
on $M_{g\,n}$\nby Daebeom Choi (UPenn) as part of Harvard MIT Algebrai
c Geometry Seminar\n\nLecture held in MIT 2-449 (Special room).\n\nAbstrac
t\nIn this work\, we develop a new method for establishing extremality in
the closed cone of curves on the moduli space of curves and determine the
extremality of many boundary 1-strata. As a consequence\, by using a gener
al criterion for non-semiampleness that extends Keel’s argument\, we dem
onstrate that a substantial portion of the cone of nef divisors on $M_{g\,
n}$ is not semiample. As an application\, we construct the first explicit
example of a non-contractible extremal ray of the closed cone of effective
curves on $M_{3\,n}$. Moreover\, we show that this extremal ray is contra
ctible in characteristic $p$. Our method relies on two main ingredients: (
1) the construction of a new collection of nef divisors on $M_{g\,n}$\, an
d (2) the identification of a tractable inductive structure on the Picard
group\, arising from Knudsen’s construction of $M_{g\,n}$.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Cela (Cambridge)
DTSTART:20251209T210000Z
DTEND:20251209T220000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/107
DESCRIPTION:Title: Brill–Noether Theory for (toric) Surfaces and Complete
Quasimaps to Blow-ups of Projective spaces\nby Alessio Cela (Cambridge
) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in MIT
2-131.\n\nAbstract\nThe classical Brill–Noether theorem states that eve
ry nondegenerate degree d map from a general curve C of genus g to proje
ctive space is a point of expected dimension in the moduli space of such m
aps. In this talk\, I will present an analogous statement for maps from C
to smooth projective toric surfaces. I will then discuss the constructio
n of the space of complete quasimaps to Bl_{P^s}^r\, obtained as a suitabl
e blow-up of the quasimap space of Ciocan-Fontanine–Kim–Maulik. This s
pace provides an expected-dimension compactification of the moduli space o
f maps\, in a fixed curve class\, from C to X. Conjecturally\, the insert
ion of tautological subschemes corresponding to geometric insertions is tr
ansverse\, lies in the locus of nondegenerate maps\, and preserves the exp
ected dimension. Using the Brill–Noether result for toric surfaces menti
oned above\, the conjecture is verified in dimension 2.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannik Schuler (ETH)
DTSTART:20251028T200000Z
DTEND:20251028T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/108
DESCRIPTION:Title: Stable maps to Calabi–Yau fivefolds\nby Yannik Schu
ler (ETH) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture hel
d in MIT 2-131.\n\nAbstract\nGromov–Witten invariants enumerate curves i
n a variety X via stable maps. However\, degenerate contributions lead to
substantial overcounting which makes these invariants far from optimal. Wh
en X is a Calabi–Yau threefold\, a set of more fundamental curve countin
g invariants is provided by Gopakumar–Vafa invariants. I will propose a
conjectural generalisation of this correspondence between Gromov–Witten
and Gopakumar–Vafa invariants to the setting of Calabi–Yau fivefolds e
quipped with a torus action. I will demonstrate the conjecture in the sett
ing of local curves. For a special type of torus action we will prove a cl
osed-form formula for the local contribution of a smooth embedded curve an
d for general torus actions the validity of the formula will be translated
into a conjectural formula for certain tautological integrals over the mo
duli of curves.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siddharth Kannan (MIT)
DTSTART:20251118T210000Z
DTEND:20251118T220000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/109
DESCRIPTION:Title: Radially aligned stable curves and applications\nby S
iddharth Kannan (MIT) as part of Harvard MIT Algebraic Geometry Seminar\n\
nLecture held in MIT 2-131.\n\nAbstract\nI will discuss a combinatorially
defined blow-up of the moduli space of curves in genus g <= 1 and then des
cribe two applications of this construction. The first application is more
combinatorial: a modular understanding of the blow-up leads to a calculat
ion scheme for the S_n-representations defined by the Chow ring of the bra
id matroid. The second application is more geometric: a combinatorial unde
rstanding of the boundary complex of the blow-up leads to a calculation of
the weight zero subspace of the compactly-supported cohomology of the mod
uli space M_1\,n(P^r\, d)\, which parameterizes degree d maps from smooth
pointed genus one curves to P^r. The talk will be based on separate joint
projects\, with Lukas Kühne and with Terry Song.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soham Karwa (Duke University)
DTSTART:20260317T190000Z
DTEND:20260317T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/110
DESCRIPTION:Title: K-affine structures on skeleta\nby Soham Karwa (Duke
University) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture h
eld in MIT 2-132.\n\nAbstract\nGiven an algebraic variety X\, one can asso
ciate a non-archimedean analytic space X^an called its analytification. Wh
ilst X^an can be very complicated\, there exists a canonical combinatorial
subspace\, called\, the essential skeleton. The skeleton has the structur
e of an integral affine manifold with singularities and is a combinatorial
shadow of X which retains a lot of geometric information about X.\n\nIn t
his talk\, we’ll consider an enhancement of an integral affine structure
on the skeleton\, called a K-affine structure\, which captures analytic i
nformation about X not seen by the integral affine structure. In particul
ar\, we’ll see how the K-affine structure recovers the periods for log C
alabi-Yau surfaces\, verifying a conjecture of Kontsevich-Soibelman. Time
permitting\, we’ll also discuss work in progress on how the K-affine str
ucture gives the essential skeleton of a Mumford curve the structure of a
ringed space and the relation between line bundles on the curve\, the skel
eton and tropical line bundles.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Petersen (Stockholm University and IAS)
DTSTART:20260505T190000Z
DTEND:20260505T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/111
DESCRIPTION:Title: Moments of families of quadratic L-functions over functio
n fields via homotopy theory\nby Dan Petersen (Stockholm University an
d IAS) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held i
n MIT 2-131.\n\nAbstract\nThis is a report of joint work with Bergström-D
iaconu-Westerland and Miller-Patzt-Randal-Williams. There is a "recipe" du
e to Conrey-Farmer-Keating-Rubinstein-Snaith which allows for precise pred
ictions for the asymptotics of moments of many different families of L-fun
ctions. We consider the family of all L-functions attached to hyperellipti
c curves over some fixed finite field. One can relate this problem to unde
rstanding the homology of the hyperelliptic mapping class group with sympl
ectic coefficients. With Bergström-Diaconu-Westerland we compute the stab
le homology groups of the hyperelliptic mapping class group with these coe
fficients\, together with their structure as Galois representations. With
Miller-Patzt-Randal-Williams we prove a uniform range for homological stab
ility with these coefficients. Together\, these results imply the CFKRS pr
edictions for all moments in the function field case\, for all sufficientl
y large (but fixed) q.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Mullane (University of Melbourne)
DTSTART:20260224T200000Z
DTEND:20260224T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/112
DESCRIPTION:Title: Isoresidual fibrations and the moduli space of pointed ra
tional curves\nby Scott Mullane (University of Melbourne) as part of H
arvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science C
enter 507.\n\nAbstract\nAfter surveying the results of the last 20 years o
n the structure of effective divisors on $\\overline{M}_{0\,n}$\, we show
that the pseudo-effective cone of divisors is not polyhedral for $n\\geq8$
. Using ideas from Teichmüller dynamics and birational geometry\, we cons
truct an extremal non-polyhedral ray of the dual cone of moving curves usi
ng residue maps of strata of meromorphic differentials.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sung Gi Park (Princeton Univ.)
DTSTART:20260127T200000Z
DTEND:20260127T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/113
DESCRIPTION:Title: From GIT to Baily-Borel: Moduli of hypersurfaces via mini
mal exponents\nby Sung Gi Park (Princeton Univ.) as part of Harvard MI
T Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center 507
.\n\nAbstract\nThe moduli space of smooth hypersurfaces in projective spac
e can be constructed as a GIT quotient by linear changes of coordinates\,
and it comes with a natural GIT compactification. In certain degrees and d
imensions\, Hodge theory provides a second compactification via the period
map\, namely the Baily-Borel compactification. Building on recent progres
s on higher singularities and a new stability criterion formulated in term
s of the minimal exponent (a refinement of the log canonical threshold)\,
I will discuss the birational geometry of these two compactifications and
describe consequences for the boundary behavior of the period map.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanlin Cai (Columbia University)
DTSTART:20260407T190000Z
DTEND:20260407T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/116
DESCRIPTION:Title: Perturbation of mixed characteristics test ideals\nby
Hanlin Cai (Columbia University) as part of Harvard MIT Algebraic Geometr
y Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nGive
n a normal integral scheme of finite type over a mixed characteristic comp
lete DVR or a perfect field of characteristic p\, one can define the notio
n of a test ideal. This sheaf is used to characterize a class of mild sing
ularities known as splinter singularities\, which are analogous to rationa
l singularities in characteristic 0. In equal characteristics\, it is a we
ll-known result that test and multiplier ideals are stable under small per
turbations. In this talk\, I will explain how to extend this stability res
ult to the mixed characteristic setting and discuss some of its applicatio
ns. Time permitting\, I will also outline the key ideas and tools from p-a
dic geometry that underlie the proof.This is based on joint work in progre
ss with Bhargav Bhatt and Linquan Ma.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denis Nesterov (ETH Zurich)
DTSTART:20260203T200000Z
DTEND:20260203T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/117
DESCRIPTION:Title: Hilbert schemes of points and Fulton-MacPherson compactif
ications\nby Denis Nesterov (ETH Zurich) as part of Harvard MIT Algebr
aic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nThe two sp
aces appearing in the title provide distinct compactifications of unordere
d configuration spaces of points on a complex variety. I will describe sev
eral ways in which they are related. In particular\, in dimension two\, I
will explain how the latter can be used to prove the Hilbert-Chow crepant
resolution conjecture\, proposed by Ruan\, which asserts an isomorphism be
tween the quantum cohomology of Hilbert schemes and the orbifold cohomolog
y of symmetric products.\n\n\nNote:\nDenis Nesterov will give special talk
s on Friday January 30 and Monday February 2\, 1:30pm-3pm in MIT 2-449. Th
e title and abstract for those talks is as follows:\n\nTitle: Wall-crossin
g for spaces of maps \n\nAbstract:\nI will discuss a wall-crossing phenome
non for spaces of maps from curves to a target variety\, from both concept
ual and computational points of view. In dimension one\, it relates stable
maps and admissible covers\, generalizing the ELSV formula and the Gromov
-Witten/Hurwitz correspondence\, and also yields a recursive formula for t
he class of hyperelliptic curves. In dimension two\, it helps compute Tore
lli pullbacks of certain classes from moduli spaces of principally polaris
ed abelian varieties. In dimension three\, it provides a construction of G
opakumar-Vafa invariants in terms of unramified maps for Fano and primitiv
e Calabi-Yau classes.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weite Pi (Bonn University)
DTSTART:20260210T200000Z
DTEND:20260210T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/118
DESCRIPTION:Title: "Perverse = Chern" and χ-independence phenomena for modu
li of 1-dimensional sheaves\nby Weite Pi (Bonn University) as part of
Harvard MIT Algebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAb
stract\nWe discuss the geometry and cohomology of Le Potier’s moduli spa
ce of 1-dimensional sheaves on the projective plane. We focus on two aspec
ts: first\, the "P=C" conjecture relating two filtrations of highly differ
ent nature on cohomology\, which can be viewed as a del Pezzo analog of th
e celebrated P=W conjecture\; second\, the so-called χ-independence pheno
menon\, which stems from enumerative geometry and predicts surprising cons
equences on the cohomology of the moduli space. After surveying known resu
lts\, I will explain how these two aspects are linked via an “associated
graded” χ-independence conjecture. Based on joint work with Yakov Kono
nov\, Woonam Lim\, and Miguel Moreira.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Woonam Lim (Yonsei University)
DTSTART:20260210T211000Z
DTEND:20260210T221000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/119
DESCRIPTION:Title: Nekrasov’s gauge origami via DT4 theory\nby Woonam
Lim (Yonsei University) as part of Harvard MIT Algebraic Geometry Seminar\
n\nLecture held in MIT 2-132.\n\nAbstract\nThe study of classical instanto
ns on spacetime has led to many interesting developments in mathematics. I
n a series of papers\, Nekrasov introduced the generalized ADHM equations\
, whose solutions are instantons on the “origami spacetime.” In this t
alk\, I will explain how to interpret gauge origami via DT4 theory. The ma
in result shows that Nekrasov’s origami partition function\, defined by
local contributions\, coincides with a global definition via Oh–Thomas c
lasses in DT4 theory. This global definition is crucial for deriving the D
yson–Schwinger equation\, which was one of Nekrasov’s main motivations
for introducing gauge origami theory. I will also briefly discuss a conje
ctural sheaf-theoretic description of gauge origami. This is joint work wi
th N. Arbesfeld and M. Kool.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raluca Vlad (Brown University)
DTSTART:20260303T200000Z
DTEND:20260303T210000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/120
DESCRIPTION:Title: Tropicalizations of locally symmetric varieties\nby R
aluca Vlad (Brown University) as part of Harvard MIT Algebraic Geometry Se
minar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nA locall
y symmetric variety is a non-compact complex algebraic variety obtained as
the quotient of a Hermitian symmetric domain by the action of an arithmet
ic group. I will start by reviewing the theory of toroidal compactificatio
ns of these varieties\, originally due to Ash-Mumford-Rapoport-Tai. Buildi
ng on this construction\, we define the tropicalization of a locally symme
tric variety to be a combinatorial object encoding the boundary strata of
a toroidal compactification of the variety. I will discuss applications of
this theory to the cohomology of moduli spaces and arithmetic groups\, wi
th an emphasis on the case of moduli of abelian varieties and general line
ar groups. Based on joint work with Assaf\, Brandt\, Bruce\, and Chan.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Bertram (University of Utah)
DTSTART:20260324T190000Z
DTEND:20260324T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/122
DESCRIPTION:Title: A modest extension of Reider's Theorem on ample divisors
on a surface\nby Aaron Bertram (University of Utah) as part of Harvard
MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center
507.\n\nAbstract\nThe derived category is a useful tool for studying class
ical problems about algebraic surfaces. \nFor example\, a wall-crossing ar
gument for moduli of derived objects was used by Arend Bayer to \ngive a n
ew proof of Lazarsfeld's theorem on the Brill-Noether generality of curves
on a K3 surface with Picard \nnumber one. This was recently extended by F
arkas\, Feyzbakhsh and Rojas to the Picard rank two case. Here\, we use a
\nnon-wall-crossing argument to give inequalities of the same form as thos
e of Reider's theorem to obtain \ninformation about the equations that cut
out the surface. This is joint work with my students Jonathon Fleck\, Lie
bo Pan and \nJoseph Sullivan.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uriya First (University of Haifa and MIT)
DTSTART:20260310T190000Z
DTEND:20260310T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/123
DESCRIPTION:Title: Number of generators: an algebraic-geometry approach\
nby Uriya First (University of Haifa and MIT) as part of Harvard MIT Algeb
raic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAb
stract\nThe Primitive Element Theorem says that a separable field extensio
n is generated by one element\, and a well-known folklore result says that
a central simple algebra (CSA) is generated by two elements over its cent
er.\nThe globalization of separable field extensions and CSAs are finite e
tale algebras and Azumaya algebras\, respectively\, and so one could ask i
f something could be said about their number of generators if the base sch
eme has dimension at most d. The same question can be asked for vector bun
dles and other types of algebra bundles. I will discuss some recent works
with Reichstein\, Williams and others where we study this question by turn
ing it into a geometric question\, thus finding both upper bounds and exam
ples requiring arbitrarily many generators. For example\, if X is a d-dime
nsional affine algebraic scheme over an infinite field\, then any finite e
tale algebra over X can be generated by d+1 elements\, and this cannot be
improved in general.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Reppen (UC Berkeley)
DTSTART:20260421T190000Z
DTEND:20260421T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/124
DESCRIPTION:Title: Singularities in the Ekedahl–Oort stratification\nb
y Stefan Reppen (UC Berkeley) as part of Harvard MIT Algebraic Geometry Se
minar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nWe study
the Ekedahl–Oort stratification on the special fiber of an abelian type
Shimura variety at a prime of good reduction. Originally defined by Oort
in the Siegel case via isomorphism classes of p-torsion\, this stratificat
ion was later extended using the language of G-zips. While the geometry of
individual strata is well understood\, much less is known about their clo
sures. In this talk\, I will present joint work with Lorenzo La Porta and
Jean-Stefan Koskivirta giving criteria for normality and Cohen–Macaulayn
ess of unions of EO strata. As applications\, we describe the smooth locus
of EO strata closures for orthogonal (type Bn) Shimura varieties and obta
in general existence results for reduced Hasse invariants.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyeonjun Park (KIAS)
DTSTART:20260428T190000Z
DTEND:20260428T200000Z
DTSTAMP:20260422T140238Z
UID:harvard-mit-ag-seminar/125
DESCRIPTION:Title: Lagrangian classes\nby Hyeonjun Park (KIAS) as part o
f Harvard MIT Algebraic Geometry Seminar\n\nLecture held in MIT 2-131.\n\n
Abstract\nTalk 1: 3-4pm\, 2-131\, 4/28\nTalk 2: 3-4pm\, 2-361\, 4/29\nTa
lk 3: 1-2pm\, 2-361\, 4/30\n\n\nModern enumerative invariants\, such as Gr
omov-Witten invariants and Donaldson-Thomas invariants\, are defined throu
gh the virtual classes. In these talks\, I will introduce Lagrangian class
es\, whose existence was conjectured by Joyce\, as a generalization of the
virtual classes via shifted symplectic geometry. This is joint work in pr
ogress with Adeel Khan\, Tasuki Kinjo\, and Pavel Safronov.\n\nIn the firs
t talk\, I will give an overview and summarize the main results. The Lagra
ngian classes are certain cohomology classes associated to (-1)-shifted La
grangian correspondences that describe the functorial behavior of the perv
erse sheaves in cohomological Donaldson-Thomas theory. From the Lagrangian
classes\, we can recover: virtual classes\; cosection-localized virtual c
lasses\; DT4 virtual classes\; cohomological Hall algebras.\n\nIn the seco
nd talk\, I will explain the construction of Lagrangian classes. This will
be analogous to the construction of the usual virtual classes once we hav
e the following two key ingredients: (1) the perverse pullbacks\, as relat
ive versions of the DT perverse sheaves\; (2) the hyperbolic dimensional r
eduction\, as a twisted version of the hyperbolic localization theorem for
vanishing cycles. I will also explain how to prove the associativity of L
agrangian classes.\n\nIn the third talk\, I will focus on applications. Us
ing the Lagrangian classes\, we can define the following enumerative struc
tures: (1) cohomological field theories for gauged linear sigma models\; (
2) relative Donaldson-Thomas invariants for log Calabi-Yau pairs of dimens
ion four\; (3) cohomological Hall algebras for 3-Calabi-Yau categories\; (
4) algebraic Fukaya categories for hyper-kahler varieties. Using the perve
rse pullbacks\, we can define the period sheaves in relative geometric Lan
glands. I will also mention some open questions and future directions.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/125/
END:VEVENT
END:VCALENDAR