BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Juliette Bruce (Brown University)
DTSTART;VALUE=DATE-TIME:20221129T200000Z
DTEND;VALUE=DATE-TIME:20221129T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/1
DESCRIPTION:Title: Top weight cohomology of A_g\nby Juliette Bruce (Brown
University) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture h
eld in Harvard Science Center 507.\n\nAbstract\nI will discuss recent work
calculating the top weight cohomology of the moduli space A_g of principa
lly polarized abelian varieties of dimension g for small values of g. The
key idea is that this piece of cohomology is encoded combinatorially via t
he relationship between the boundary complex of a compactification of A_g
and the moduli space of tropical abelian varieties. This is joint work wit
h Madeline Brandt\, Melody Chan\, Margarida Melo\, Gwyneth Moreland\, and
Corey Wolfe.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tasuki Kinjo (University of Tokyo)
DTSTART;VALUE=DATE-TIME:20221206T213000Z
DTEND;VALUE=DATE-TIME:20221206T223000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/2
DESCRIPTION:Title: Cohomological Donaldson-Thomas theory for 2-Calabi--Yau cat
egories\nby Tasuki Kinjo (University of Tokyo) as part of Harvard MIT
Algebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nCoho
mological Donaldson-Thomas (CoDT) invariants were introduced by Kontsevich
-Soibelman and Brav-Bussi-Dupont-Joyce-Szendroi as categorifications of th
e Donaldson-Thomas invariants counting objects in 3-Calabi-Yau categories.
In this talk\, I will explain applications of the CoDT theory to the coho
mological study of the moduli of objects in 2-Calabi-Yau categories. Among
other things\, I will construct a coproduct on the Borel-Moore homology o
f the moduli stack of objects in these categories and establish a PBW-type
statement for the Kapranov-Vasserot cohomological Hall algebras. This tal
k is based on a joint work in progress with Ben Davison.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Padmavathi Srinivasan (ICERM)
DTSTART;VALUE=DATE-TIME:20230418T190000Z
DTEND;VALUE=DATE-TIME:20230418T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/3
DESCRIPTION:Title: A canonical algebraic cycle associated to a curve in its Ja
cobian\nby Padmavathi Srinivasan (ICERM) as part of Harvard MIT Algebr
aic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbs
tract\nWe will talk about the Ceresa class\, which is the image under a cy
cle class map of a canonical homologically trivial algebraic cycle associa
ted to a curve in its Jacobian. In his 1983 thesis\, Ceresa showed that th
e generic curve of genus at least 3 has nonvanishing Ceresa cycle modulo a
lgebraic equivalence. Strategies for proving Fermat curves have infinite o
rder Ceresa cycles due to B. Harris\, Bloch\, Bertolini-Darmon-Prasanna\,
Eskandari-Murty use a variety of ideas ranging from computation of explici
t iterated period integrals\, special values of p-adic L functions and poi
nts of infinite order on the Jacobian of Fermat curves. In fact\, Bloch's
results about the Ceresa cycle of Fermat quartics provided the first concr
ete evidence for the generalization of the BSD conjecture to the Bloch-Bei
linson conjectures.\n\nWe will survey several recent results about the Cer
esa cycle and the Ceresa class. The Ceresa class vanishes for all hyperell
iptic curves and was expected to be nonvanishing for non-hyperelliptic cur
ves. We will present joint work with Dean Bisogno\, Wanlin Li and Daniel L
itt\, where we construct a non-hyperelliptic genus 3 quotient of the Frick
e--Macbeath curve with torsion Ceresa class\, using the character theory o
f the automorphism group of the curve\, namely\, PSL2(F8).\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi Lombardi (University of Milan)
DTSTART;VALUE=DATE-TIME:20230131T200000Z
DTEND;VALUE=DATE-TIME:20230131T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/4
DESCRIPTION:Title: On the invariance of Hodge numbers under derived equivalenc
e\nby Luigi Lombardi (University of Milan) as part of Harvard MIT Alge
braic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nA
bstract\nA conjecture of Orlov predicts the invariance of the Hodge number
s of a smooth projective complex variety under derived equivalence. For in
stance this has been verified in the case of varieties of general type. In
this talk\, I will examine the case of varieties that are fibered by vari
eties of general type through the Albanese map. For this class of varietie
s I will prove the derived invariance of Hodge numbers of type $h^{0\,p}$\
, together with a few other invariants arising from the Albanese map. This
talk is based on a joint work with F. Caucci and G. Pareschi.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Küronya (Goethe-Universität Frankfurt)
DTSTART;VALUE=DATE-TIME:20230214T200000Z
DTEND;VALUE=DATE-TIME:20230214T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/5
DESCRIPTION:Title: Newton-Okounkov bodies and local positivity\nby Alex K
üronya (Goethe-Universität Frankfurt) as part of Harvard MIT Algebraic G
eometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract
\nThe purpose of this talk is to discuss Newton-Okounkov bodies\, \na conv
ex geometric construction associated to divisors on projective \nvarieties
. We will touch on their relationship with local positivity\, \nmultiplica
tive filtrations on section rings\, and applications.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Marian (Northeastern University)
DTSTART;VALUE=DATE-TIME:20221206T200000Z
DTEND;VALUE=DATE-TIME:20221206T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/6
DESCRIPTION:Title: On quot schemes of rank zero quotients over a curve\nby
Alina Marian (Northeastern University) as part of Harvard MIT Algebraic G
eometry Seminar\n\nLecture held in MIT 2-132.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samir Canning (ETH Zurich)
DTSTART;VALUE=DATE-TIME:20221212T200000Z
DTEND;VALUE=DATE-TIME:20221212T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/7
DESCRIPTION:Title: The Chow ring of the moduli space of degree 2 K3 surfaces\nby Samir Canning (ETH Zurich) as part of Harvard MIT Algebraic Geometr
y Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nThe
intersection theory of the moduli space of K3 surfaces polarized by a latt
ice is a subject of recent interest because of its deep connections with a
wide variety of mathematics\, including the intersection theory of moduli
spaces of curves and the study of modular forms. Oprea and Pandharipande
conjectured that the tautological rings of these moduli spaces of K3 surfa
ces are highly structured in a way that mirrors the picture for the moduli
space of curves. I will discuss the proof of this conjecture in the case
of K3 surfaces polarized by a degree 2 line bundle. This is joint work wit
h Dragos Oprea and Rahul Pandharipande.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sung Gi Park (Harvard University)
DTSTART;VALUE=DATE-TIME:20230207T200000Z
DTEND;VALUE=DATE-TIME:20230207T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/8
DESCRIPTION:Title: Kodaira dimension and hyperbolicity for smooth families of
varieties\nby Sung Gi Park (Harvard University) as part of Harvard MIT
Algebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nIn
this talk\, I will discuss the behavior of positivity\, hyperbolicity\, an
d Kodaira dimension under smooth morphisms of complex quasi-projective man
ifolds. This includes a vast generalization of a classical result: a fibra
tion from a projective surface of non-negative Kodaira dimension to a proj
ective line has at least three singular fibers. Furthermore\, I will expla
in a proof of Popa's conjecture on the superadditivity of the log Kodaira
dimension over bases of dimension at most three. These theorems are applic
ations of the main technical result\, namely the logarithmic base change t
heorem.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Hotchkiss (University of Michigan)
DTSTART;VALUE=DATE-TIME:20230221T200000Z
DTEND;VALUE=DATE-TIME:20230221T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/9
DESCRIPTION:Title: The period-index problem over the complex numbers\nby J
ames Hotchkiss (University of Michigan) as part of Harvard MIT Algebraic G
eometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract
\nThe period-index problem is a longstanding question about the complexity
of Brauer classes over a field. I will discuss some Hodge-theoretic aspec
ts of the problem for complex function fields\, and give some applications
to Brauer groups and the integral Hodge conjecture.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asher Auel (Dartmouth)
DTSTART;VALUE=DATE-TIME:20230228T200000Z
DTEND;VALUE=DATE-TIME:20230228T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/10
DESCRIPTION:Title: Maximal Brill-Noether loci\nby Asher Auel (Dartmouth)
as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Harva
rd Science Center 507.\n\nAbstract\nBrill-Noether theory answers the quest
ion of whether a general curve of genus $g$ admits $g^r_d$\, a linear syst
em of rank $r$ and degree $d$. A refined Brill-Noether theory hopes to an
swer the question of whether a "general curve with a $g^r_d$" admits a $g^
{r'}_{d'}$. In other words\, we want to know about the relative position
between Brill-Noether loci in the moduli space of curves of genus $g$. I'
ll explain a strategy for distinguishing Brill-Noether loci by studying th
e lifting of linear systems on curves in polarized K3 surfaces\, which mot
ivates a conjecture identifying the maximal Brill-Noether loci with respec
t to containment. Via an analysis of the stability of Lazarsfeld-Mukai bun
dles\, we obtain new lifting results for linear systems of rank 3 which su
ffice to prove the maximal Brill-Noether loci conjecture in genus 9-19\, 2
2\, and 23. This is joint work with Richard Haburcak.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Lacini (University of Kansas)
DTSTART;VALUE=DATE-TIME:20230307T200000Z
DTEND;VALUE=DATE-TIME:20230307T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/11
DESCRIPTION:Title: Syzygies of adjoint linear series on projective varieties<
/a>\nby Justin Lacini (University of Kansas) as part of Harvard MIT Algebr
aic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbs
tract\nSyzygies of algebraic varieties have long been a topic of intense i
nterest among algebraists and geometers alike. Starting with the pioneerin
g work of Mark Green on curves\, numerous attempts have been made to exten
d these results to higher dimensions. Ein and Lazarsfeld proved that if A
is a very ample line bundle\, then K_X + mA satisfies property N_p for any
m>=n+1+p. It has ever since been an open question if the same holds true
for A ample and basepoint free. In joint work with Purnaprajna Bangere we
give a positive answer to this question.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomer Schlank (MIT)
DTSTART;VALUE=DATE-TIME:20230314T190000Z
DTEND;VALUE=DATE-TIME:20230314T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/12
DESCRIPTION:Title: Higher Tsen Theorem\nby Tomer Schlank (MIT) as part of
Harvard MIT Algebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nA
bstract\nTsen's Theorem gives a simple sufficient criterion for an algebr
aic variety to have a point over a complex function field.\nIn the talk we
shall discuss a way to define on the collection of such points a structur
e of a stack and show that this stack is homologically contractible.\nWe s
hall explain a variant of this phenomenon that can be employed for the stu
dy of Beilinson-Drinfeld Opers for reductive groups.\nThis is joint work w
ith D. Beraldo and D. Kazhdan.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (Yale University)
DTSTART;VALUE=DATE-TIME:20230321T190000Z
DTEND;VALUE=DATE-TIME:20230321T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/13
DESCRIPTION:Title: Non-abelian Hodge theory and the P=W conjecture\nby Ju
nliang Shen (Yale University) as part of Harvard MIT Algebraic Geometry Se
minar\n\nLecture held in MIT 2-132.\n\nAbstract\nIn the first part of my t
alk\, I will introduce the P=W conjecture by de Cataldo\, Hausel\, and Mig
liorini (2010)\, predicting that the perverse filtration associated with t
he Hitchin system is identified with the weight filtration associated with
the corresponding character variety\, via non-abelian Hodge theory. Then
I will discuss a proof of the conjecture in joint work with Davesh Maulik\
, where we combine some ideas from enumerative geometry and representation
theory.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melody Chan (Brown University)
DTSTART;VALUE=DATE-TIME:20230328T190000Z
DTEND;VALUE=DATE-TIME:20230328T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/14
DESCRIPTION:Title: The weight 0 compactly supported Euler characteristic of m
oduli spaces of marked hyperelliptic curves\nby Melody Chan (Brown Uni
versity) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held
in Harvard Science Center 507.\n\nAbstract\nJoint work with Madeline Bran
dt and Siddarth Kannan. We use moduli\nspaces of G-admissible covers and
tropical geometry to give a\nsum-over-graphs formula for the weight-0 comp
actly supported Euler\ncharacteristic of the moduli spaces H_{g\,n} of n-m
arked hyperelliptic\ncurves of genus g\, as a virtual representation of S_
n. Computer\ncalculations then enable fully explicit formulas for the abo
ve in\nsmall genus. My aim is to make this talk accessible to anyone with
\npassing familiarity with M_g and its Deligne-Mumford compactification.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gavril Farkas (Humboldt University Berlin)
DTSTART;VALUE=DATE-TIME:20230404T190000Z
DTEND;VALUE=DATE-TIME:20230404T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/15
DESCRIPTION:Title: Resonance and Koszul modules in algebraic geometry\nby
Gavril Farkas (Humboldt University Berlin) as part of Harvard MIT Algebra
ic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbst
ract\nInspired from ideas in topology\, Koszul modules and the associated
resonance varieties turned out to have important algebro-geometric applica
tions for instance to (i) Green's Conjecture on syzygies of canonical curv
es\, (ii) stabilization of cohomology of projective varieties in arbitrary
characteristics and (iii) Chen invariants of hyperplane arrangements. I w
ill discuss new developments related to this circle of ideas obtained in j
oint work with Aprodu\, Raicu and Suciu.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Collins (MIT)
DTSTART;VALUE=DATE-TIME:20230411T190000Z
DTEND;VALUE=DATE-TIME:20230411T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/16
DESCRIPTION:Title: Mirror symmetry\, stability conditions and geometric invar
iant theory\nby Tristan Collins (MIT) as part of Harvard MIT Algebraic
Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nBridgeland st
ability conditions were originally motivated by the concept of Pi stabilit
y in theoretical physics\, as introduced in work of M. Douglas. Pi stabil
ity is an attempt to describe BPS states in string theory compactification
s. Alternatively\, BPS states in string theory can often be described by
solutions of certain nonlinear partial differential equations. In this ta
lk I will explain how\, starting from nonlinear PDEs\, ideas in GIT lead t
o a version of algebraic stability which is similar to Bridgeland stabilit
y. In particular\, I will explain how in several examples in dimension 2\
, GIT stability for line bundles implies Bridgeland stability\, but not co
nversely. In particular\, this yields effective tests for Bridgeland stab
ility in many examples.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dawei Chen (Boston College)
DTSTART;VALUE=DATE-TIME:20230425T190000Z
DTEND;VALUE=DATE-TIME:20230425T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/17
DESCRIPTION:Title: Counting differentials with fixed residues\nby Dawei C
hen (Boston College) as part of Harvard MIT Algebraic Geometry Seminar\n\n
Lecture held in Harvard Science Center 507.\n\nAbstract\nIn this talk\, we
investigate meromorphic differentials on the Riemann sphere with a single
zero and several poles of predetermined orders. Our aim is to determine t
he number of such differentials that satisfy the condition where the resid
ue at each pole is fixed. This question was previously explored by Gendron
and Tahar\, who employed graph counting techniques derived from the flat
geometry of differentials. We introduce a new approach using intersection
theory on moduli spaces of differentials. This is joint work with Miguel P
rado Godoy.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastian Casalaina-Martin (University of Colorado)
DTSTART;VALUE=DATE-TIME:20230502T190000Z
DTEND;VALUE=DATE-TIME:20230502T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/18
DESCRIPTION:Title: Moduli spaces of cubic hypersurfaces\nby Sebastian Cas
alaina-Martin (University of Colorado) as part of Harvard MIT Algebraic Ge
ometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\
nIn this talk I will give an overview of some recent work\, joint with Sam
uel Grushevsky\, Klaus Hulek\, and Radu Laza\, on the geometry and topolog
y of compactifications of the moduli spaces of cubic threefolds and cubic
surfaces. A focus of the talk will be on some results regarding non-isomor
phic smooth compactifications of the moduli space of cubic surfaces\, show
ing that two natural desingularizations of the moduli space have the same
cohomology\, and are both blow-ups of the moduli space at the same point\,
but are nevertheless\, not isomorphic\, and in fact\, not even K-equivale
nt.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Bitoun (University of Calgary)
DTSTART;VALUE=DATE-TIME:20230509T190000Z
DTEND;VALUE=DATE-TIME:20230509T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/19
DESCRIPTION:Title: On the D-module of an isolated singularity.\nby Thomas
Bitoun (University of Calgary) as part of Harvard MIT Algebraic Geometry
Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nLet Z be the germ of a
complex hypersurface isolated singularity of equation f. We consider the f
amily of analytic D-modules generated by the powers of 1/f and relate it t
o the pole order filtration on the de Rham cohomology of the complement of
\\{f=0\\}. This work builds on Vilonen’s characterization of the inters
ection homology D-module.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No seminar
DTSTART;VALUE=DATE-TIME:20230516T190000Z
DTEND;VALUE=DATE-TIME:20230516T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/20
DESCRIPTION:by No seminar as part of Harvard MIT Algebraic Geometry Semina
r\n\nLecture held in Harvard Science Center 507 or MIT 2-132.\nAbstract: T
BA\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Schnell (SUNY Stony Brook)
DTSTART;VALUE=DATE-TIME:20230315T190000Z
DTEND;VALUE=DATE-TIME:20230315T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/21
DESCRIPTION:Title: Hodge theory and Lagrangian fibrations (special time/locat
ion: 2-255)\nby Christian Schnell (SUNY Stony Brook) as part of Harva
rd MIT Algebraic Geometry Seminar\n\nLecture held in special location: 2-
255.\n\nAbstract\nThis is a talk about Lagrangian fibrations on holomorphi
c symplectic manifolds\, for example the Hitchin fibration (on the moduli
space of Higgs bundles over a curve). The general fiber of such a Lagrangi
an fibration is an abelian variety\, but the singular fibers are rather my
sterious. There were several beautiful conjectures about the Hodge theory
of Lagrangian fibrations\, proposed by Junliang Shen\, Qizheng Yin\, and D
avesh Maulik. I will try to introduce the conjectures and give an idea of
the proof.\n\nThis talk will be in 2-255 at MIT.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Tholozan (École Normale Supérieure)
DTSTART;VALUE=DATE-TIME:20230523T190000Z
DTEND;VALUE=DATE-TIME:20230523T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/22
DESCRIPTION:Title: Complex variations of Hodge structures of rank 2 over curv
es\nby Nicolas Tholozan (École Normale Supérieure) as part of Harvar
d MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center
507.\n\nAbstract\nThrough the work of Simpson\, complex variations of hod
ge structures (C-VHS) play a central role in the study of the moduli space
of local systems over a complex algebraic variety. In this talk I will co
nsider one of the simplest examples\, namely C-VHS of rank 2 over curves.
These objects are known to hyperbolic geometers as « branched hyperbolic
surfaces ».\n\nI will review what is known about their monodromy\, and di
scuss in particular a joint result with Bertrand Deroin: every PSL(2\,R)-l
ocal system of Euler class 2g-3 over a curve of genus g admits an isomonod
romic deformation that supports a C-VHS.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jun-Yong Park (University of Melbourne)
DTSTART;VALUE=DATE-TIME:20230426T173000Z
DTEND;VALUE=DATE-TIME:20230426T183000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/23
DESCRIPTION:Title: Height moduli on algebraic stacks and counting families of
varieties (special time and location SC 221)\nby Jun-Yong Park (Unive
rsity of Melbourne) as part of Harvard MIT Algebraic Geometry Seminar\n\nL
ecture held in Harvard Science Center 221 (special location).\n\nAbstract\
nI will begin by reviewing the classical algorithm of Tate with some expli
cit polynomial calculations. Combining this with twisted stable maps theor
y leads us to the height moduli of rational points of fixed stacky height
on the fine modular curve Mbar_{1\,1} over global function fields. We will
then compute arithmetic invariants of elliptic surfaces moduli via topolo
gical methods and give applications to counting elliptic curves over Fq(t)
.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miguel Moreira (MIT)
DTSTART;VALUE=DATE-TIME:20230912T190000Z
DTEND;VALUE=DATE-TIME:20230912T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/25
DESCRIPTION:Title: Enumerative geometry\, wall-crossing and Virasoro constrai
nts\nby Miguel Moreira (MIT) as part of Harvard MIT Algebraic Geometry
Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nGiven a moduli space o
f either sheaves on a smooth projective variety or a moduli space of repre
sentations of a quiver\, there are several invariants that we can extract.
One of the ways to get numbers out of a moduli space is to integrate (pos
sibly against a virtual fundamental class) certain tautological classes. S
uch numbers often have interesting structures behind\, and I will talk abo
ut two: how they change when one changes a stability condition (wall-cross
ing formulas) and some universal and explicit linear relations that those
invariants always seem to satisfy (Virasoro constraints). Both of these ph
enomena are related to a vertex algebra found by D. Joyce. For simplicity
I will mostly focus on the case of representations of a quiver. The talk i
s based on joint work with A. Bojko and W. Lim.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elden Elmanto (University of Toronto)
DTSTART;VALUE=DATE-TIME:20230919T190000Z
DTEND;VALUE=DATE-TIME:20230919T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/26
DESCRIPTION:Title: Cycling in Cambridge\nby Elden Elmanto (University of
Toronto) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held
in MIT 2-132.\n\nAbstract\nI spent most of my time here cycling (or is it
biking?) and thinking about algebraic cycles from a homotopical viewpoint
. I will speak about the latter. In joint work with Matthew Morrow\, we de
veloped a theory of motivic cohomology of schemes beyond the case of smoot
h schemes over a field. I will explain the cycle-theoretic aspects of this
construction\, focusing on the case of surfaces\, revisiting older result
s of Krishna and Srinivas.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Satriano (University of Waterloo)
DTSTART;VALUE=DATE-TIME:20230926T190000Z
DTEND;VALUE=DATE-TIME:20230926T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/27
DESCRIPTION:Title: Beyond twisted maps: crepant resolutions of log terminal s
ingularities and a motivic McKay correspondence\nby Matthew Satriano (
University of Waterloo) as part of Harvard MIT Algebraic Geometry Seminar\
n\nLecture held in Harvard Science Center 507.\n\nAbstract\nCrepant resolu
tions have inspired connections between birational geometry\, derived cate
gories\, representation theory\, and motivic integration. In this talk\, w
e prove that every variety with log-terminal singularities admits a crepan
t resolution by a smooth stack. We additionally prove a motivic McKay corr
espondence for stack-theoretic resolutions. Finally\, we show how our work
naturally leads to a generalization of twisted mapping spaces. No prior k
nowledge of stacks will be assumed. This is joint work with Jeremy Usatine
.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brad Dirks (Stony Brook)
DTSTART;VALUE=DATE-TIME:20231003T190000Z
DTEND;VALUE=DATE-TIME:20231003T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/28
DESCRIPTION:Title: The minimal exponent of LCI subvarieties\nby Brad Dirk
s (Stony Brook) as part of Harvard MIT Algebraic Geometry Seminar\n\nLectu
re held in Harvard Science Center 507.\n\nAbstract\nClassification of sing
ularities is an interesting problem in many areas of algebraic geometry\,
like the minimal model program. One classical approach is to assign to a v
ariety a rational number\, its log canonical threshold. For complex hypers
urface singularities\, this invariant has been refined by M. Saito to the
minimal exponent. This invariant is related to Bernstein-Sato polynomials\
, Hodge ideals and higher du Bois and higher rational singularities.\n\nIn
joint work with Qianyu Chen\, Mircea Mustață and Sebastián Olano\, we
defined the minimal exponent for LCI subvarieties of smooth complex variet
ies. We relate it to local cohomology\, higher du Bois and higher rational
singularities. I will describe what was done in the hypersurface case\, g
ive our definition in the LCI case and explain the relation to local cohom
ology modules and the classification of singularities.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Pieloch (MIT)
DTSTART;VALUE=DATE-TIME:20231010T190000Z
DTEND;VALUE=DATE-TIME:20231010T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/29
DESCRIPTION:Title: Uniruling projective families over $\\mathbb{CP}^1$ with r
ational (multi)sections\nby Alex Pieloch (MIT) as part of Harvard MIT
Algebraic Geometry Seminar\n\nLecture held in MIT 2-131.\n\nAbstract\nWe w
ill discuss a result which states that every projective family over $\\mat
hbb{CP}^1$ with at most two singular fibres is uniruled by rational (multi
)sections. We obtain these rational curves by using techniques from sympl
ectic geometry. In this talk\, we will focus on (1) discussing the motiva
tion for this work from Hodge theory and (2) presenting the geometric cons
tructions and ideas involved in our proofs. No knowledge of symplectic ge
ometry is required.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Dinkins (MIT)
DTSTART;VALUE=DATE-TIME:20231017T190000Z
DTEND;VALUE=DATE-TIME:20231017T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/30
DESCRIPTION:Title: Generalized quantum difference equations for quiver variet
ies\nby Hunter Dinkins (MIT) as part of Harvard MIT Algebraic Geometry
Seminar\n\nLecture held in MIT 2-143.\n\nAbstract\nCurve counts inside ce
rtain varieties are constrained by an equation called the quantum differen
ce equation. Okounkov and Smirnov described the quantum difference equatio
n for Nakajima quiver varieties in terms of a quantum group. There is a na
tural modification of their description\, which leads to a collection of "
exotic" quantum difference equations\, one for each alcove in a certain hy
perplane arrangement. Our main result is an enumerative-geometric descript
ion of the fundamental solution of these exotic equations. I will give an
overview of these ideas\, illustrating the results for the example of the
Hilbert scheme of points in the complex plane.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Gross (Cambridge)
DTSTART;VALUE=DATE-TIME:20231024T190000Z
DTEND;VALUE=DATE-TIME:20231024T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/31
DESCRIPTION:Title: Mirror symmetry and partial compactifications of K3 moduli
\nby Mark Gross (Cambridge) as part of Harvard MIT Algebraic Geometry
Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nI will
talk about work with Hacking\, Keel and Siebert on using mirror construct
ions to provide partial compactifications of the moduli of K3 surfaces. St
arting with a one-parameter maximally\nunipotent degeneration of Picard ra
nk 19 K3 surfaces\, we construct\, using methods of myself and Siebert\, a
mirror family which is defined in a formal neighbourhood of a union of st
rata of a toric variety whose fan is defined\, to first approximation\, as
the Mori fan of the original degeneration. This\nformal family may then b
e glued in to the moduli space of polarized K3 surfaces to obtain a partia
l compactification. Perhaps the most significant by-product of this constr
uction is the existence of theta functions in this formal neighbourhood\,
certain canonical bases for sections of powers of the\npolarizing line bun
dle.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakub Witaszek (Princeton)
DTSTART;VALUE=DATE-TIME:20231031T190000Z
DTEND;VALUE=DATE-TIME:20231031T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/32
DESCRIPTION:Title: Singularities in mixed characteristic via the Riemann-Hilb
ert correspondence\nby Jakub Witaszek (Princeton) as part of Harvard M
IT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center 50
7.\n\nAbstract\nIn my talk\, I will start by reviewing how various propert
ies of characteristic zero singularities can be understood topologically b
y ways of the Riemann-Hilbert correspondence. After that\, I will explain
how similar ideas can be applied in the study of mixed characteristic sing
ularities. This is based on a joint work (in progress) with Bhargav Bhatt\
, Linquan Ma\, Zsolt Patakfalvi\, Karl Schwede\, Kevin Tucker\, and Joe Wa
ldron.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Talk Cancelled (Talk Cancelled)
DTSTART;VALUE=DATE-TIME:20231107T200000Z
DTEND;VALUE=DATE-TIME:20231107T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/33
DESCRIPTION:Title: Talk Cancelled\nby Talk Cancelled (Talk Cancelled) as
part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard
Science Center 507.\n\nAbstract\nI will discuss an elementary notion -- th
e angle rank of a polynomial -- and an application to the Tate conjecture
for Abelian varieties over finite fields.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iacopo Brivio (Harvard University (CMSA))
DTSTART;VALUE=DATE-TIME:20231114T200000Z
DTEND;VALUE=DATE-TIME:20231114T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/34
DESCRIPTION:Title: Superadditivity of anticanonical Iitaka dimension in posit
ive characteristic\nby Iacopo Brivio (Harvard University (CMSA)) as pa
rt of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Sc
ience Center 507.\n\nAbstract\nGiven a fibration $f\\colon X\\to Y$ of smo
oth complex projective with general fiber $F$\, the celebrated Iitaka conj
ecture predicts the inequality $\\kappa(K_X)\\geq \\kappa(K_F)+\\kappa(K_Y
)$. Recently Chang showed that\, under some natural conditions\, the inequ
ality $\\kappa(-K_X)\\leq \\kappa(-K_F)+\\kappa(-K_Y)$ holds.\n\nIn this t
alk I will show that\, despite the failure in positive characteristic of b
oth the Iitaka conjecture and Chang's theorem\, it is possible to recover
the latter for "tame" positive characteristic fibrations. This is based on
joint work with M. Benozzo and C.-K. Chang.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:César Lozano Huerta (Universidad Nacional Autónoma de México)
DTSTART;VALUE=DATE-TIME:20231121T200000Z
DTEND;VALUE=DATE-TIME:20231121T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/35
DESCRIPTION:Title: The Noether-Lefschetz loci formed by determinantal surface
s in projective 3-space.\nby César Lozano Huerta (Universidad Naciona
l Autónoma de México) as part of Harvard MIT Algebraic Geometry Seminar\
n\nLecture held in Harvard Science Center 507.\n\nAbstract\nSolomon Lefsch
etz showed that the Picard group of a general surface in P3 of degree grea
ter than three is ZZ. That is\, the vast majority of surfaces in P3 have t
he smallest possible Picard group. The set of surfaces of degree greater t
han 3 on which this theorem fails is called the Noether-Lefschetz locus. T
his locus has infinite components and their dimensions are somehow mysteri
ous.\n\nIn this talk\, I will calculate the dimension of infinite Noether-
Lefschetz components that are simple in a sense\, but still give us an ide
a of the complexity of the entire Noether-Lefschetz locus. This is joint w
ork with Montserrat Vite and Manuel Leal.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emelie Arvidsson (University of Utah)
DTSTART;VALUE=DATE-TIME:20231128T200000Z
DTEND;VALUE=DATE-TIME:20231128T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/36
DESCRIPTION:Title: Properties of log canonical singularities in positive char
acteristic\nby Emelie Arvidsson (University of Utah) as part of Harvar
d MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center
507.\n\nAbstract\nWe will investigate if some well known properties of lo
g canonical singularities over the complex numbers still hold true over pe
rfect fields of positive characteristic and over excellent rings with perf
ect residue fields. We will discuss both pathological behavior in characte
ristic p as well as some positive results for threefolds. We will see that
the pathological behavior of these singularities in positive characterist
ic is closely linked to the failure of certain vanishing theorems in posit
ive characteristic. Additionally\, we will explore how these questions are
related to the moduli theory of varieties of general type.\n\nThis is bas
ed on joint work with F. Bernasconi and Zs. Patakfalvi\, as well as joint
work with Q. Posva.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Baudin (EPFL Lausanne)
DTSTART;VALUE=DATE-TIME:20231205T200000Z
DTEND;VALUE=DATE-TIME:20231205T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/37
DESCRIPTION:Title: On Ueno's conjecture in positive characteristics\nby J
eff Baudin (EPFL Lausanne) as part of Harvard MIT Algebraic Geometry Semin
ar\n\nLecture held in Harvard Science Center 507.\n\nAbstract\nIn characte
ristic zero\, Ueno's conjecture states that if X is a smooth projective va
riety with Kodaira dimension zero\, then its Albanese morphism in an algeb
raic fiber space and the Kodaira dimension of the general fiber is again z
ero. This was proven by Cao and Păun in 2016. \n\nBuilding on the generic
vanishing techniques of Hacon and Patakfalvi\, we prove a positive charac
teristic version of this result. We use it to deduce new cases of Iitaka's
subadditivity conjecture in positive characteristics. The goal of this ta
lk is to explain how these techniques work\, and how we can use them to pr
ove such results.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Perry (University of Michigan)
DTSTART;VALUE=DATE-TIME:20231212T200000Z
DTEND;VALUE=DATE-TIME:20231212T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/38
DESCRIPTION:Title: The period-index conjecture for abelian threefolds\nby
Alex Perry (University of Michigan) as part of Harvard MIT Algebraic Geom
etry Seminar\n\nLecture held in MIT 2-131.\n\nAbstract\nThe period-index c
onjecture asks for a precise bound on one measure of complexity of a Braue
r class (its index) in terms of another (its period). I will discuss joint
work with James Hotchkiss which proves this conjecture for Brauer classes
on abelian threefolds.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carl Lian (Tufts University)
DTSTART;VALUE=DATE-TIME:20240206T200000Z
DTEND;VALUE=DATE-TIME:20240206T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/39
DESCRIPTION:Title: Enumerativity of fixed-domain Gromov-Witten invariants
\nby Carl Lian (Tufts University) as part of Harvard MIT Algebraic Geometr
y Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nIt is well-understood
that Gromov-Witten (GW) invariants often fail to be enumerative. For exam
ple\, when r is at least 3\, the higher-genus GW invariants of P^r fail to
count smooth curves in projective space in any transparent sense. The sit
uation seems to be better when one fixes the complex structure of the doma
in curve. It was originally speculated that if X is a Fano variety\, then
the "fixed-domain" GW count of curves of sufficiently large degree passing
through the maximal number of general points is enumerative. I will discu
ss some positive and negative results in this direction\, focusing on the
case of hypersurfaces. The most recent results are joint with Roya Behesht
i\, Brian Lehmann\, Eric Riedl\, Jason Starr\, and Sho Tanimoto\, and buil
d on earlier work with Rahul Pandharipande and Alessio Cela.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Canceled
DTSTART;VALUE=DATE-TIME:20240213T200000Z
DTEND;VALUE=DATE-TIME:20240213T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/40
DESCRIPTION:Title: Canceled\nby Canceled as part of Harvard MIT Algebraic
Geometry Seminar\n\nLecture held in MIT 2-132.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Montserrat Teixidor (Tufts University)
DTSTART;VALUE=DATE-TIME:20240220T200000Z
DTEND;VALUE=DATE-TIME:20240220T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/41
DESCRIPTION:Title: Brill-Noether loci\nby Montserrat Teixidor (Tufts Univ
ersity) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held
in Harvard Science Center 507.\n\nAbstract\nBrill-Noether loci are defined
as the set of curves of genus g that have an unexpected linear series of
degree d and dimension r.\n\nPflueger showed that these loci are non-empty
when the expected codimension is at most g-3. By studying linear series o
n chains of elliptic curves\, we give a new proof of a slightly refined ve
rsion of this result. We can also look at the behavior of the generic curv
e in the locus.\n\nAn interesting conjecture of Auel and Haburcak states
that these loci are distinct and not contained in each other\, unless they
come from adding or removing fixed points. Their proof made use of curves
contained in K3 surfaces and was sufficient to prove the result in small
genus. Using chains of elliptic curves\, we can obtain additional informat
ion.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maksym Fedorchuk (Boston College)
DTSTART;VALUE=DATE-TIME:20240227T200000Z
DTEND;VALUE=DATE-TIME:20240227T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/42
DESCRIPTION:Title: CM-minimizers and standard models of Fano fibrations over
curves\nby Maksym Fedorchuk (Boston College) as part of Harvard MIT Al
gebraic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nA rece
nt achievement in K-stability of Fano varieties is an\nalgebro-geometric c
onstruction of a projective moduli space of\nK-polystable Fanos. The ample
line bundle on this moduli space is the\nCM line bundle of Tian. One of t
he consequences of the general theory\nis that given a family of K-stable
Fanos over a punctured curve\, the\npolystable filling is the one that min
imizes the degree of the CM line\nbundle after every *finite base change
*. A natural question is to\nask what are the CM-minimizers *without<
/i> base change. In\nanswering this question\, we arrive at a theory of Ko
llár stability\nfor fibrations over one-dimensional bases\, and standard
models of Fano\nfibrations. After explaining the general theory\, I will s
ketch work in\nprogress on standard models of quartic threefold hypersurfa
ces. This\ntalk is based on joint work with Hamid Abban and Igor Krylov.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marta Benozzo (Imperial College)
DTSTART;VALUE=DATE-TIME:20240305T200000Z
DTEND;VALUE=DATE-TIME:20240305T210000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/43
DESCRIPTION:Title: On the canonical bundle formula in positive characteristic
\nby Marta Benozzo (Imperial College) as part of Harvard MIT Algebraic
Geometry Seminar\n\nLecture held in Harvard Science Center 507.\n\nAbstra
ct\nAn important problem in birational geometry is trying to relate in a m
eaningful way the canonical bundles of the source and the base of a fibrat
ion. The first instance of such a formula is Kodaira’s canonical bundle
formula for surfaces which admit a fibration with elliptic fibres. It desc
ribes the relation between the canonical bundles in terms of the singulari
ties of the fibres and their j-invariants.\nIn higher dimension\, we do no
t have an equivalent of the j-invariant\, but we can still define a moduli
part. Over fields of characteristic 0\, positivity properties of the modu
li part have been studied using variations of Hodge structures. Recently\,
the problem has been approached with techniques from the minimal model pr
ogram. These methods can be used to prove a canonical bundle formula resul
t in positive characteristic.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Marquand (NYU)
DTSTART;VALUE=DATE-TIME:20240312T190000Z
DTEND;VALUE=DATE-TIME:20240312T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/44
DESCRIPTION:Title: The defect of a cubic threefold\nby Lisa Marquand (NYU
) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in Har
vard Science Center 507.\n\nAbstract\nThe defect of a cubic threefold with
isolated singularities is a measure of the failure of Poincare duality\,
and also the failure to be Q-factorial. From the work of Cheltsov\, a cubi
c threefold with only nodal singularities is Q factorial if and only if th
ere are at most 5 nodes. We investigate the defect of cubic threefolds wit
h worse than nodal isolated singularities\, and provide a geometric method
to compute this global invariant. One can then compute the Mixed Hodge st
ructure on the middle cohomology of the cubic threefold\, in terms of the
defect (a global invariant) and local invariants (Du Bois and Link invaria
nts) determined by the singularity types. We then relate the defect to geo
metric properties of the cubic threefold\, showing it is positive if and o
nly if the cubic contains a plane or a rational normal cubic scroll. The f
ocus of this work is to provide more insight into the existence of reducib
le fibers for compactified intermediate jacobian fibrations associated to
a smooth (not necessarily general) cubic fourfold. This is joint work with
Sasha Viktorova.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changho Han (Waterloo)
DTSTART;VALUE=DATE-TIME:20240319T190000Z
DTEND;VALUE=DATE-TIME:20240319T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/45
DESCRIPTION:Title: Extending the torelli map to alternative compactifications
of the moduli space of curves\nby Changho Han (Waterloo) as part of H
arvard MIT Algebraic Geometry Seminar\n\nLecture held in Harvard Science C
enter 507.\n\nAbstract\nIt is well-known that the Torelli map\, that turns
a smooth curve of genus g into its Jacobian (a principally polarized abel
ian variety of dimension g)\, extends to a map from the Deligne—Mumford
moduli of stable curves to the moduli of semi-abelic varieties by Alexeev.
Moreover\, it is also known that the Torelli map does not extend over the
alternative compactifications of the moduli of curves as described by the
Hassett—Keel program\, including the moduli of pseudostable curves (can
have nodes and cusps but not elliptic tails). But it is not yet known whe
ther the Torelli map extends over alternative compactifications of the mod
uli of curves described by Smyth\; what about the moduli of curves of genu
s g with rational m-fold singularities\, where m is a positive integer bou
nded above? As a joint work in progress with Jesse Kass and Matthew Satria
no\, I will describe moduli spaces of curves with m-fold singularities (wi
th topological constraints) and describe how far the Torelli map extends o
ver such spaces into the Alexeev compactifications.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dhruv Ranganathan (Cambridge)
DTSTART;VALUE=DATE-TIME:20240326T190000Z
DTEND;VALUE=DATE-TIME:20240326T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/46
DESCRIPTION:Title: A degeneration of the Hilbert scheme\nby Dhruv Rangana
than (Cambridge) as part of Harvard MIT Algebraic Geometry Seminar\n\nLect
ure held in MIT 2-449 (note special room!).\n\nAbstract\nSpecial Room: 2-
449\n\nGrothendieck's Hilbert scheme is a compact parameter space for subs
chemes of a projective scheme X. It is one of the basic moduli spaces in a
lgebraic geometry\, in the sense that it is the starting point for the con
struction of many others. One simple question about the Hilbert scheme is
the following: as X undergoes a nice degeneration\, what is the right way
to degenerate the Hilbert scheme of X along with it? One possible answer\,
proposed in the PhD thesis of Kennedy-Hunt\, comes from an object called
the logarithmic Hilbert scheme. I will give an introduction to this circle
of these ideas\, explain the basic geometric properties of the logarithmi
c Hilbert scheme\, and sketch connections with certain moduli spaces of hi
gher dimensional varieties. The talk reports on work of Kennedy-Hunt\, joi
nt work with Kennedy-Hunt\, and joint work with Maulik.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julianna Tymoczko (Smith College)
DTSTART;VALUE=DATE-TIME:20240402T190000Z
DTEND;VALUE=DATE-TIME:20240402T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/47
DESCRIPTION:Title: Webs and Schubert calculus for Springer fibers\nby Jul
ianna Tymoczko (Smith College) as part of Harvard MIT Algebraic Geometry S
eminar\n\nLecture held in MIT 2-132.\n\nAbstract\nClassical Schubert calcu
lus analyzes the geometry of the flag variety\, namely the space of nested
subspaces $V_1 \\subseteq V_2 \\subseteq \\cdots \\subseteq \\mathbb{C}^n
$\, asking enumerative questions about intersections of linear spaces that
turn out to be equivalent to deep problems in combinatorics and represent
ation theory. In this talk\, we'll describe some recent results in the Sc
hubert calculus of Springer fibers. Given a nilpotent linear operator $X$
\, the Springer fiber of $X$ is the subvariety of flags that are fixed by
$X$ in the sense that $XV_i \\subseteq V_i$ for all $i$. The top-dimensio
nal cohomology of Springer fibers admits a representation of the symmetric
group first discovered by Tonny Springer as the seminal example of a geom
etric representation. Where classical Schubert calculus describes geometr
y governed by permutations\, that of Springer fibers incorporates the comb
inatorics both of permutations and of partitions. We'll describe new resu
lts about this geometry in more detail\, including evidence that from a ge
ometric and topological perspective\, the best combinatorial model for Spr
inger fibers comes from representation-theoretic objects called webs.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Esser (Princeton)
DTSTART;VALUE=DATE-TIME:20240409T190000Z
DTEND;VALUE=DATE-TIME:20240409T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/48
DESCRIPTION:Title: The Dual Complex of a G-variety\nby Louis Esser (Princ
eton) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held in
Harvard Science Center 507.\n\nAbstract\nWe introduce a new invariant of
G-varieties\, the dual complex\, which roughly measures how divisors in th
e complement of the free locus intersect. We show that the top homology gr
oup of this complex is an equivariant birational invariant of G-varieties.
As an application\, we demonstrate the non-linearizability of certain lar
ge abelian group actions on smooth hypersurfaces in projective space of an
y dimension and degree at least 3.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Han-Bom Moon (Fordham University)
DTSTART;VALUE=DATE-TIME:20240416T190000Z
DTEND;VALUE=DATE-TIME:20240416T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/49
DESCRIPTION:Title: Derived category of moduli space of vector bundles on a cu
rve\nby Han-Bom Moon (Fordham University) as part of Harvard MIT Algeb
raic Geometry Seminar\n\nLecture held in MIT 2-132.\n\nAbstract\nThe deriv
ed category of moduli spaces of vector bundles on a curve is expected to b
e decomposed into the derived categories of symmetric products of the base
curve. I will briefly explain the expectation and known results\, and som
e consequences. This is joint work in progress with Kyoung-Seog Lee.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Larson (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20240423T190000Z
DTEND;VALUE=DATE-TIME:20240423T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/50
DESCRIPTION:Title: The Chow ring of the universal Picard stack over the hyper
elliptic locus\nby Hannah Larson (UC Berkeley) as part of Harvard MIT
Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center 507.\
n\nAbstract\nUnderstanding the line bundles on curves are essential to und
erstanding the curves themselves. As such\, the universal Picard stack J^d
_g --> M_g parametrizing degree d line bundles on genus g curves is an imp
ortant object of study. Recently\, progress has been made on the intersect
ion theory of M_g in low genus by stratifying the moduli space by gonality
. The smallest piece in this stratification is the hyperelliptic locus. Mo
tivated by this\, I'll present several results about the restriction of J^
d_g to the hyperelliptic locus\, denoted J^d_{2\,g}. These include a prese
ntation of the rational Chow ring of J^d_{2\,g}. I also determine the inte
gral Picard group of J^d_{2\,g}\, completing (and extending to the PGL_2-e
quivariant case) prior work of Erman and Wood.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qile Chen (Boston College)
DTSTART;VALUE=DATE-TIME:20240430T190000Z
DTEND;VALUE=DATE-TIME:20240430T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/51
DESCRIPTION:Title: Campana rational connectedness\nby Qile Chen (Boston C
ollege) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held
in MIT 2-132.\n\nAbstract\nThe notion of Campana points were introduced by
Campana and Abramovich\, which interpolate between rational points and in
tegral points. In this talk\, we will focus on the geometric side and intr
oduce Campana rational connectedness --- a version of rational connectedne
ss for varieties with simple normal crossings boundaries. We further prove
that over function fields\, weak approximations by Campana points at good
places hold assuming Campana rational connectedness of fibers\, generaliz
ing a theorem of Hassett and Tschinkel. We further verify Campana rational
connectedness for many basic examples. Our approach relies on the theory
of stable log maps and their moduli. This is a joint work in progress with
Brian Lehmann and Sho Tanimoto.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joe Harris (Harvard University)
DTSTART;VALUE=DATE-TIME:20240507T190000Z
DTEND;VALUE=DATE-TIME:20240507T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/52
DESCRIPTION:Title: The Enriques Conjectures\nby Joe Harris (Harvard Unive
rsity) as part of Harvard MIT Algebraic Geometry Seminar\n\nLecture held i
n Harvard Science Center 507.\n\nAbstract\nTwo fundamental facts about the
moduli space M_g of smooth curves of genus g are what are called Harer's
theorems: that the Picard group of M_g is of rank one\, generated (over th
e rational numbers) by the Hodge class\; and that the relative Picard grou
p of the universal curve over M_g is also of rank one\, generated by the r
elative dualizing sheaf. We can make analogous statements about the Severi
variety of plane curves and the Hurwitz space parametrizing branched cove
rs\, which are still open\; in fact\, the former was conjectured by Enriqu
es more than a century ago and remains open.\n\nIn this talk I'd like to d
escribe all of these theorems/conjectures\, and the implications among the
m\, including Isabel Vogt's recent work on Severi varieties. I'll be worki
ng entirely with rational coefficients\, so torsion classes\, which are fa
r more mysterious\, will not enter into it.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Borys Kadets (Hebrew University of Jerusalem)
DTSTART;VALUE=DATE-TIME:20240402T203000Z
DTEND;VALUE=DATE-TIME:20240402T213000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/56
DESCRIPTION:Title: Curves with many degree $d$ points (Joint with the MIT num
ber theory seminar\, note the special time and location)\nby Borys Kad
ets (Hebrew University of Jerusalem) as part of Harvard MIT Algebraic Geom
etry Seminar\n\nLecture held in MIT 2-449.\n\nAbstract\nWhen does a nice c
urve $X$ over a number field $k$ have infinitely many closed points of deg
ree $d$?\nFaltings' theorem allows us to rephrase this problem in purely a
lgebro-geometric terms\, though the resulting geometric question is far fr
om being fully solved. Previous work gave easy to state answers to the pro
blem for degrees $2$ (Harris-Silverman) and $3$ (Abramovich-Harris)\, but
also uncovered exotic constructions of such curves in all degrees $d \\geq
slant 4$ (Debarre-Fahlaoui). I will describe recent progress on the proble
m\, which answers the question in the large genus case. Along the way we u
ncover systematic explanations for the Debarre-Fahlaoui counstructions and
provide a complete geometric answer for $d \\leqslant 5$. The talk is bas
ed on joint work with Isabel Vogt.\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Hase-Liu (Columbia University)
DTSTART;VALUE=DATE-TIME:20241001T190000Z
DTEND;VALUE=DATE-TIME:20241001T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/57
DESCRIPTION:by Matthew Hase-Liu (Columbia University) as part of Harvard M
IT Algebraic Geometry Seminar\n\nLecture held in Harvard Science Center 50
7.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:César Lozano Huerta (Universidad Nacional Autónoma de México)
DTSTART;VALUE=DATE-TIME:20240625T190000Z
DTEND;VALUE=DATE-TIME:20240625T200000Z
DTSTAMP;VALUE=DATE-TIME:20240804T060653Z
UID:harvard-mit-ag-seminar/58
DESCRIPTION:Title: Geometry of syzygies of sheaves on P2 via interpolation an
d Bridgeland stability.\nby César Lozano Huerta (Universidad Nacional
Autónoma de México) as part of Harvard MIT Algebraic Geometry Seminar\n
\nLecture held in Harvard Science Center 232.\n\nAbstract\nThe minimal fre
e resolution of a sheaf on P2\, such as a vector bundle or the ideal sheaf
of points\, carries important information about its moduli space. However
\, how it may do so has remained unclear.\n\nThis talk aims to clarify the
previous situation and\, I will compute the cone of effective divisors of
moduli spaces of sheaves using syzygies.\n\nNote the special room on the
second floor\n
LOCATION:https://researchseminars.org/talk/harvard-mit-ag-seminar/58/
END:VEVENT
END:VCALENDAR
*