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BEGIN:VEVENT
SUMMARY:Juliette Bruce (Brown University)
DTSTART:20221129T200000Z
DTEND:20221129T210000Z
DTSTAMP:20260404T095028Z
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\nLe
cture held in Harvard Science Center 507.\n\nAbstract\nI will discuss rece
nt work calculating the top weight cohomology of the moduli space A_g of p
rincipally polarized abelian varieties of dimension g for small values of
g. The key idea is that this piece of cohomology is encoded combinatoriall
y via the relationship between the boundary complex of a compactification
of A_g and the moduli space of tropical abelian varieties. This is joint w
ork with Madeline Brandt\, Melody Chan\, Margarida Melo\, Gwyneth Moreland
\, and Corey Wolfe.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tasuki Kinjo (University of Tokyo)
DTSTART:20221206T213000Z
DTEND:20221206T223000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/2
DESCRIPTION:Title: Cohomological Donaldson-Thomas theory for 2-Calabi--
Yau categories\nby Tasuki Kinjo (University of Tokyo) as part of Harva
rd MIT Algebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstrac
t\nCohomological Donaldson-Thomas (CoDT) invariants were introduced by Kon
tsevich-Soibelman and Brav-Bussi-Dupont-Joyce-Szendroi as categorification
s of the Donaldson-Thomas invariants counting objects in 3-Calabi-Yau cate
gories. In this talk\, I will explain applications of the CoDT theory to t
he cohomological study of the moduli of objects in 2-Calabi-Yau categories
. Among other things\, I will construct a coproduct on the Borel-Moore hom
ology of the moduli stack of objects in these categories and establish a P
BW-type statement for the Kapranov-Vasserot cohomological Hall algebras. T
his talk is based on a joint work in progress with Ben Davison.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/2
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Padmavathi Srinivasan (ICERM)
DTSTART:20230418T190000Z
DTEND:20230418T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/3
DESCRIPTION:Title: A canonical algebraic cycle associated to a curve in
its Jacobian\nby Padmavathi Srinivasan (ICERM) as part of Harvard MIT
Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center 507.
\n\nAbstract\nWe will talk about the Ceresa class\, which is the image und
er a cycle class map of a canonical homologically trivial algebraic cycle
associated to a curve in its Jacobian. In his 1983 thesis\, Ceresa showed
that the generic curve of genus at least 3 has nonvanishing Ceresa cycle m
odulo algebraic equivalence. Strategies for proving Fermat curves have inf
inite order Ceresa cycles due to B. Harris\, Bloch\, Bertolini-Darmon-Pras
anna\, Eskandari-Murty use a variety of ideas ranging from computation of
explicit iterated period integrals\, special values of p-adic L functions
and points of infinite order on the Jacobian of Fermat curves. In fact\, B
loch's results about the Ceresa cycle of Fermat quartics provided the firs
t concrete evidence for the generalization of the BSD conjecture to the Bl
och-Beilinson conjectures.\n\nWe will survey several recent results about
the Ceresa cycle and the Ceresa class. The Ceresa class vanishes for all h
yperelliptic curves and was expected to be nonvanishing for non-hyperellip
tic curves. We will present joint work with Dean Bisogno\, Wanlin Li and D
aniel Litt\, where we construct a non-hyperelliptic genus 3 quotient of th
e Fricke--Macbeath curve with torsion Ceresa class\, using the character t
heory of the automorphism group of the curve\, namely\, PSL2(F8).\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/3
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi Lombardi (University of Milan)
DTSTART:20230131T200000Z
DTEND:20230131T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/4
DESCRIPTION:Title: On the invariance of Hodge numbers under derived equ
ivalence\nby Luigi Lombardi (University of Milan) as part of Harvard M
IT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center 50
7.\n\nAbstract\nA conjecture of Orlov predicts the invariance of the Hodge
numbers of a smooth projective complex variety under derived equivalence.
For instance this has been verified in the case of varieties of general t
ype. In this talk\, I will examine the case of varieties that are fibered
by varieties of general type through the Albanese map. For this class of v
arieties I will prove the derived invariance of Hodge numbers of type $h^{
0\,p}$\, together with a few other invariants arising from the Albanese ma
p. This talk is based on a joint work with F. Caucci and G. Pareschi.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/4
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Küronya (Goethe-Universität Frankfurt)
DTSTART:20230214T200000Z
DTEND:20230214T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/5
DESCRIPTION:Title: Newton-Okounkov bodies and local positivity\nby
Alex Küronya (Goethe-Universität Frankfurt) as part of Harvard MIT Algeb
raic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAb
stract\nThe purpose of this talk is to discuss Newton-Okounkov bodies\, \n
a convex geometric construction associated to divisors on projective \nvar
ieties. We will touch on their relationship with local positivity\, \nmult
iplicative filtrations on section rings\, and applications.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/5
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Marian (Northeastern University)
DTSTART:20221206T200000Z
DTEND:20221206T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/6
DESCRIPTION:Title: On quot schemes of rank zero quotients over a curve<
/a>\nby Alina Marian (Northeastern University) as part of Harvard MIT Alge
braic Geometry Seminar\n\nLecture held in MIT 2-132.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/6
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samir Canning (ETH Zurich)
DTSTART:20221212T200000Z
DTEND:20221212T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/7
DESCRIPTION:Title: The Chow ring of the moduli space of degree 2 K3 sur
faces\nby Samir Canning (ETH Zurich) as part of Harvard MIT Algebraic
Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstrac
t\nThe intersection theory of the moduli space of K3 surfaces polarized by
a lattice 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 Pandhar
ipande conjectured that the tautological rings of these moduli spaces of K
3 surfaces 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 th
e case of K3 surfaces polarized by a degree 2 line bundle. This is joint w
ork with Dragos Oprea and Rahul Pandharipande.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/7
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sung Gi Park (Harvard University)
DTSTART:20230207T200000Z
DTEND:20230207T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/8
DESCRIPTION:Title: Kodaira dimension and hyperbolicity for smooth famil
ies of varieties\nby Sung Gi Park (Harvard University) as part of Harv
ard MIT Algebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstra
ct\nIn this talk\, I will discuss the behavior of positivity\, hyperbolici
ty\, and Kodaira dimension under smooth morphisms of complex quasi-project
ive manifolds. This includes a vast generalization of a classical result:
a fibration from a projective surface of non-negative Kodaira dimension to
a projective line has at least three singular fibers. Furthermore\, I wil
l explain a proof of Popa's conjecture on the superadditivity of the log K
odaira dimension over bases of dimension at most three. These theorems are
applications of the main technical result\, namely the logarithmic base c
hange theorem.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/8
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Hotchkiss (University of Michigan)
DTSTART:20230221T200000Z
DTEND:20230221T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/9
DESCRIPTION:Title: The period-index problem over the complex numbers\nby James Hotchkiss (University of Michigan) as part of Harvard MIT Alge
braic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nA
bstract\nThe period-index problem is a longstanding question about the com
plexity of Brauer classes over a field. I will discuss some Hodge-theoreti
c aspects of the problem for complex function fields\, and give some appli
cations to Brauer groups and the integral Hodge conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/9
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asher Auel (Dartmouth)
DTSTART:20230228T200000Z
DTEND:20230228T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/10
DESCRIPTION:Title: Maximal Brill-Noether loci\nby Asher Auel (Dart
mouth) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held i
n Harvard Science Center 507.\n\nAbstract\nBrill-Noether theory answers th
e question of whether a general curve of genus $g$ admits $g^r_d$\, a line
ar system of rank $r$ and degree $d$. A refined Brill-Noether theory hope
s to answer the question of whether a "general curve with a $g^r_d$" admit
s a $g^{r'}_{d'}$. In other words\, we want to know about the relative po
sition between Brill-Noether loci in the moduli space of curves of genus $
g$. I'll explain a strategy for distinguishing Brill-Noether loci by stud
ying the lifting of linear systems on curves in polarized K3 surfaces\, wh
ich motivates a conjecture identifying the maximal Brill-Noether loci with
respect to containment. Via an analysis of the stability of Lazarsfeld-Mu
kai bundles\, we obtain new lifting results for linear systems of rank 3 w
hich suffice to prove the maximal Brill-Noether loci conjecture in genus 9
-19\, 22\, and 23. This is joint work with Richard Haburcak.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Lacini (University of Kansas)
DTSTART:20230307T200000Z
DTEND:20230307T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/11
DESCRIPTION:Title: Syzygies of adjoint linear series on projective var
ieties\nby Justin Lacini (University of Kansas) as part of Harvard MIT
Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center 507.
\n\nAbstract\nSyzygies of algebraic varieties have long been a topic of in
tense interest among algebraists and geometers alike. Starting with the pi
oneering work of Mark Green on curves\, numerous attempts have been made t
o extend these results to higher dimensions. Ein and Lazarsfeld proved tha
t 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 hold
s true for A ample and basepoint free. In joint work with Purnaprajna Bang
ere we give a positive answer to this question.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomer Schlank (MIT)
DTSTART:20230314T190000Z
DTEND:20230314T200000Z
DTSTAMP:20260404T095028Z
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 2-13
2.\n\nAbstract\nTsen's Theorem gives a simple sufficient criterion for an
algebraic 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 s
tructure of a stack and show that this stack is homologically contractible
.\nWe shall explain a variant of this phenomenon that can be employed for
the study of Beilinson-Drinfeld Opers for reductive groups.\nThis is joint
work with D. Beraldo and D. Kazhdan.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (Yale University)
DTSTART:20230321T190000Z
DTEND:20230321T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/13
DESCRIPTION:Title: Non-abelian Hodge theory and the P=W conjecture
\nby Junliang Shen (Yale University) as part of Harvard MIT Algebraic Geom
etry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nIn the first part
of my talk\, I will introduce the P=W conjecture by de Cataldo\, Hausel\,
and Migliorini (2010)\, predicting that the perverse filtration associated
with the Hitchin system is identified with the weight filtration associat
ed 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 represe
ntation theory.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melody Chan (Brown University)
DTSTART:20230328T190000Z
DTEND:20230328T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/14
DESCRIPTION:Title: The weight 0 compactly supported Euler characterist
ic of moduli spaces of marked hyperelliptic curves\nby Melody Chan (Br
own University) as part of Harvard MIT Algebraic Geometry Seminar\n\nLectu
re held in Harvard Science Center 507.\n\nAbstract\nJoint work with Madeli
ne Brandt and Siddarth Kannan. We use moduli\nspaces of G-admissible cove
rs and tropical geometry to give a\nsum-over-graphs formula for the weight
-0 compactly supported Euler\ncharacteristic of the moduli spaces H_{g\,n}
of n-marked hyperelliptic\ncurves of genus g\, as a virtual representatio
n of S_n. Computer\ncalculations then enable fully explicit formulas for
the above in\nsmall genus. My aim is to make this talk accessible to anyo
ne with\npassing familiarity with M_g and its Deligne-Mumford compactifica
tion.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gavril Farkas (Humboldt University Berlin)
DTSTART:20230404T190000Z
DTEND:20230404T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/15
DESCRIPTION:Title: Resonance and Koszul modules in algebraic geometry<
/a>\nby Gavril Farkas (Humboldt University Berlin) as part of Harvard MIT
Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\
n\nAbstract\nInspired from ideas in topology\, Koszul modules and the asso
ciated resonance varieties turned out to have important algebro-geometric
applications for instance to (i) Green's Conjecture on syzygies of canonic
al curves\, (ii) stabilization of cohomology of projective varieties in ar
bitrary characteristics and (iii) Chen invariants of hyperplane arrangemen
ts. I will discuss new developments related to this circle of ideas obtain
ed in joint work with Aprodu\, Raicu and Suciu.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Collins (MIT)
DTSTART:20230411T190000Z
DTEND:20230411T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/16
DESCRIPTION:Title: Mirror symmetry\, stability conditions and geometri
c invariant theory\nby Tristan Collins (MIT) as part of Harvard MIT Al
gebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nBridge
land stability conditions were originally motivated by the concept of Pi s
tability in theoretical physics\, as introduced in work of M. Douglas. Pi
stability is an attempt to describe BPS states in string theory compactif
ications. Alternatively\, BPS states in string theory can often be descri
bed by solutions of certain nonlinear partial differential equations. In
this talk I will explain how\, starting from nonlinear PDEs\, ideas in GIT
lead to a version of algebraic stability which is similar to Bridgeland s
tability. In particular\, I will explain how in several examples in dimen
sion 2\, GIT stability for line bundles implies Bridgeland stability\, but
not conversely. In particular\, this yields effective tests for Bridgela
nd stability in many examples.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dawei Chen (Boston College)
DTSTART:20230425T190000Z
DTEND:20230425T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/17
DESCRIPTION:Title: Counting differentials with fixed residues\nby
Dawei Chen (Boston College) as part of Harvard MIT Algebraic Geometry Semi
nar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nIn this ta
lk\, we investigate meromorphic differentials on the Riemann sphere with a
single zero and several poles of predetermined orders. Our aim is to dete
rmine the number of such differentials that satisfy the condition where th
e residue at each pole is fixed. This question was previously explored by
Gendron and Tahar\, who employed graph counting techniques derived from th
e flat geometry of differentials. We introduce a new approach using inters
ection theory on moduli spaces of differentials. This is joint work with M
iguel Prado Godoy.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Casalaina-Martin (University of Colorado)
DTSTART:20230502T190000Z
DTEND:20230502T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/18
DESCRIPTION:Title: Moduli spaces of cubic hypersurfaces\nby Sebast
ian Casalaina-Martin (University of Colorado) as part of Harvard MIT Algeb
raic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAb
stract\nIn this talk I will give an overview of some recent work\, joint w
ith Samuel Grushevsky\, Klaus Hulek\, and Radu Laza\, on the geometry and
topology of compactifications of the moduli spaces of cubic threefolds and
cubic surfaces. A focus of the talk will be on some results regarding non
-isomorphic smooth compactifications of the moduli space of cubic surfaces
\, showing that two natural desingularizations of the moduli space have th
e 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-e
quivalent.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Bitoun (University of Calgary)
DTSTART:20230509T190000Z
DTEND:20230509T200000Z
DTSTAMP:20260404T095028Z
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 Ge
ometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nLet Z be the ger
m of a complex hypersurface isolated singularity of equation f. We conside
r the family of analytic D-modules generated by the powers of 1/f and rela
te it to the pole order filtration on the de Rham cohomology of the comple
ment of \\{f=0\\}. This work builds on Vilonen’s characterization of the
intersection homology D-module.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No seminar
DTSTART:20230516T190000Z
DTEND:20230516T200000Z
DTSTAMP:20260404T095028Z
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://stable.researchseminars.org/talk/harvard-mit-ag-seminar/2
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Schnell (SUNY Stony Brook)
DTSTART:20230315T190000Z
DTEND:20230315T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/21
DESCRIPTION:Title: Hodge theory and Lagrangian fibrations (special tim
e/location: 2-255)\nby Christian Schnell (SUNY Stony Brook) as part o
f Harvard MIT Algebraic Geometry Seminar\n\nLecture held in special locati
on: 2-255.\n\nAbstract\nThis is a talk about Lagrangian fibrations on hol
omorphic symplectic manifolds\, for example the Hitchin fibration (on the
moduli space of Higgs bundles over a curve). The general fiber of such a L
agrangian fibration is an abelian variety\, but the singular fibers are ra
ther mysterious. There were several beautiful conjectures about the Hodge
theory of Lagrangian fibrations\, proposed by Junliang Shen\, Qizheng Yin\
, and Davesh Maulik. I will try to introduce the conjectures and give an i
dea of the proof.\n\nThis talk will be in 2-255 at MIT.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/2
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Tholozan (École Normale Supérieure)
DTSTART:20230523T190000Z
DTEND:20230523T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/22
DESCRIPTION:Title: Complex variations of Hodge structures of rank 2 ov
er curves\nby Nicolas Tholozan (École Normale Supérieure) as part of
Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science
Center 507.\n\nAbstract\nThrough the work of Simpson\, complex variations
of hodge structures (C-VHS) play a central role in the study of the modul
i space of local systems over a complex algebraic variety. In this talk I
will consider one of the simplest examples\, namely C-VHS of rank 2 over c
urves. These objects are known to hyperbolic geometers as « branched hype
rbolic surfaces ».\n\nI will review what is known about their monodromy\,
and discuss in particular a joint result with Bertrand Deroin: every PSL(
2\,R)-local system of Euler class 2g-3 over a curve of genus g admits an i
somonodromic deformation that supports a C-VHS.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/2
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jun-Yong Park (University of Melbourne)
DTSTART:20230426T173000Z
DTEND:20230426T183000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/23
DESCRIPTION:Title: Height moduli on algebraic stacks and counting fami
lies of varieties (special time and location SC 221)\nby Jun-Yong Park
(University of Melbourne) as part of Harvard MIT Algebraic Geometry Semin
ar\n\nLecture held in Harvard Science Center 221 (special location).\n\nAb
stract\nI will begin by reviewing the classical algorithm of Tate with som
e explicit polynomial calculations. Combining this with twisted stable map
s theory 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
topological methods and give applications to counting elliptic curves ove
r Fq(t).\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/2
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miguel Moreira (MIT)
DTSTART:20230912T190000Z
DTEND:20230912T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/25
DESCRIPTION:Title: Enumerative geometry\, wall-crossing and Virasoro c
onstraints\nby Miguel Moreira (MIT) as part of Harvard MIT Algebraic G
eometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nGiven a moduli
space of either sheaves on a smooth projective variety or a moduli space o
f representations of a quiver\, there are several invariants that we can e
xtract. One of the ways to get numbers out of a moduli space is to integra
te (possibly against a virtual fundamental class) certain tautological cla
sses. Such numbers often have interesting structures behind\, and I will t
alk about two: how they change when one changes a stability condition (wal
l-crossing formulas) and some universal and explicit linear relations that
those invariants always seem to satisfy (Virasoro constraints). Both of t
hese phenomena are related to a vertex algebra found by D. Joyce. For simp
licity I will mostly focus on the case of representations of a quiver. The
talk is based on joint work with A. Bojko and W. Lim.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/2
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elden Elmanto (University of Toronto)
DTSTART:20230919T190000Z
DTEND:20230919T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/26
DESCRIPTION:Title: Cycling in Cambridge\nby Elden Elmanto (Univers
ity of Toronto) as part of Harvard MIT Algebraic Geometry Seminar\n\nLectu
re held in MIT 2-132.\n\nAbstract\nI spent most of my time here cycling (o
r is it biking?) and thinking about algebraic cycles from a homotopical vi
ewpoint. I will speak about the latter. In joint work with Matthew Morrow\
, we developed a theory of motivic cohomology of schemes beyond the case o
f smooth schemes over a field. I will explain the cycle-theoretic aspects
of this construction\, focusing on the case of surfaces\, revisiting older
results of Krishna and Srinivas.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/2
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Satriano (University of Waterloo)
DTSTART:20230926T190000Z
DTEND:20230926T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/27
DESCRIPTION:Title: Beyond twisted maps: crepant resolutions of log ter
minal singularities and a motivic McKay correspondence\nby Matthew Sat
riano (University of Waterloo) as part of Harvard MIT Algebraic Geometry S
eminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nCrepant
resolutions have inspired connections between birational geometry\, deriv
ed categories\, representation theory\, and motivic integration. In this t
alk\, we prove that every variety with log-terminal singularities admits a
crepant resolution by a smooth stack. We additionally prove a motivic McK
ay correspondence for stack-theoretic resolutions. Finally\, we show how o
ur work naturally leads to a generalization of twisted mapping spaces. No
prior knowledge of stacks will be assumed. This is joint work with Jeremy
Usatine.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/2
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brad Dirks (Stony Brook)
DTSTART:20231003T190000Z
DTEND:20231003T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/28
DESCRIPTION:Title: The minimal exponent of LCI subvarieties\nby Br
ad Dirks (Stony Brook) as part of Harvard MIT Algebraic Geometry Seminar\n
\nLecture held in Harvard Science Center 507.\n\nAbstract\nClassification
of singularities is an interesting problem in many areas of algebraic geom
etry\, like the minimal model program. One classical approach is to assign
to a variety a rational number\, its log canonical threshold. For complex
hypersurface singularities\, this invariant has been refined by M. Saito
to the minimal exponent. This invariant is related to Bernstein-Sato polyn
omials\, Hodge ideals and higher du Bois and higher rational singularities
.\n\nIn joint work with Qianyu Chen\, Mircea Mustață and Sebastián Olan
o\, we defined the minimal exponent for LCI subvarieties of smooth complex
varieties. We relate it to local cohomology\, higher du Bois and higher r
ational singularities. I will describe what was done in the hypersurface c
ase\, give our definition in the LCI case and explain the relation to loca
l cohomology modules and the classification of singularities.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/2
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Pieloch (MIT)
DTSTART:20231010T190000Z
DTEND:20231010T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/29
DESCRIPTION:Title: Uniruling projective families over $\\mathbb{CP}^1$
with rational (multi)sections\nby Alex Pieloch (MIT) as part of Harva
rd MIT Algebraic Geometry Seminar\n\nLecture held in MIT 2-131.\n\nAbstrac
t\nWe will discuss a result which states that every projective family over
$\\mathbb{CP}^1$ with at most two singular fibres is uniruled by rational
(multi)sections. We obtain these rational curves by using techniques fro
m symplectic geometry. In this talk\, we will focus on (1) discussing the
motivation for this work from Hodge theory and (2) presenting the geometr
ic constructions and ideas involved in our proofs. No knowledge of symple
ctic geometry is required.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/2
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Dinkins (MIT)
DTSTART:20231017T190000Z
DTEND:20231017T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/30
DESCRIPTION:Title: Generalized quantum difference equations for quiver
varieties\nby Hunter Dinkins (MIT) as part of Harvard MIT Algebraic G
eometry Seminar\n\nLecture held in MIT 2-143.\n\nAbstract\nCurve counts in
side certain varieties are constrained by an equation called the quantum d
ifference equation. Okounkov and Smirnov described the quantum difference
equation for Nakajima quiver varieties in terms of a quantum group. There
is a natural modification of their description\, which leads to a collecti
on of "exotic" quantum difference equations\, one for each alcove in a cer
tain hyperplane arrangement. Our main result is an enumerative-geometric d
escription of the fundamental solution of these exotic equations. I will g
ive an overview of these ideas\, illustrating the results for the example
of the Hilbert scheme of points in the complex plane.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/3
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Gross (Cambridge)
DTSTART:20231024T190000Z
DTEND:20231024T200000Z
DTSTAMP:20260404T095028Z
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 Ge
ometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\
nI will talk about work with Hacking\, Keel and Siebert on using mirror co
nstructions to provide partial compactifications of the moduli of K3 surfa
ces. Starting with a one-parameter maximally\nunipotent degeneration of Pi
card rank 19 K3 surfaces\, we construct\, using methods of myself and Sieb
ert\, a mirror family which is defined in a formal neighbourhood of a unio
n of strata of a toric variety whose fan is defined\, to first approximati
on\, as the Mori fan of the original degeneration. This\nformal family may
then be glued in to the moduli space of polarized K3 surfaces to obtain a
partial compactification. Perhaps the most significant by-product of this
construction is the existence of theta functions in this formal neighbour
hood\, certain canonical bases for sections of powers of the\npolarizing l
ine bundle.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/3
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakub Witaszek (Princeton)
DTSTART:20231031T190000Z
DTEND:20231031T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/32
DESCRIPTION:Title: Singularities in mixed characteristic via the Riema
nn-Hilbert correspondence\nby Jakub Witaszek (Princeton) as part of Ha
rvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Ce
nter 507.\n\nAbstract\nIn my talk\, I will start by reviewing how various
properties of characteristic zero singularities can be understood topologi
cally by ways of the Riemann-Hilbert correspondence. After that\, I will e
xplain how similar ideas can be applied in the study of mixed characterist
ic singularities. This is based on a joint work (in progress) with Bhargav
Bhatt\, Linquan Ma\, Zsolt Patakfalvi\, Karl Schwede\, Kevin Tucker\, and
Joe Waldron.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/3
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Talk Cancelled (Talk Cancelled)
DTSTART:20231107T200000Z
DTEND:20231107T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/33
DESCRIPTION:Title: Talk Cancelled\nby Talk Cancelled (Talk Cancell
ed) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in H
arvard Science Center 507.\n\nAbstract\nI will discuss an elementary notio
n -- the angle rank of a polynomial -- and an application to the Tate conj
ecture for Abelian varieties over finite fields.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/3
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iacopo Brivio (Harvard University (CMSA))
DTSTART:20231114T200000Z
DTEND:20231114T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/34
DESCRIPTION:Title: Superadditivity of anticanonical Iitaka dimension i
n positive characteristic\nby Iacopo Brivio (Harvard University (CMSA)
) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Har
vard Science Center 507.\n\nAbstract\nGiven a fibration $f\\colon X\\to Y$
of smooth complex projective with general fiber $F$\, the celebrated Iita
ka conjecture predicts the inequality $\\kappa(K_X)\\geq \\kappa(K_F)+\\ka
ppa(K_Y)$. Recently Chang showed that\, under some natural conditions\, th
e inequality $\\kappa(-K_X)\\leq \\kappa(-K_F)+\\kappa(-K_Y)$ holds.\n\nIn
this talk I will show that\, despite the failure in positive characterist
ic of both the Iitaka conjecture and Chang's theorem\, it is possible to r
ecover the latter for "tame" positive characteristic fibrations. This is b
ased on joint work with M. Benozzo and C.-K. Chang.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/3
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:César Lozano Huerta (Universidad Nacional Autónoma de México)
DTSTART:20231121T200000Z
DTEND:20231121T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/35
DESCRIPTION:Title: The Noether-Lefschetz loci formed by determinantal
surfaces in projective 3-space.\nby César Lozano Huerta (Universidad
Nacional Autónoma de México) as part of Harvard MIT Algebraic Geometry S
eminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nSolomon
Lefschetz showed that the Picard group of a general surface in P3 of degr
ee greater than three is ZZ. That is\, the vast majority of surfaces in P3
have the smallest possible Picard group. The set of surfaces of degree gr
eater than 3 on which this theorem fails is called the Noether-Lefschetz l
ocus. This locus has infinite components and their dimensions are somehow
mysterious.\n\nIn this talk\, I will calculate the dimension of infinite N
oether-Lefschetz components that are simple in a sense\, but still give us
an idea of the complexity of the entire Noether-Lefschetz locus. This is
joint work with Montserrat Vite and Manuel Leal.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/3
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emelie Arvidsson (University of Utah)
DTSTART:20231128T200000Z
DTEND:20231128T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/36
DESCRIPTION:Title: Properties of log canonical singularities in positi
ve characteristic\nby Emelie Arvidsson (University of Utah) as part of
Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science
Center 507.\n\nAbstract\nWe will investigate if some well known propertie
s of log canonical singularities over the complex numbers still hold true
over perfect fields of positive characteristic and over excellent rings wi
th perfect residue fields. We will discuss both pathological behavior in c
haracteristic p as well as some positive results for threefolds. We will s
ee that the pathological behavior of these singularities in positive chara
cteristic is closely linked to the failure of certain vanishing theorems i
n positive characteristic. Additionally\, we will explore how these questi
ons are related to the moduli theory of varieties of general type.\n\nThis
is based on joint work with F. Bernasconi and Zs. Patakfalvi\, as well as
joint work with Q. Posva.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/3
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Baudin (EPFL Lausanne)
DTSTART:20231205T200000Z
DTEND:20231205T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/37
DESCRIPTION:Title: On Ueno's conjecture in positive characteristics\nby Jeff Baudin (EPFL Lausanne) as part of Harvard MIT Algebraic Geometr
y Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nIn c
haracteristic zero\, Ueno's conjecture states that if X is a smooth projec
tive variety with Kodaira dimension zero\, then its Albanese morphism in a
n algebraic fiber space and the Kodaira dimension of the general fiber is
again zero. This was proven by Cao and Păun in 2016. \n\nBuilding on the
generic vanishing techniques of Hacon and Patakfalvi\, we prove a positive
characteristic version of this result. We use it to deduce new cases of I
itaka's subadditivity conjecture in positive characteristics. The goal of
this talk is to explain how these techniques work\, and how we can use the
m to prove such results.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/3
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Perry (University of Michigan)
DTSTART:20231212T200000Z
DTEND:20231212T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/38
DESCRIPTION:Title: The period-index conjecture for abelian threefolds<
/a>\nby Alex Perry (University of Michigan) as part of Harvard MIT Algebra
ic Geometry Seminar\n\nLecture held in MIT 2-131.\n\nAbstract\nThe period-
index conjecture asks for a precise bound on one measure of complexity of
a Brauer class (its index) in terms of another (its period). I will discus
s joint work with James Hotchkiss which proves this conjecture for Brauer
classes on abelian threefolds.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/3
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Lian (Tufts University)
DTSTART:20240206T200000Z
DTEND:20240206T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/39
DESCRIPTION:Title: Enumerativity of fixed-domain Gromov-Witten invaria
nts\nby Carl Lian (Tufts University) as part of Harvard MIT Algebraic
Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nIt is well-und
erstood that Gromov-Witten (GW) invariants often fail to be enumerative. F
or example\, 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 situation seems to be better when one fixes the complex structure of t
he domain 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 wil
l discuss some positive and negative results in this direction\, focusing
on the case of hypersurfaces. The most recent results are joint with Roya
Beheshti\, Brian Lehmann\, Eric Riedl\, Jason Starr\, and Sho Tanimoto\, a
nd build on earlier work with Rahul Pandharipande and Alessio Cela.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/3
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Canceled
DTSTART:20240213T200000Z
DTEND:20240213T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/40
DESCRIPTION:Title: Canceled\nby Canceled as part of Harvard MIT Al
gebraic Geometry Seminar\n\nLecture held in MIT 2-132.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/4
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Montserrat Teixidor (Tufts University)
DTSTART:20240220T200000Z
DTEND:20240220T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/41
DESCRIPTION:Title: Brill-Noether loci\nby Montserrat Teixidor (Tuf
ts University) as part of Harvard MIT Algebraic Geometry Seminar\n\nLectur
e 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 ser
ies of degree d and dimension r.\n\nPflueger showed that these loci are no
n-empty when the expected codimension is at most g-3. By studying linear s
eries on chains of elliptic curves\, we give a new proof of a slightly ref
ined version of this result. We can also look at the behavior of the gener
ic curve in the locus.\n\nAn interesting conjecture of Auel and Haburcak
states that these loci are distinct and not contained in each other\, unle
ss 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 i
nformation.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/4
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maksym Fedorchuk (Boston College)
DTSTART:20240227T200000Z
DTEND:20240227T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/42
DESCRIPTION:Title: CM-minimizers and standard models of Fano fibration
s over curves\nby Maksym Fedorchuk (Boston College) as part of Harvard
MIT Algebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\
nA recent achievement in K-stability of Fano varieties is an\nalgebro-geom
etric construction of a projective moduli space of\nK-polystable Fanos. Th
e ample line bundle on this moduli space is the\nCM line bundle of Tian. O
ne of the consequences of the general theory\nis that given a family of K-
stable Fanos over a punctured curve\, the\npolystable filling is the one t
hat minimizes the degree of the CM line\nbundle after every finite base
change. A natural question is to\nask what are the CM-minimizers w
ithout base change. In\nanswering this question\, we arrive at a theor
y of Kollár stability\nfor fibrations over one-dimensional bases\, and st
andard models of Fano\nfibrations. After explaining the general theory\, I
will sketch work in\nprogress on standard models of quartic threefold hyp
ersurfaces. This\ntalk is based on joint work with Hamid Abban and Igor Kr
ylov.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/4
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marta Benozzo (Imperial College)
DTSTART:20240305T200000Z
DTEND:20240305T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/43
DESCRIPTION:Title: On the canonical bundle formula in positive charact
eristic\nby Marta Benozzo (Imperial College) as part of Harvard MIT Al
gebraic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\
nAbstract\nAn important problem in birational geometry is trying to relate
in a meaningful way the canonical bundles of the source and the base of a
fibration. The first instance of such a formula is Kodaira’s canonical
bundle formula for surfaces which admit a fibration with elliptic fibres.
It describes the relation between the canonical bundles in terms of the si
ngularities of the fibres and their j-invariants.\nIn higher dimension\, w
e do not have an equivalent of the j-invariant\, but we can still define a
moduli part. Over fields of characteristic 0\, positivity properties of t
he moduli part have been studied using variations of Hodge structures. Rec
ently\, the problem has been approached with techniques from the minimal m
odel program. These methods can be used to prove a canonical bundle formul
a result in positive characteristic.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/4
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Marquand (NYU)
DTSTART:20240312T190000Z
DTEND:20240312T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/44
DESCRIPTION:Title: The defect of a cubic threefold\nby Lisa Marqua
nd (NYU) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held
in Harvard Science Center 507.\n\nAbstract\nThe defect of a cubic threefo
ld with isolated singularities is a measure of the failure of Poincare dua
lity\, and also the failure to be Q-factorial. From the work of Cheltsov\,
a cubic threefold with only nodal singularities is Q factorial if and onl
y if there are at most 5 nodes. We investigate the defect of cubic threefo
lds with worse than nodal isolated singularities\, and provide a geometric
method to compute this global invariant. One can then compute the Mixed H
odge structure on the middle cohomology of the cubic threefold\, in terms
of the defect (a global invariant) and local invariants (Du Bois and Link
invariants) determined by the singularity types. We then relate the defect
to geometric properties of the cubic threefold\, showing it is positive i
f and only if the cubic contains a plane or a rational normal cubic scroll
. The focus of this work is to provide more insight into the existence of
reducible fibers for compactified intermediate jacobian fibrations associa
ted to a smooth (not necessarily general) cubic fourfold. This is joint wo
rk with Sasha Viktorova.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/4
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changho Han (Waterloo)
DTSTART:20240319T190000Z
DTEND:20240319T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/45
DESCRIPTION:Title: Extending the torelli map to alternative compactifi
cations of the moduli space of curves\nby Changho Han (Waterloo) as pa
rt of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Sc
ience Center 507.\n\nAbstract\nIt is well-known that the Torelli map\, tha
t turns a smooth curve of genus g into its Jacobian (a principally polariz
ed abelian variety of dimension g)\, extends to a map from the Deligne—M
umford moduli of stable curves to the moduli of semi-abelic varieties by A
lexeev. Moreover\, it is also known that the Torelli map does not extend o
ver the alternative compactifications of the moduli of curves as described
by the Hassett—Keel program\, including the moduli of pseudostable curv
es (can have nodes and cusps but not elliptic tails). But it is not yet kn
own whether the Torelli map extends over alternative compactifications of
the moduli of curves described by Smyth\; what about the moduli of curves
of genus g with rational m-fold singularities\, where m is a positive inte
ger bounded above? As a joint work in progress with Jesse Kass and Matthew
Satriano\, I will describe moduli spaces of curves with m-fold singularit
ies (with topological constraints) and describe how far the Torelli map ex
tends over such spaces into the Alexeev compactifications.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/4
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dhruv Ranganathan (Cambridge)
DTSTART:20240326T190000Z
DTEND:20240326T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/46
DESCRIPTION:Title: A degeneration of the Hilbert scheme\nby Dhruv
Ranganathan (Cambridge) as part of Harvard MIT Algebraic Geometry Seminar\
n\nLecture held in MIT 2-449 (note special room!).\n\nAbstract\nSpecial Ro
om: 2-449\n\nGrothendieck's Hilbert scheme is a compact parameter space f
or subschemes of a projective scheme X. It is one of the basic moduli spac
es in algebraic geometry\, in the sense that it is the starting point for
the construction of many others. One simple question about the Hilbert sch
eme is the following: as X undergoes a nice degeneration\, what is the rig
ht way to degenerate the Hilbert scheme of X along with it? One possible a
nswer\, 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 log
arithmic Hilbert scheme\, and sketch connections with certain moduli space
s of higher dimensional varieties. The talk reports on work of Kennedy-Hun
t\, joint work with Kennedy-Hunt\, and joint work with Maulik.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/4
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julianna Tymoczko (Smith College)
DTSTART:20240402T190000Z
DTEND:20240402T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/47
DESCRIPTION:Title: Webs and Schubert calculus for Springer fibers\
nby Julianna Tymoczko (Smith College) as part of Harvard MIT Algebraic Geo
metry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nClassical Schuber
t calculus analyzes the geometry of the flag variety\, namely the space of
nested subspaces $V_1 \\subseteq V_2 \\subseteq \\cdots \\subseteq \\math
bb{C}^n$\, asking enumerative questions about intersections of linear spac
es that turn out to be equivalent to deep problems in combinatorics and re
presentation theory. In this talk\, we'll describe some recent results in
the Schubert calculus of Springer fibers. Given a nilpotent linear opera
tor $X$\, the Springer fiber of $X$ is the subvariety of flags that are fi
xed by $X$ in the sense that $XV_i \\subseteq V_i$ for all $i$. The top-d
imensional cohomology of Springer fibers admits a representation of the sy
mmetric group first discovered by Tonny Springer as the seminal example of
a geometric representation. Where classical Schubert calculus describes
geometry governed by permutations\, that of Springer fibers incorporates t
he combinatorics both of permutations and of partitions. We'll describe n
ew results about this geometry in more detail\, including evidence that fr
om a geometric and topological perspective\, the best combinatorial model
for Springer fibers comes from representation-theoretic objects called web
s.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/4
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Esser (Princeton)
DTSTART:20240409T190000Z
DTEND:20240409T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/48
DESCRIPTION:Title: The Dual Complex of a G-variety\nby Louis Esser
(Princeton) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture
held in Harvard Science Center 507.\n\nAbstract\nWe introduce a new invari
ant of G-varieties\, the dual complex\, which roughly measures how divisor
s in the complement of the free locus intersect. We show that the top homo
logy group of this complex is an equivariant birational invariant of G-var
ieties. As an application\, we demonstrate the non-linearizability of cert
ain large abelian group actions on smooth hypersurfaces in projective spac
e of any dimension and degree at least 3.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/4
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Han-Bom Moon (Fordham University)
DTSTART:20240416T190000Z
DTEND:20240416T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/49
DESCRIPTION:Title: Derived category of moduli space of vector bundles
on a curve\nby Han-Bom Moon (Fordham University) as part of Harvard MI
T Algebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nTh
e derived category of moduli spaces of vector bundles on a curve is expect
ed to be decomposed into the derived categories of symmetric products of t
he base curve. I will briefly explain the expectation and known results\,
and some consequences. This is joint work in progress with Kyoung-Seog Lee
.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/4
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Larson (UC Berkeley)
DTSTART:20240423T190000Z
DTEND:20240423T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/50
DESCRIPTION:Title: The Chow ring of the universal Picard stack over th
e hyperelliptic locus\nby Hannah Larson (UC Berkeley) as part of Harva
rd MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Cente
r 507.\n\nAbstract\nUnderstanding the line bundles on curves are essential
to understanding the curves themselves. As such\, the universal Picard st
ack J^d_g --> M_g parametrizing degree d line bundles on genus g curves is
an important object of study. Recently\, progress has been made on the in
tersection theory of M_g in low genus by stratifying the moduli space by g
onality. The smallest piece in this stratification is the hyperelliptic lo
cus. Motivated by this\, I'll present several results about the restrictio
n of J^d_g to the hyperelliptic locus\, denoted J^d_{2\,g}. These include
a presentation of the rational Chow ring of J^d_{2\,g}. I also determine t
he integral Picard group of J^d_{2\,g}\, completing (and extending to the
PGL_2-equivariant case) prior work of Erman and Wood.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/5
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qile Chen (Boston College)
DTSTART:20240430T190000Z
DTEND:20240430T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/51
DESCRIPTION:Title: Campana rational connectedness\nby Qile Chen (B
oston College) as part of Harvard MIT Algebraic Geometry Seminar\n\nLectur
e held in MIT 2-132.\n\nAbstract\nThe notion of Campana points were introd
uced by Campana and Abramovich\, which interpolate between rational points
and integral points. In this talk\, we will focus on the geometric side a
nd introduce Campana rational connectedness --- a version of rational conn
ectedness for varieties with simple normal crossings boundaries. We furthe
r prove that over function fields\, weak approximations by Campana points
at good places hold assuming Campana rational connectedness of fibers\, ge
neralizing a theorem of Hassett and Tschinkel. We further verify Campana r
ational connectedness for many basic examples. Our approach relies on the
theory of stable log maps and their moduli. This is a joint work in progre
ss with Brian Lehmann and Sho Tanimoto.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/5
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Harris (Harvard University)
DTSTART:20240507T190000Z
DTEND:20240507T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/52
DESCRIPTION:Title: The Enriques Conjectures\nby Joe Harris (Harvar
d University) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture
held in Harvard Science Center 507.\n\nAbstract\nTwo fundamental facts ab
out the moduli space M_g of smooth curves of genus g are what are called H
arer's theorems: that the Picard group of M_g is of rank one\, generated (
over the rational numbers) by the Hodge class\; and that the relative Pica
rd group of the universal curve over M_g is also of rank one\, generated b
y the relative dualizing sheaf. We can make analogous statements about the
Severi variety of plane curves and the Hurwitz space parametrizing branch
ed covers\, which are still open\; in fact\, the former was conjectured by
Enriques more than a century ago and remains open.\n\nIn this talk I'd li
ke to describe all of these theorems/conjectures\, and the implications am
ong them\, including Isabel Vogt's recent work on Severi varieties. I'll b
e working entirely with rational coefficients\, so torsion classes\, which
are far more mysterious\, will not enter into it.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/5
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Borys Kadets (Hebrew University of Jerusalem)
DTSTART:20240402T203000Z
DTEND:20240402T213000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/56
DESCRIPTION:Title: Curves with many degree $d$ points (Joint with the
MIT number theory seminar\, note the special time and location)\nby Bo
rys Kadets (Hebrew University of Jerusalem) as part of Harvard MIT Algebra
ic Geometry Seminar\n\nLecture held in MIT 2-449.\n\nAbstract\nWhen does a
nice curve $X$ over a number field $k$ have infinitely many closed points
of degree $d$?\nFaltings' theorem allows us to rephrase this problem in p
urely algebro-geometric terms\, though the resulting geometric question is
far from being fully solved. Previous work gave easy to state answers to
the problem for degrees $2$ (Harris-Silverman) and $3$ (Abramovich-Harris)
\, but also uncovered exotic constructions of such curves in all degrees $
d \\geqslant 4$ (Debarre-Fahlaoui). I will describe recent progress on the
problem\, which answers the question in the large genus case. Along the w
ay we uncover systematic explanations for the Debarre-Fahlaoui counstructi
ons and provide a complete geometric answer for $d \\leqslant 5$. The talk
is based on joint work with Isabel Vogt.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/5
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Hase-Liu (Columbia University)
DTSTART:20241001T190000Z
DTEND:20241001T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/57
DESCRIPTION:Title: A circle method for algebraic geometers\nby Mat
thew Hase-Liu (Columbia University) as part of Harvard MIT Algebraic Geome
try Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nBr
owning and Vishe studied the moduli space of smooth genus zero curves of f
ixed degree on a smooth low-degree hypersurface using the circle method\,
a technique from analytic number theory. I'll explain how their strategy c
an be interpreted completely algebro-geometrically\, and then use this per
spective to generalize their results to the higher genus setting. Time per
mitting\, I'll also discuss some applications to Geometric Manin's conject
ure and terminal singularities of these moduli spaces\, the latter of whic
h is joint work with Jakob Glas.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/5
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:César Lozano Huerta (Universidad Nacional Autónoma de México)
DTSTART:20240625T190000Z
DTEND:20240625T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/58
DESCRIPTION:Title: Geometry of syzygies of sheaves on P2 via interpola
tion and Bridgeland stability.\nby César Lozano Huerta (Universidad N
acional Autónoma de México) as part of Harvard MIT Algebraic Geometry Se
minar\n\nLecture held in Harvard Science Center 232.\n\nAbstract\nThe mini
mal free resolution of a sheaf on P2\, such as a vector bundle or the idea
l sheaf of points\, carries important information about its moduli space.
However\, how it may do so has remained unclear.\n\nThis talk aims to clar
ify the previous situation and\, I will compute the cone of effective divi
sors of moduli spaces of sheaves using syzygies.\n\nNote the special room
on the second floor\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/5
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yajnaseni Dutta (Leiden University)
DTSTART:20240924T190000Z
DTEND:20240924T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/59
DESCRIPTION:Title: Twisted Intermediate Jacobian Fibrations\nby Ya
jnaseni Dutta (Leiden University) as part of Harvard MIT Algebraic Geometr
y Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nIn t
his talk\, I will report on a joint work in progress with D. Mattei and E.
Shinder\, where we construct\, using Hodge modules\, a group scheme that
can be thought of as the intermediate Jacobian of a certain complete famil
y of cubic threefolds. We show that the group scheme acts on a well-known
abelian fibration. The action gives rise to twisted versions of the abelia
n fibration. This is similar to twisting genus 1 fibrations with irreducib
le fibres via its Tate-Shafarevich group.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/5
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andres Fernandez Herrero (University of Pennsylvania)
DTSTART:20240910T190000Z
DTEND:20240910T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/60
DESCRIPTION:Title: Decomposition theorem for the logarithmic Hitchin f
ibration\nby Andres Fernandez Herrero (University of Pennsylvania) as
part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in MIT 2-13
2.\n\nAbstract\nThe focus of this talk will be the moduli space of logarit
hmic G-Higgs bundles on a smooth projective curve\, where G is a reductive
group. I will explain some recent progress towards understanding the int
ersection cohomology of this moduli space: a description of the decomposit
ion theorem for the corresponding Hitchin fibration. This is based on wor
k in progress joint with Mark de Cataldo\, Roberto Fringuelli and Mirko Ma
uri.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/6
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusuf Mustopa (University of Massachusetts)
DTSTART:20241008T190000Z
DTEND:20241008T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/61
DESCRIPTION:Title: Convex Fujita Numbers and Projective Bundles\nb
y Yusuf Mustopa (University of Massachusetts) as part of Harvard MIT Algeb
raic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nThe Fujit
a Freeness Conjecture predicts that for an ample line bundle $L$ on a smoo
th projective variety $X$ of dimension $n\,$ the adjoint bundle $K \\otime
s L^{\\otimes m}$ is basepoint free for $m \\geq n+1\,$ and is currently o
pen for all $n \\geq 6.$ A numerical\n(and a priori stronger) form of thi
s conjecture\, whose hypothesis replaces the condition on $m$ with conditi
ons on intersection numbers involving $L\,$ was proposed by Helmke in 1997
. As an 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 Fu}(X)$ of $X\,$ which measures "how soon" the global generation tak
es effect. In this talk\, I will discuss ongoing joint work with Jiaming
Chen\, Alex Kuronya\, and Jakob Stix on the possible values of ${\\rm Fu}(
X)\,$ with emphasis on the case where $X$ is a projectivized vector bundle
.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/6
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Paul Brasselet (CNRS)
DTSTART:20241112T190000Z
DTEND:20241112T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/62
DESCRIPTION:Title: Characteristic classes of singular varieties\nb
y Jean-Paul Brasselet (CNRS) as part of Harvard MIT Algebraic Geometry Sem
inar\n\nLecture held in Harvard Science Center Hall A.\n\nAbstract\nIn the
case of manifolds\, Hirzebruch showed how to unify the theories of charac
teristic classes of Chern\, Todd and Thom-Hirzebruch. These three theories
have been generalized to the case of singular complex algebraic varieties
as natural transformations of functors. We show how motivic theory allows
these natural transformations to be unified and what the underlying probl
ems are.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/6
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kendric Schefers (Stony Brook University)
DTSTART:20241210T200000Z
DTEND:20241210T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/63
DESCRIPTION:Title: Microlocal perspective on homology\nby Kendric
Schefers (Stony Brook University) as part of Harvard MIT Algebraic Geometr
y Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nThe difference betwee
n the homology and cohomology of a space can be seen as a measure of the s
ingularity of that space. This measure can be made precise for special fib
ers of maps between smooth varieties by introducing the so-called "microlo
cal homology" of such a map\, an object which records the singularities of
the special fiber as well as the codirections in which those singularitie
s arise.\n\nIn this talk\, we show that the microlocal homology is in fact
intrinsic to the special fiber—independent of its particular presentati
on—by relating it to an object of (-1)-shifted symplectic geometry: the
canonical perverse sheaf categorifying Donaldson-Thomas invariants introdu
ced by Joyce et al. Time permitting\, we will relate the microlocal homolo
gy to the singular support theory of coherent sheave\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/6
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Church (Stanford University)
DTSTART:20240917T190000Z
DTEND:20240917T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/64
DESCRIPTION:Title: Curves on complete intersections and measures of ir
rationality\nby Benjamin Church (Stanford University) as part of Harva
rd MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Cente
r 507.\n\nAbstract\nGiven a projective variety $X$\, it is always covered
by curves obtained by taking the intersection with a linear subspace. We s
tudy whether there exist curves on $X$ that have smaller numerical invaria
nts than those of the linear slices. If $X$ is a general complete intersec
tion of large degrees\, we show that there are no curves on $X$ of smaller
degree\, nor are there curves of asymptotically smaller gonality. This ve
rifies a folklore conjecture on the degrees of subvarieties of complete in
tersections as well as a conjecture of Bastianelli--De Poi--Ein--Lazarsfel
d--Ullery on measures of irrationality for complete intersections. This is
joint work with Nathan Chen and Junyan Zhao.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/6
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Brazelton (Harvard University)
DTSTART:20241015T190000Z
DTEND:20241015T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/65
DESCRIPTION:Title: Symmetry in classical enumerative geometry\nby
Thomas Brazelton (Harvard University) as part of Harvard MIT Algebraic Geo
metry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\n
In this talk we'll discuss an equivariant principle of conservation of num
ber\, proven using methods from equivariant homotopy theory. It roughly st
ates that in the presence of symmetry\, not only the number of solutions i
s conserved\, but their symmetries are as well. For instance when a cubic
surface is defined by a symmetric polynomial\, its 27 lines always carry t
he same S4 action. We apply this idea in joint work with C. Bethea to comp
ute bitangents to smooth plane quartics with nontrivial automorphism group
s\, where we see that homotopical techniques directly reveal patterns whic
h are not obvious from a classical moduli perspective. We will also discus
s work with S. Raman\, in which we initiate a study of Galois groups of sy
mmetric enumerative problems\, leveraging tools from Hodge theory and comp
utational numerical analysis.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/6
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anh Đức Võ (Harvard University)
DTSTART:20241022T190000Z
DTEND:20241022T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/66
DESCRIPTION:Title: Du Bois complexes and singularities\nby Anh Đ
ức Võ (Harvard University) as part of Harvard MIT Algebraic Geometry Se
minar\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 overv
iew of classical notions: rational and Du Bois singularities. I will then
discuss their recent extensions to k-rational and k-Du Bois singularities\
, both for local complete intersections (LCIs) and non-LCI varieties. Addi
tionally\, I will discuss results on the injectivity and vanishing propert
ies of Du Bois complexes in the context of these generalizations. This tal
k is based on joint works with Mihnea Popa\, Wanchun Shen\, and Sridhar Ve
nkatesh.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/6
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Botta (Columbia University)
DTSTART:20241029T190000Z
DTEND:20241029T200000Z
DTSTAMP:20260404T095028Z
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 Algebrai
c Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nThe Maulik-O
kounkov Lie algebra associated to a quiver Q controls the R-matrix formali
sm developed by Maulik and Okounkov in the context of quantum cohomology o
f Nakajima quiver varieties. On the other hand\, the BPS Lie algebra origi
nates from cohomological DT theory\, particularly from the theory of cohom
ological Hall algebras associated with 3 Calabi-Yau categories. In this ta
lk\, I will explain how to identify the MO Lie algebra of an arbitrary qui
ver with the (appropriate) BPS Lie algebra. The bridge to compare these se
emingly diverse words is the theory of non-abelian stable envelopes\, whic
h is exploited to relate representations of the MO Lie algebra to represen
tations of the BPS Lie algebra. In conclusion\, I will apply this result t
o deduce Okounkov's conjecture\, equating the graded dimensions of the MO
Lie algebra with the coefficients of Kac polynomials. This is joint work w
ith Ben Davison.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/6
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Younghan Bae (University of Michigan)
DTSTART:20241105T200000Z
DTEND:20241105T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/68
DESCRIPTION:Title: Fourier transformation and the Abel-Jacobi section<
/a>\nby Younghan Bae (University of Michigan) as part of Harvard MIT Algeb
raic Geometry 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 Jacobi
an over the moduli space of smooth genus g curves with n sections\, the Ab
el-Jacobi section maps a marked curve (C\, x1\, ...\, xn) to a line bundle
O(v1.x1+ ... + vn.xn). Using the Fourier-Mukai transform\, this locus can
be expressed as a power of twisted theta divisor. When the curve acquires
nodal singularities\, the relative Jacobian can be compactified via stabl
e rank 1 torsion-free sheaves. After blowing up the base\, the Abel-Jacobi
section extends and its class can be computed using Pixton's formula on t
he universal double ramification cycle formula.\n\nIn this talk\, we propo
se a conjectural closed formula for the pushforward of monomials of diviso
r classes on compactified Jacobians. This conjecture is motivated by an ex
plicit computation of Fourier transform on the compactified Jacobian and c
ombinatorial properties of the Pixton's formula. We verify the conjecture
over various open loci of the base. This is joint work in progress with Sa
mouil Molcho and Aaron Pixton.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/6
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hélène Esnault (Harvard University)
DTSTART:20241119T200000Z
DTEND:20241119T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/69
DESCRIPTION:Title: A non-abelian version of Deligne's Fixed Part Theor
em\nby Hélène Esnault (Harvard University) as part of Harvard MIT Al
gebraic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\
nAbstract\nWe prove a non-abelian version of Deligne’s Fix Part Theorem.
It\nis a statement which is purely anchored in complex geometry. The\nrea
son for the consideration is a vaster program which aims at\nunderstanding
some aspects of the monodromy-weight conjecture\nin unequal characteristi
c by ’tilting it’ to a complex situation for\nwhich we have the tools
developed notably by Morihiko Saito and\nTakuro Mochizuki. This lecture fo
cuses on a small part of it.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/6
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Petrov (MIT)
DTSTART:20241126T200000Z
DTEND:20241126T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/70
DESCRIPTION:Title: De Rham cohomology of varieties in positive charact
eristic\nby Alexander Petrov (MIT) as part of Harvard MIT Algebraic Ge
ometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\
nHodge theory provides an additional structure of Hodge decomposition on t
he cohomology of a smooth proper variety over complex numbers\, and implie
s cohomology vanishing results such as Kodaira vanishing. For varieties in
positive characteristic Hodge decomposition in general fails to exist\, b
ut Deligne and Illusie found a very satisfactory substitute for Hodge theo
ry that applies to smooth proper varieties over $\\mathbf{F}_p$ that lift
to $\\mathbf{Z}/p^2$ and have dimension $\\leq p$. They proved that in thi
s case the algebraic de Rham complex is quasi-isomorphic to the direct sum
of its cohomology sheaves\, which induces a decomposition of de Rham coho
mology into the direct sum of Hodge cohomology groups\, and implies Kodair
a vanishing.\n\nFor liftable varieties of larger dimension Hodge decomposi
tion might still fail to exist\, but there are more narrow classes of vari
eties of 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
cohomology via the de Rham stack\, introduced in positive characteristic
by Drinfeld and Bhatt-Lurie.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/7
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Halpern-Leistner (Cornell University)
DTSTART:20241203T200000Z
DTEND:20241203T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/71
DESCRIPTION:Title: Dispatches from the ends of the stability manifold<
/a>\nby Daniel Halpern-Leistner (Cornell University) as part of Harvard MI
T Algebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nTh
e manifold of Bridgeland stability conditions parameterizes a homological
structure on a triangulated category that is analogous to a Kaehler struct
ure on a projective variety. Recently\, I have introduced a noncommutative
minimal model program\, which proposes to identify canonical (semiorthogo
nal)decompositions of derived categories of coherent sheaves by studying p
aths in the stability manifold converging to certain points at infinity. I
will discuss a partial compactification of the stability manifold\, the s
pace of augmented stability conditions\, which makes this picture more pre
cise. To do this\, I will introduce a structure on a triangulated category
that we call a multi-scale decomposition\, which generalizes a semiorthog
onal decomposition\, and a new moduli space of genus zero curves equipped
with meromorphic differentials. The main conjecture about the space of aug
mented stability conditions is that it is a manifold with corners (in a sp
ecific way that I will explain). One consequence: If this conjecture holds
for any smooth and proper dg-category\, then any stability condition on a
smooth and proper dg-category admits proper moduli spaces of semistable o
bjects.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/7
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Doran (University of Alberta\, Bard College\, and CMSA)
DTSTART:20241217T200000Z
DTEND:20241217T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/72
DESCRIPTION:Title: Bounding the Complexity of Feynman Integrals with H
odge Theory\nby Charles Doran (University of Alberta\, Bard College\,
and CMSA) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture hel
d in Harvard Science Center 507.\n\nAbstract\nTwenty years ago\, Bloch\, E
snault\, and Kreimer introduced an algebro-geometric formulation of Feynma
n integration\, building on Griffiths' theory of variation of mixed Hodge
structure. Explicit computation for specific Feynman graphs with all para
meters has proved an elusive goal. With Andrew Harder and Pierre Vanhove\
, we use quadric bundles to establish a complexity bound on the motives un
derlying an infinite collection of two-loop Feynman integrals. For anothe
r family of graphs with unbounded loop order\, we describe the geometry an
d Hodge theory of the Feynman motives of Calabi-Yau type.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/7
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ashvin Swaminathan (Harvard University)
DTSTART:20250304T200000Z
DTEND:20250304T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/75
DESCRIPTION:Title: A positive proportion of hyperelliptic curves have
no unexpected quadratic points\nby Ashvin Swaminathan (Harvard Univers
ity) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in
Harvard Science Center 507.\n\nAbstract\nWe prove that when even-degree hy
perelliptic curves are ordered by the sizes of their coefficients\, a posi
tive proportion of them have no unexpected quadratic points --- i.e.\, no
points defined over quadratic fields except for those that arise by pullin
g back rational points from P^1. To obtain this result\, we combine a gene
ralization 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 hy
perelliptic curves. This is joint work with Manjul Bhargava\, Jef Laga\, a
nd Arul Shankar.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/7
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sándor Kovács (University of Washington)
DTSTART:20250124T200000Z
DTEND:20250124T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/76
DESCRIPTION:Title: KSB stability is automatic in codimension 3\nby
Sándor Kovács (University of Washington) as part of Harvard MIT Algebra
ic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbst
ract\nI will start with a review of KSB/A stability\, especially their loc
al version and then discuss joint work with János Kollár\, showing that
it is enough to check these conditions\, including flatness\, up to codime
nsion 2. This implies that we have a very good understanding of this stabi
lity condition in general\, because local KSB-stability is trivial at codi
mension 1 points\, and quite well understood at codimension 2 points\, sin
ce we have a complete classification of 2-dimensional slc singularities.\n
\nNote the special date. The time and location are the usual.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/7
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:SPRING BREAK
DTSTART:20250318T190000Z
DTEND:20250318T200000Z
DTSTAMP:20260404T095028Z
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://stable.researchseminars.org/talk/harvard-mit-ag-seminar/7
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yoon-Joo Kim (Columbia University)
DTSTART:20250204T200000Z
DTEND:20250204T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/78
DESCRIPTION:Title: The Néron model of a Lagrangian fibration\nby
Yoon-Joo Kim (Columbia University) as part of Harvard MIT Algebraic Geomet
ry Seminar\n\nLecture held in Harvard Science Center 507 or MIT 2-132.\n\n
Abstract\nSingular fibers in minimal elliptic fibrations were classified b
y Kodaira and Néron in the 1960s. In his proof\, Néron constructed and s
ystematically used a special group scheme acting on an elliptic fibration.
This group scheme is now called the Néron model.\nA Lagrangian fibration
is a higher-dimensional generalization of an elliptic fibration. Néron
’s theory is restricted to 1-dimensional bases\, so one cannot use Néro
n’s original approach to study higher-dimensional Lagrangian fibrations.
The higher-dimensional analog of Néron’s definition was recently propo
sed by David Holmes. Quite unfortunately\, Holmes also showed that such a
generalized Néron model often fails to exist\, even in simple cases.\nIn
this talk\, we show that Holmes’s generalized Néron model does exist fo
r an arbitrary projective Lagrangian fibration of a smooth symplectic vari
ety\, under a single assumption that the Lagrangian fibration has no fully
-nonreduced fibers. This generalizes Néron’s result to many higher-dime
nsional Lagrangian fibrations. Such a construction has several application
s. First\, it extends Ngô's results on Hitchin fibrations to many Lagrang
ian fibrations. Second\, it allows Lagrangian fibrations to be considered
as a minimal model-compactification of a smooth commutative group scheme-t
orsor. Third\, it provides a tool to study birational behaviors of Lagrang
ian fibrations. Finally\, the notion of a Tate-Shafarevich twist can be un
derstood via the Néron model.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/7
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Ibáñez Núñez (Columbia University)
DTSTART:20250401T190000Z
DTEND:20250401T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/79
DESCRIPTION:Title: Euler characteristic of Artin stacks and intrinsic
Donaldson-Thomas theory\nby Andrés Ibáñez Núñez (Columbia Univers
ity) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in
MIT 2-131.\n\nAbstract\nThe Euler characteristic of an Artin stack over th
e complex numbers is not a priori well-defined\, due to the presence of no
n-zero cohomology in infinitely many degrees. We will show how to fix the
definition by introducing a combinatorial gadget that we call the componen
t lattice of the stack. This will allow us to define a certain algebraic s
tructure on the ring of naive motives over the stack\, akin to a Hall alge
bra. This Hall structure produces a motivic invariant of the stack for whi
ch the Euler characteristic is well-defined\, a fact that we call the no-p
ole theorem.\n\nIn the case of (-1)-shifted symplectic stacks\, our machin
ery produces generalized Donaldson-Thomas invariants. When the stack param
etrizes objects in an abelian category\, one recovers Joyce-Song invariant
s. Thus our work is a generalization of Donaldson-Thomas theory to abstrac
t stacks. We will explain how the intrinsic set-up also allows to simplify
the foundations of (usual) motivic Donaldson-Thomas theory considerably.\
n\nThis is joint work with Chenjing Bu and Tasuki Kinjo.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/7
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lenny Taelman (University of Amsterdam)
DTSTART:20250128T200000Z
DTEND:20250128T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/80
DESCRIPTION:Title: Deformations of Calabi—Yau varieties in character
istic p\nby Lenny Taelman (University of Amsterdam) as part of Harvard
MIT Algebraic Geometry Seminar\n\nLecture held in MIT 2-361.\n\nAbstract\
nA smooth projective variety X is said to be Calabi-Yau if its canonical b
undle is trivial. I will discuss joint work with Lukas Brantner\, in which
we use derived algebraic geometry to study deformations of Calabi-Yau var
ieties in characteristic p. We prove a positive characteristic analogue of
the Bogomolov-Tian-Todorov theorem (which states that deformations of Cal
abi-Yau varieties in characteristic 0 are unobstructed)\, and show that 'o
rdinary' Calabi-Yau varieties admit canonical lifts to characteristic zero
(generalising earlier results of Serre-Tate for abelian varieties\, and D
eligne and Nygaard for K3 surfaces). In this talk\, no prior knowledge of
derived algebraic geometry will be assumed.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/8
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan Zavyalov (Princeton University)
DTSTART:20250408T190000Z
DTEND:20250408T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/81
DESCRIPTION:Title: The trace morphism and Poincaré duality in p-adic
non-archimedean geometry\nby Bogdan Zavyalov (Princeton University) as
part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard
Science Center 507.\n\nAbstract\nI will explain a construction of the tra
ce morphism for smooth morphism \nof analytic adic spaces. Then I will exp
lain how one can use this trace to prove various \nPoincare Duality type r
esults. In particular\, I will discuss a new easy proof of Poincare Dualit
y \nfor F_p-cohomology groups of smooth proper p-adic rigid-analytic space
s and an appropriate\ngeneralization of this result to arbitrary proper mo
rphisms.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/8
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Bakker (UIC)
DTSTART:20250506T190000Z
DTEND:20250506T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/82
DESCRIPTION:Title: The linear Shafarevich conjecture for quasiprojecti
ve varieties (part 2)\nby Ben Bakker (UIC) as part of Harvard MIT Alge
braic Geometry Seminar\n\nLecture held in MIT 2-131.\n\nAbstract\nShafarev
ich asked 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 almos
t faithful representation of its fundamental group---by Eyssidieux--Katzar
kov--Pantev--Ramachandran using techniques from non-abelian Hodge theory.
In joint work with Y. Brunebarbe and J. Tsimerman\, we prove a version of
the linear Shafarevich conjecture for quasiprojective varieties. The pro
of relies on a number of recent advances in non-abelian Hodge theory in th
e non-proper case.\n\nIn the first talk I will outline the general strateg
y and explain why non-abelian Hodge theory naturally shows up in the conte
xt of Shafarevich's question. In the second talk I will provide some deta
ils of the proof\, including the role played by the twistor geometry of th
e stack of local systems and the algebraic integrability of Katzarkov--Zuo
foliations. As a bonus\, I will also explain how these techniques prove
the algebraicity of Shafarevich morphisms\, which generalizes Griffiths' c
onjecture on the algebraicity of the images of period maps to arbitrary lo
cal systems.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/8
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillermo Peñafort Sanchis (University of Valencia)
DTSTART:20250211T200000Z
DTEND:20250211T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/83
DESCRIPTION:Title: Open problems about deformations of singular holomo
rphic map germs\nby Guillermo Peñafort Sanchis (University of Valenci
a) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Ha
rvard Science Center 507.\n\nAbstract\nThe theory of deformations of germs
of holomorphic mappings and the theory of deformations of germs of comple
x hypersurfaces share many features\, which become apparent once one knows
how to translate from one to the other. But\, for any result about hypers
urfaces\, the corresponding result about mappings tends to be much harder
to prove. In this talk we will discuss open problems about singular mappin
gs\, based on the following known results about isolated hypersurface sing
ularities:\n \n\n· The Milnor number is greater than or equal to the Tjur
ina number and their quotient cannot exceed the dimension of th
e ambient space.\n\n \n· If two hypersurfaces have the same topological t
ype\, then their Milnor numbers are equal.\n \n\n· Singularities cannot b
e split in two without giving rise to non-trivial homology.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/8
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vasudevan Srinivas (Tata and Univ. of Buffalo)
DTSTART:20250415T190000Z
DTEND:20250415T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/84
DESCRIPTION:Title: Some finiteness results for the etale fundamental g
roup in positive characteristics\nby Vasudevan Srinivas (Tata and Univ
. of Buffalo) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture
held in Harvard Science Center 507.\n\nAbstract\nThis talk will discuss s
ome results 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 the tame fundamental group is finitely presented for such a variety w
hich 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 p
rojective variety to admit a lifting to characteristic 0\, in terms of the
structure of its etale fundamental group as a profinite group. We will fi
nally touch on some open questions.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/8
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sameera Vemulapalli (Harvard University)
DTSTART:20250218T200000Z
DTEND:20250218T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/85
DESCRIPTION:Title: Brill--Noether theory of smooth plane curves\nb
y Sameera Vemulapalli (Harvard University) as part of Harvard MIT Algebrai
c Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstr
act\nGiven a smooth curve C\, it is natural to ask: what are all the degre
e $d$ maps from $C$ into a projective space $\\mathbb{P}^r$? The study of
this question is called Brill-Noether theory. Given a curve $C$\, the data
of a degree d map $C \\rightarrow \\mathbb{P}^r$ is equivalent to the dat
a of a degree $d$ line bundle on $C$ together with a choice of $r + 1$ glo
bal sections having no common zeros. As such\, a central object of study i
s the Brill–Noether locus $W^r_d(C)$\, which is defined to be the space
of degree $d$ line bundles on $C$ with at least $r+1$ global sections.\n\n
The famous Brill-Noether theorem gives a nice description of $W^r_d(C)$ wh
en $C$ 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 B
rill-Noether theorem! In this talk\, I'll describe joint work with Hannah
Larson\, in which we describe the Brill-Noether theory of smooth plane cu
rves (and more generally\, curves on Hirzebruch surfaces)\, using tools fr
om arithmetic statistics.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/8
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Lehmann (Boston College)
DTSTART:20250325T190000Z
DTEND:20250325T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/86
DESCRIPTION:Title: Homological stability for rational curves on quarti
c del Pezzo surfaces\nby Brian Lehmann (Boston College) as part of Har
vard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Cen
ter 507.\n\nAbstract\nThe moduli space of rational curves on a Fano variet
y is expected to exhibit "motivic" stability. Both Manin's conjecture (ov
er a finite field) and the Cohen-Jones-Segal conjecture (over the complex
numbers) are instances of this meta-conjecture.\n\nI will discuss ongoing
joint work with Ronno Das\, Sho Tanimoto\, and Philip Tosteson in which we
prove versions of these two conjectures for degree 4 del Pezzo surfaces.
The proofs share a common method\, demonstrating the compatibility of the
se conjectures in this special case. Our work builds upon a new technique
developed previously by Das-Tosteson using additional arguments from alge
braic geometry\, topology\, and number theory.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/8
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Izzet Coskun (UIC)
DTSTART:20250422T190000Z
DTEND:20250422T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/87
DESCRIPTION:Title: Brill-Noether for moduli spaces of sheaves on surfa
ces\nby Izzet Coskun (UIC) as part of Harvard MIT Algebraic Geometry S
eminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nIn this
talk\, I will discuss recent work on Brill-Noether theory for moduli spac
es of sheaves on surfaces. I will first discuss the cohomology of the gene
ral stable sheaf on surfaces such as K3 and abelian surfaces. If time per
mits\, I will describe some recent results on the cohomology jumping loci.
This talk is based on joint work with Jack Huizenga\, Howard Nuer\, Neela
rnab Raha and Kota Yoshioka.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/8
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lei Wu (Zhejiang University)
DTSTART:20250429T190000Z
DTEND:20250429T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/88
DESCRIPTION:Title: Geometry of Bernstein-Sato ideals\nby Lei Wu (Z
hejiang University) as part of Harvard MIT Algebraic Geometry Seminar\n\nL
ecture held in Harvard Science Center 507.\n\nAbstract\nIn studying Mellin
transforms of multivariable polynomial functions\, Gelfand defined the so
-called Archimedean zeta function of a polynomial and conjectured that the
archimedean zeta function has a meromorphic continuation on the whole com
plex plane in 1950s. Bernstein introduced the so-called Bernstein-Sato pol
ynomial (or b-function) and solved the conjecture in the 1970s. In this ta
lk\, I will discuss how we can generalize the construction of Bernstein fo
r a finite union of polynomial functions by defining Bernstein-Sato ideals
following the ideas of Sabbah. Then I will discuss geometric properties o
f such ideals and prove that the variety of the Bernstein-Sato ideal is de
fined over Q and each of its irreducible components is a translated linear
subspace\, generalizing a classical result of Kashiwara for b-functions.\
n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/8
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ishan Levy (University of Copenhagen)
DTSTART:20250513T190000Z
DTEND:20250513T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/89
DESCRIPTION:Title: Hurwitz spaces and the asymptotic Picard rank conje
cture\nby Ishan Levy (University of Copenhagen) as part of Harvard MIT
Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center 507.
\n\nAbstract\nI will explain work joint with Aaron Landesman where we prov
e that for a finite group G and conjugacy invariant subset c\, Hurwitz spa
ces parameterizing connected G-covers of the complement of a configuration
of points on a disk with monodromy in c satisfy homological stability. We
use this to prove that the Hurwitz stack parameterizing simply branched d
egree d covers of P^1 with n branch points has trivial rational Picard gro
up when n is much larger than d.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/8
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ajith Urundolil Kumaran (MIT)
DTSTART:20250225T200000Z
DTEND:20250225T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/90
DESCRIPTION:Title: Refined tropical curve counting with descendants\nby Ajith Urundolil Kumaran (MIT) as part of Harvard MIT Algebraic Geome
try Seminar\n\nLecture held in MIT 2-131.\n\nAbstract\nWe introduce the en
umerative geometry of curves in the algebraic torus $(\\mathbb{C}^\\ast)^2
$. We show that a certain class of invariants associated with moduli space
s of curves in $(\\mathbb{C}^\\ast)^2$ can be calculated explicitly using
a refined tropical correspondence theorem. If time permits we will explain
how the proof relies on higher double ramification cycles and work of Bur
yak-Rossi on integrable systems on the moduli space of curves. This is joi
nt work with Patrick Kennedy-Hunt and Qaasim Shafi.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/9
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Jovinelly (Brown University)
DTSTART:20250311T190000Z
DTEND:20250311T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/91
DESCRIPTION:Title: Free Curves in Singular Varieties\nby Eric Jovi
nelly (Brown University) as part of Harvard MIT Algebraic Geometry Seminar
\n\nLecture held in MIT 2-131.\n\nAbstract\nRational curves are intricatel
y linked to the birational geometry of varieties containing them. Certain
curves\, called free curves\, have the nicest deformation properties. Ho
wever\, it is unknown whether mildly singular Fano varieties contain free
rational curves in their smooth locus. In this talk\, we discuss free cur
ves of higher genus. Using recent results about tangent bundles\, we prov
e that any klt Fano variety has higher genus free curves. We then use the
existence of such free curves to get some applications: we prove the exis
tence of free rational curves in terminal Fano threefolds\; obtain an opti
mal upper bound on the length of extremal rays in the Kleiman-Mori cone of
any klt pair\; and study the fundamental group of the smooth locus of a F
ano variety. This is joint work with Brian Lehmann and Eric Riedl.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/9
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Klingler (Humboldt Univ.)
DTSTART:20251111T200000Z
DTEND:20251111T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/92
DESCRIPTION:Title: Special loci for local systems\nby Bruno Klingl
er (Humboldt Univ.) as part of Harvard MIT Algebraic Geometry Seminar\n\nL
ecture held in Harvard Science Center 507.\n\nAbstract\nGiven a local syst
em on a complex algebraic variety\, what are the subvarieties on which the
monodromy drops? The talk will discuss these monodromy special loci\, a n
atural generalisation of (the positive period dimension components of) the
Hodge loci.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/9
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Bryan (University of British Columbia)
DTSTART:20250527T190000Z
DTEND:20250527T200000Z
DTSTAMP:20260404T095028Z
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 A
lgebraic Geometry Seminar\n\nLecture held in MIT 2-131.\n\nAbstract\nWe gi
ve a quiver description of the space of genus 0 parameterized maps to vari
ous Generalized Flag Varieties. In the 90s it was proven that for maps of
large degree\, these spaces are good homotopy approximations to the space
of all continuous maps — the double loops spaces that appear in the Bott
Periodicity theorem (both the 2-fold and 8-fold periodicity theorems). Ou
r quiver description recovers Bott Periodicity in the large rank and degre
e limit and can thus be regarded as a finite dimensional\, algebraic refin
ement of Bott Periodicity. This is joint work with Ravi Vakil.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/9
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Bakker (UIC)
DTSTART:20250505T190000Z
DTEND:20250505T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/95
DESCRIPTION:Title: The linear Shafarevich conjecture for quasiprojecti
ve varieties (part 1)\nby Ben Bakker (UIC) as part of Harvard MIT Alge
braic Geometry Seminar\n\nLecture held in MIT 2-449 (special date/time!).\
n\nAbstract\nShafarevich asked whether the universal cover of a smooth pro
jective variety X is always holomorphically convex\, meaning it admits a p
roper map to a Stein space. This was proven in the linear case---namely w
hen X admits an almost faithful representation of its fundamental group---
by Eyssidieux--Katzarkov--Pantev--Ramachandran using techniques from non-a
belian Hodge theory. In joint work with Y. Brunebarbe and J. Tsimerman\,
we prove a version of the linear Shafarevich conjecture for quasiprojectiv
e varieties. The proof relies on a number of recent advances in non-abeli
an Hodge theory in the non-proper case.\n\nIn the first talk I will outlin
e the general strategy and explain why non-abelian Hodge theory naturally
shows up in the context of Shafarevich's question. In the second talk I w
ill provide some details of the proof\, including the role played by the t
wistor geometry of the stack of local systems and the algebraic integrabil
ity of Katzarkov--Zuo foliations. As a bonus\, I will also explain how th
ese techniques prove the algebraicity of Shafarevich morphisms\, which gen
eralizes Griffiths' conjecture on the algebraicity of the images of period
maps to arbitrary local systems.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/9
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Hacon (University of Utah)
DTSTART:20251021T190000Z
DTEND:20251021T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/96
DESCRIPTION:Title: The cone theorem for Kähler varieties\nby Chri
stopher Hacon (University of Utah) as part of Harvard MIT Algebraic Geomet
ry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nThe
re has been substantial recent progress towards the minimal model program
for Kähler varieties. In this talk I will discuss a recent proof of the
Cone Theorem for Kähler varieties of arbitrary dimension and related resu
lts such as the canonical bundle formula\, subadjunction and Wenhao Ou's r
ecent breakthrough result on the characterization of uniruled compact Käh
ler manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/9
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Grushevsky (SUNY Stony Brook)
DTSTART:20250923T200000Z
DTEND:20250923T210000Z
DTSTAMP:20260404T095028Z
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
Geometry Seminar\n\nLecture held in MIT 2-131.\n\nAbstract\nWe present res
ults on the maximal dimension of compact subvarieties of the moduli space
of abelian varieties and of moduli of complex curves of compact type. Equi
valently\, this is the maximal dimension of a compact complex parameter sp
ace for a maximally varying family of abelian varieties/curves\, etc. Base
d on joint work with Mondello\, Salvati Manni\, Tsimerman.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/9
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debaditya Raychadhury (University of Arizona)
DTSTART:20250909T190000Z
DTEND:20250909T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/98
DESCRIPTION:Title: Singularities of secant varieties\nby Debaditya
Raychadhury (University of Arizona) as part of Harvard MIT Algebraic Geom
etry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nS
ecant varieties are classical objects in algebraic geometry. Given a smoot
h projective variety inside a projective space\, its secant variety is by
definition the closure of the union of secant lines. It is almost always s
ingular and sits inside the same projective space by its construction. In
this talk\, we will discuss the singularities of secant varieties when the
embedding is sufficiently positive. In particular\, we will study the Du
Bois complex of secant varieties and will also discuss about its local coh
omology modules. The results are obtained in various collaborations with Q
. Chen\, B. Dirks\, S. Olano and L. Song.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/9
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yongnam Lee (IBS-Center for Complex Geometry)
DTSTART:20250930T190000Z
DTEND:20250930T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/99
DESCRIPTION:Title: Compact moduli of elliptic surfaces with a multiple
fiber\nby Yongnam Lee (IBS-Center for Complex Geometry) as part of Ha
rvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Ce
nter 507.\n\nAbstract\nMotivated by Miranda and Ascher-Bejleri's works on
compactifications of the moduli space of rational elliptic surfaces with a
section\, we study constructions and boundaries of compact moduli spaces
of elliptic surfaces with a multiple fiber.\n\nIn a joint work with Donggu
n Lee\, we propose an approach to understanding the limit surfaces when a
multiple fiber degenerates into an additive type singular fiber\, via Q-Go
renstein smoothings of slc surfaces. And in ongoing work with Dori Bejler
i and Donggun Lee\, we study compact moduli spaces of the rational ellipti
c surfaces of index 2 and of Enriques surfaces with bisections using the t
heory of twisted stable maps.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/9
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyunsuk Kim (University of Michigan)
DTSTART:20250916T190000Z
DTEND:20250916T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/100
DESCRIPTION:Title: Hodge theory of toric singularities\nby Hyunsu
k Kim (University of Michigan) as part of Harvard MIT Algebraic Geometry S
eminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nA toric
variety is a normal variety containing an algebraic torus as an open dens
e subset whose action on itself extends to the whole space. They provide a
fruitful interplay between algebraic geometry and convex geometry since p
roperties on one side (e.g. smoothness\, compactness) can be translated in
to properties involving discrete objects (e.g. cones\, fans\, polytopes).
I will talk about singularities of these varieties from a Hodge theoretic
point of view\, with applications towards local cohomology and singular co
homology\, based on joint works with Sridhar Venkatesh.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
00/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruijie Yang (University of Kansas)
DTSTART:20251014T190000Z
DTEND:20251014T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/101
DESCRIPTION:Title: p-adic zeta function\, Hodge theory and hyperplane
arrangements\nby Ruijie Yang (University of Kansas) as part of Harvar
d MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center
507.\n\nAbstract\nIn 1988\, Igusa observed a mysterious relationship betw
een the poles of the p-adic zeta function and the roots of the Bernstein-S
ato polynomial. This relationship was later formulated precisely by Denef
and Loeser and is now known as the Strong Monodromy Conjecture. In the spe
cial case of hyperplane arrangements\, Budur\, Mustațǎ and Teitler propo
sed the n/d conjecture in 2009\, which asserts that if a polynomial define
s a central\, essential\, and indecomposable hyperplane arrangement of deg
ree d in C^n\, then -n/d must be a root of its b-function. They showed tha
t the n/d conjecture implies the Strong Monodromy Conjecture for hyperplan
e arrangements. \n\nIn this talk\, I will discuss my recent joint work wit
h Dougal Davis on a proof of the n/d conjecture\, which draws on the theor
y of complex mixed Hodge modules of Sabbah and Schnell\, as well as our ne
w ''wall-crossing'' theory for V-filtrations of holonomic D-modules along
local complete intersections. The latter is inspired by the recent breakth
rough by Davis-Vilonen on the Schmid-Vilonen conjecture\, which characteri
zes the unitarity of a representation of a real Lie group via Hodge theory
. Furthermore\, we also prove that the pole order of the Igusa zeta functi
on is less than or equal to the multiplicity of the b-function along the r
eal part 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://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
01/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Johnston (MIT)
DTSTART:20251104T210000Z
DTEND:20251104T220000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/102
DESCRIPTION:Title: Quantum periods\, toric degenerations and intrinsi
c mirror symmetry\nby Sam Johnston (MIT) as part of Harvard MIT Algebr
aic Geometry Seminar\n\nLecture held in MIT 2-131.\n\nAbstract\nMirror sym
metry for Fano varieties predicts a relation between the enumerative geome
try of a Fano variety Y and the complex geometry of a Landau-Ginzburg mode
l\, realized as a pair (X\,W) with X a quasi-projective variety and W a re
gular function 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 rec
ent work which shows how the intrinsic mirror construction of Gross and Si
ebert naturally produce LG models associated to a pair (Y\,D)\, assuming m
ilder conditions on the singularities of D than typically required for the
intrinsic mirror construction. In particular\, we show that classical per
iods of this LG model recover the quantum periods of Y\, and that these pe
riods are 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 na
turally give rise to Laurent polynomial mirrors and corresponding toric de
generations. As an example\, we consider Y = Gr(n-k\,n)\, D a particular c
hoice of anticanonical divisor with affine cluster variety complement and
give an explicit description of the intrinsic LG model in terms of Plücke
r coordinates on Gr(k\,n)\, recovering mirrors constructed and investigate
d by Marsh-Rietsch and Rietsch-Williams.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
02/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Svaldi (Università degli Studi di Milano)
DTSTART:20251007T190000Z
DTEND:20251007T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/103
DESCRIPTION:Title: Boundedness theorems for fibered varieties with tr
ivial canonical bundle\nby Roberto Svaldi (Università degli Studi di
Milano) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held
in Harvard Science Center 507.\n\nAbstract\nI will explain ideas and techn
iques behind recent new results showing that several classes of fibered va
rieties with trivial canonical bundle are bounded\, that is\, they are par
ametrised by finitely many families of deformations.\nNamely\, I will show
how abelian or K3 fibered Calabi—Yau varieties are bounded\, up to simp
le birational equivalences\, in the algebraic category\, and how the same
results holds in the analytic category for Lagrangian holomorphic symplect
ic varieties.\nThis is joint work with Engel\, Filipazzi\, Greer\, Mauri.\
n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
03/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Thimm (UBC)
DTSTART:20251202T210000Z
DTEND:20251202T220000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/105
DESCRIPTION:Title: Wall-Crossing and the DT/PT3 Descendant Correspond
ence\nby Felix Thimm (UBC) as part of Harvard MIT Algebraic Geometry S
eminar\n\nLecture held in MIT 2-131.\n\nAbstract\nDonaldson–Thomas and P
andharipande–Thomas invariants are two ways of counting curves in Calabi
-Yau 3-folds\, related by a change of stability conditions. Wall-crossing
is a technique that allows us to compare enumerative invariants under such
a change in stability condition. It has emerged as a powerful tool for co
mputations and in the study of properties of generating series of various
types of enumerative invariants. I will present joint work with N. Kuhn an
d H. Liu on how to use localization of virtual classes to wall-cross more
general invariants with descendant insertions. In the process I will expla
in how Juanolou's trick from more classical algebraic geometry comes in as
a useful and central ingredient.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
05/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daebeom Choi (UPenn)
DTSTART:20251216T210000Z
DTEND:20251216T220000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/106
DESCRIPTION:Title: Extremal effective curves and non-semiample line b
undles on $M_{g\,n}$\nby Daebeom Choi (UPenn) as part of Harvard MIT A
lgebraic Geometry Seminar\n\nLecture held in MIT 2-449 (Special room).\n\n
Abstract\nIn this work\, we develop a new method for establishing extremal
ity in the closed cone of curves on the moduli space of curves and determi
ne the extremality of many boundary 1-strata. As a consequence\, by using
a general criterion for non-semiampleness that extends Keel’s argument\,
we demonstrate that a substantial portion of the cone of nef divisors on
$M_{g\,n}$ is not semiample. As an application\, we construct the first ex
plicit example of a non-contractible extremal ray of the closed cone of ef
fective curves on $M_{3\,n}$. Moreover\, we show that this extremal ray is
contractible in characteristic $p$. Our method relies on two main ingredi
ents: (1) the construction of a new collection of nef divisors on $M_{g\,n
}$\, and (2) the identification of a tractable inductive structure on the
Picard group\, arising from Knudsen’s construction of $M_{g\,n}$.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
06/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Cela (Cambridge)
DTSTART:20251209T210000Z
DTEND:20251209T220000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/107
DESCRIPTION:Title: Brill–Noether Theory for (toric) Surfaces and Co
mplete Quasimaps to Blow-ups of Projective spaces\nby Alessio Cela (Ca
mbridge) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held
in MIT 2-131.\n\nAbstract\nThe classical Brill–Noether theorem states t
hat every nondegenerate degree d map from a general curve C of genus g t
o projective space is a point of expected dimension in the moduli space of
such maps. In this talk\, I will present an analogous statement for maps
from C to smooth projective toric surfaces. I will then discuss the const
ruction of the space of complete quasimaps to Bl_{P^s}^r\, obtained as a s
uitable blow-up of the quasimap space of Ciocan-Fontanine–Kim–Maulik.
This space provides an expected-dimension compactification of the moduli s
pace of maps\, in a fixed curve class\, from C to X. Conjecturally\, the
insertion of tautological subschemes corresponding to geometric insertions
is transverse\, lies in the locus of nondegenerate maps\, and preserves t
he expected dimension. Using the Brill–Noether result for toric surfaces
mentioned above\, the conjecture is verified in dimension 2.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
07/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannik Schuler (ETH)
DTSTART:20251028T200000Z
DTEND:20251028T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/108
DESCRIPTION:Title: Stable maps to Calabi–Yau fivefolds\nby Yann
ik Schuler (ETH) as part of Harvard MIT Algebraic Geometry Seminar\n\nLect
ure held in MIT 2-131.\n\nAbstract\nGromov–Witten invariants enumerate c
urves in a variety X via stable maps. However\, degenerate contributions l
ead to substantial overcounting which makes these invariants far from opti
mal. When X is a Calabi–Yau threefold\, a set of more fundamental curve
counting invariants is provided by Gopakumar–Vafa invariants. I will pro
pose a conjectural generalisation of this correspondence between Gromov–
Witten and Gopakumar–Vafa invariants to the setting of Calabi–Yau five
folds equipped with a torus action. I will demonstrate the conjecture in t
he setting of local curves. For a special type of torus action we will pro
ve a closed-form formula for the local contribution of a smooth embedded c
urve and for general torus actions the validity of the formula will be tra
nslated into a conjectural formula for certain tautological integrals over
the moduli of curves.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
08/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siddharth Kannan (MIT)
DTSTART:20251118T210000Z
DTEND:20251118T220000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/109
DESCRIPTION:Title: Radially aligned stable curves and applications\nby Siddharth Kannan (MIT) as part of Harvard MIT Algebraic Geometry Sem
inar\n\nLecture held in MIT 2-131.\n\nAbstract\nI will discuss a combinato
rially defined blow-up of the moduli space of curves in genus g <= 1 and t
hen describe two applications of this construction. The first application
is more combinatorial: a modular understanding of the blow-up leads to a c
alculation scheme for the S_n-representations defined by the Chow ring of
the braid matroid. The second application is more geometric: a combinatori
al understanding of the boundary complex of the blow-up leads to a calcula
tion of the weight zero subspace of the compactly-supported cohomology of
the moduli 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://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
09/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soham Karwa (Duke University)
DTSTART:20260317T190000Z
DTEND:20260317T200000Z
DTSTAMP:20260404T095028Z
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\nLe
cture held in MIT 2-132.\n\nAbstract\nGiven an algebraic variety X\, one c
an associate a non-archimedean analytic space X^an called its analytificat
ion. Whilst X^an can be very complicated\, there exists a canonical combin
atorial subspace\, called\, the essential skeleton. The skeleton has the s
tructure of an integral affine manifold with singularities and is a combin
atorial shadow of X which retains a lot of geometric information about X.\
n\nIn this talk\, we’ll consider an enhancement of an integral affine st
ructure on the skeleton\, called a K-affine structure\, which captures ana
lytic information about X not seen by the integral affine structure. In p
articular\, we’ll see how the K-affine structure recovers the periods fo
r log Calabi-Yau surfaces\, verifying a conjecture of Kontsevich-Soibelman
. Time permitting\, we’ll also discuss work in progress on how the K-aff
ine structure gives the essential skeleton of a Mumford curve the structur
e of a ringed space and the relation between line bundles on the curve\, t
he skeleton and tropical line bundles.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Petersen (Stockholm University and IAS)
DTSTART:20260505T190000Z
DTEND:20260505T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/111
DESCRIPTION:by Dan Petersen (Stockholm University and IAS) as part of Harv
ard MIT Algebraic Geometry Seminar\n\nLecture held in MIT 2-131.\nAbstract
: TBA\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Mullane (University of Melbourne)
DTSTART:20260224T200000Z
DTEND:20260224T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/112
DESCRIPTION:Title: Isoresidual fibrations and the moduli space of poi
nted rational curves\nby Scott Mullane (University of Melbourne) as pa
rt of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Sc
ience Center 507.\n\nAbstract\nAfter surveying the results of the last 20
years on the structure of effective divisors on $\\overline{M}_{0\,n}$\, w
e show that the pseudo-effective cone of divisors is not polyhedral for $n
\\geq8$. Using ideas from Teichmüller dynamics and birational geometry\,
we construct an extremal non-polyhedral ray of the dual cone of moving cur
ves using residue maps of strata of meromorphic differentials.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sung Gi Park (Princeton Univ.)
DTSTART:20260127T200000Z
DTEND:20260127T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/113
DESCRIPTION:Title: From GIT to Baily-Borel: Moduli of hypersurfaces v
ia minimal exponents\nby Sung Gi Park (Princeton Univ.) as part of Har
vard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Cen
ter 507.\n\nAbstract\nThe moduli space of smooth hypersurfaces in projecti
ve space can be constructed as a GIT quotient by linear changes of coordin
ates\, and it comes with a natural GIT compactification. In certain degree
s and dimensions\, Hodge theory provides a second compactification via the
period map\, namely the Baily-Borel compactification. Building on recent
progress on higher singularities and a new stability criterion formulated
in terms of the minimal exponent (a refinement of the log canonical thresh
old)\, I will discuss the birational geometry of these two compactificatio
ns and describe consequences for the boundary behavior of the period map.\
n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanlin Cai (Columbia University)
DTSTART:20260407T190000Z
DTEND:20260407T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/116
DESCRIPTION:Title: Perturbation of mixed characteristics test ideals<
/a>\nby Hanlin Cai (Columbia University) as part of Harvard MIT Algebraic
Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstrac
t\nGiven a normal integral scheme of finite type over a mixed characterist
ic complete DVR or a perfect field of characteristic p\, one can define th
e notion of a test ideal. This sheaf is used to characterize a class of mi
ld singularities known as splinter singularities\, which are analogous to
rational singularities in characteristic 0. In equal characteristics\, it
is a well-known result that test and multiplier ideals are stable under sm
all perturbations. In this talk\, I will explain how to extend this stabil
ity result to the mixed characteristic setting and discuss some of its app
lications. Time permitting\, I will also outline the key ideas and tools f
rom p-adic geometry that underlie the proof.This is based on joint work in
progress with Bhargav Bhatt and Linquan Ma.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denis Nesterov (ETH Zurich)
DTSTART:20260203T200000Z
DTEND:20260203T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/117
DESCRIPTION:Title: Hilbert schemes of points and Fulton-MacPherson co
mpactifications\nby Denis Nesterov (ETH Zurich) as part of Harvard MIT
Algebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nThe
two spaces appearing in the title provide distinct compactifications of u
nordered configuration spaces of points on a complex variety. I will descr
ibe several ways in which they are related. In particular\, in dimension t
wo\, I will explain how the latter can be used to prove the Hilbert-Chow c
repant resolution conjecture\, proposed by Ruan\, which asserts an isomorp
hism between the quantum cohomology of Hilbert schemes and the orbifold co
homology of symmetric products.\n\n\nNote:\nDenis Nesterov will give speci
al talks on Friday January 30 and Monday February 2\, 1:30pm-3pm in MIT 2-
449. The title and abstract for those talks is as follows:\n\nTitle: Wall-
crossing for spaces of maps \n\nAbstract:\nI will discuss a wall-crossing
phenomenon for spaces of maps from curves to a target variety\, from both
conceptual 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 formul
a for the class of hyperelliptic curves. In dimension two\, it helps compu
te Torelli pullbacks of certain classes from moduli spaces of principally
polarised abelian varieties. In dimension three\, it provides a constructi
on of Gopakumar-Vafa invariants in terms of unramified maps for Fano and p
rimitive Calabi-Yau classes.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weite Pi (Bonn University)
DTSTART:20260210T200000Z
DTEND:20260210T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/118
DESCRIPTION:Title: "Perverse = Chern" and χ-independence phenomena f
or moduli of 1-dimensional sheaves\nby Weite Pi (Bonn University) as p
art of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in MIT 2-132
.\n\nAbstract\nWe discuss the geometry and cohomology of Le Potier’s mod
uli space of 1-dimensional sheaves on the projective plane. We focus on tw
o aspects: first\, the "P=C" conjecture relating two filtrations of highly
different nature on cohomology\, which can be viewed as a del Pezzo analo
g of the celebrated P=W conjecture\; second\, the so-called χ-independenc
e phenomenon\, which stems from enumerative geometry and predicts surprisi
ng consequences on the cohomology of the moduli space. After surveying kno
wn results\, I will explain how these two aspects are linked via an “ass
ociated graded” χ-independence conjecture. Based on joint work with Yak
ov Kononov\, Woonam Lim\, and Miguel Moreira.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Woonam Lim (Yonsei University)
DTSTART:20260210T211000Z
DTEND:20260210T221000Z
DTSTAMP:20260404T095028Z
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 S
eminar\n\nLecture held in MIT 2-132.\n\nAbstract\nThe study of classical i
nstantons on spacetime has led to many interesting developments in mathema
tics. In a series of papers\, Nekrasov introduced the generalized ADHM equ
ations\, whose solutions are instantons on the “origami spacetime.” In
this talk\, I will explain how to interpret gauge origami via DT4 theory.
The main result shows that Nekrasov’s origami partition function\, defi
ned by local contributions\, coincides with a global definition via Oh–T
homas classes in DT4 theory. This global definition is crucial for derivin
g the Dyson–Schwinger equation\, which was one of Nekrasov’s main moti
vations for introducing gauge origami theory. I will also briefly discuss
a conjectural sheaf-theoretic description of gauge origami. This is joint
work with N. Arbesfeld and M. Kool.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raluca Vlad (Brown University)
DTSTART:20260303T200000Z
DTEND:20260303T210000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/120
DESCRIPTION:Title: Tropicalizations of locally symmetric varieties\nby Raluca Vlad (Brown University) as part of Harvard MIT Algebraic Geom
etry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nA
locally symmetric variety is a non-compact complex algebraic variety obta
ined as the quotient of a Hermitian symmetric domain by the action of an a
rithmetic group. I will start by reviewing the theory of toroidal compacti
fications of these varieties\, originally due to Ash-Mumford-Rapoport-Tai.
Building on this construction\, we define the tropicalization of a locall
y symmetric variety to be a combinatorial object encoding the boundary str
ata of a toroidal compactification of the variety. I will discuss applicat
ions of this theory to the cohomology of moduli spaces and arithmetic grou
ps\, with an emphasis on the case of moduli of abelian varieties and gener
al linear groups. Based on joint work with Assaf\, Brandt\, Bruce\, and Ch
an.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Bertram (University of Utah)
DTSTART:20260324T190000Z
DTEND:20260324T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/122
DESCRIPTION:Title: A modest extension of Reider's Theorem on ample di
visors 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 studyin
g classical problems about algebraic surfaces. \nFor example\, a wall-cros
sing argument for moduli of derived objects was used by Arend Bayer to \ng
ive a new proof of Lazarsfeld's theorem on the Brill-Noether generality of
curves on a K3 surface with Picard \nnumber one. This was recently extend
ed by Farkas\, 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 those of Reider's theorem to obtain \ninformation about the equations t
hat cut out the surface. This is joint work with my students Jonathon Flec
k\, Liebo Pan and \nJoseph Sullivan.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uriya First (University of Haifa and MIT)
DTSTART:20260310T190000Z
DTEND:20260310T200000Z
DTSTAMP:20260404T095028Z
UID:harvard-mit-ag-seminar/123
DESCRIPTION:Title: Number of generators: an algebraic-geometry approa
ch\nby Uriya First (University of Haifa and MIT) as part of Harvard MI
T Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center 507
.\n\nAbstract\nThe Primitive Element Theorem says that a separable field e
xtension is generated by one element\, and a well-known folklore result sa
ys that a central simple algebra (CSA) is generated by two elements over i
ts center.\nThe globalization of separable field extensions and CSAs are f
inite etale algebras and Azumaya algebras\, respectively\, and so one coul
d ask if something could be said about their number of generators if the b
ase scheme has dimension at most d. The same question can be asked for vec
tor bundles and other types of algebra bundles. I will discuss some recent
works with Reichstein\, Williams and others where we study this question
by turning it into a geometric question\, thus finding both upper bounds a
nd examples requiring arbitrarily many generators. For example\, if X is a
d-dimensional affine algebraic scheme over an infinite field\, then any f
inite etale algebra over X can be generated by d+1 elements\, and this can
not be improved in general.\n
LOCATION:https://stable.researchseminars.org/talk/harvard-mit-ag-seminar/1
23/
END:VEVENT
END:VCALENDAR