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BEGIN:VEVENT
SUMMARY:Kiumars Kaveh (University of Pittsburgh)
DTSTART;VALUE=DATE-TIME:20211102T130000Z
DTEND;VALUE=DATE-TIME:20211102T143000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/1
DESCRIPTION:Title: Vector bundles on toric varieties\nby Kiumars Kaveh (University of
Pittsburgh) as part of IPM Algebraic Geometry Seminar\n\n\nAbstract\nIn th
is talk we review construction of toric varieties and classification of (t
orus equivariant) line bundles and vector bundles on them (after Klyachko)
. We interpret Klyachko's data of a vector bundle as a "piecewise linear m
ap" into the Tits building of the general linear group GL(r). This "buildi
ng" perspective helps to approach many questions about vector bundles on t
oric varieties in a new light. As an application of this idea\, we obtain
a classification of (torus equivariant) vector bundles on toric schemes in
terms of "piecewise affine maps" to the Bruhat-Tits building of GL(r). Th
is is work in progress with Chris Manon and Boris Tsvelikhovsky. I try to
cover most of the background material.\n\nhttps://zoom.us/join\n\nMeeting
ID: 9086116889\n\nPasscode: 13440 $\\times$ the number of lines on a cubic
surface\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Jafari (Sharif University of Technology)
DTSTART;VALUE=DATE-TIME:20211116T130000Z
DTEND;VALUE=DATE-TIME:20211116T143000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/2
DESCRIPTION:Title: Grothendieck Galois theory and some of its applications in combinatoric
s\nby Amir Jafari (Sharif University of Technology) as part of IPM Alg
ebraic Geometry Seminar\n\n\nAbstract\nThis is going to be a report of my
ongoing joint research project with Mr. Moghaddamzadeh on finite projectiv
e geometries. However\, a good portion of the talk will be spent on explai
ning Grothendieck's generalizations of Galois theory.\n\nhttps://zoom.us/j
oin\n\nMeeting ID: 9086116889\n\nPasscode: 13440 $\\times$ the number of l
ines on a cubic surface\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amin Gholampour (University of Maryland)
DTSTART;VALUE=DATE-TIME:20211130T130000Z
DTEND;VALUE=DATE-TIME:20211130T143000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/3
DESCRIPTION:Title: 2-dimensional stable pairs on 4-folds\nby Amin Gholampour (Universi
ty of Maryland) as part of IPM Algebraic Geometry Seminar\n\n\nAbstract\nI
will discuss a 2-dimensional stable pair theory of nonsingular complex 4-
folds that is parallel to Pandharipande-Thomas' 1-dimensional stable pair
theory of 3-folds. The stable pairs of a 4-fold are related to its 2-dimen
sional subschemes via wall-crossings in the space of polynomial stability
conditions. In Calabi-Yau case\, Oh-Thomas theory is applied to define inv
ariants counting these stable pairs under some restrains. This is a joint
work with Yunfeng Jiang and Jason Lo.\n\nhttps://zoom.us/join\n\nMeeting I
D: 9086116889\n\nPasscode: 13440 $\\times$ the number of lines on a cubic
surface\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abbas Nasrollah Nejad (Institute for Advanced Studies in Basic Sci
ences)
DTSTART;VALUE=DATE-TIME:20211214T130000Z
DTEND;VALUE=DATE-TIME:20211214T143000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/4
DESCRIPTION:Title: The relation type of singular space of hypersurfaces\nby Abbas Nasr
ollah Nejad (Institute for Advanced Studies in Basic Sciences) as part of
IPM Algebraic Geometry Seminar\n\n\nAbstract\nIn this talk\, we will intro
duce the notion of relation type of formal and analytic algebras and show
that it is well defined by using of André-Quillen homology. In particular
\, the relation type is an invariant of an affine algebraic variety and a
complex space germ. We will discuss and essay to explain the relation type
of singular subscheme of isolated hypersurface singularities. This talk i
s based on joint ongoing work with Maryam Akhavin.\n\nhttps://zoom.us/join
\n\nMeeting ID: 9086116889\n\nPasscode: 13440 $\\times$ the number of line
s on a cubic surface\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tahereh Aladpoosh (Institute for Research in Fundamental Sciences
(IPM))
DTSTART;VALUE=DATE-TIME:20211228T130000Z
DTEND;VALUE=DATE-TIME:20211228T143000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/5
DESCRIPTION:Title: Postulation of generic lines and a multiple line in $\\mathbb{P}^n$
\nby Tahereh Aladpoosh (Institute for Research in Fundamental Sciences (IP
M)) as part of IPM Algebraic Geometry Seminar\n\n\nAbstract\nA well-known
theorem by Hartshorne and Hirschowitz states that a generic configuration
of lines has good postulation. So what about non-reduced configurations? C
an adding a multiple line to the configuration still preserve it’s good
postulation? This is the question we mainly deal with in this talk. In the
first part of the talk we introduce the postulation problem for projectiv
e schemes\, then we discuss the problem for the family of schemes supporte
d on generic linear configurations\, which are the ones of particular inte
rest. In the second part of the talk we focus on the postulation of generi
c lines and one multiple line in projective space. We give our main theore
m providing a complete description to the case of lines and a double line\
, then we propose a conjecture to the general case\, finally we discuss wh
at is known about the conjecture and more recent results on it.\n\nhttps:/
/zoom.us/join\n\nMeeting ID: 9086116889\n\nPasscode: 13440 $\\times$ the n
umber of lines on a cubic surface\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Esmail Arasteh Rad (Institute for Research in Fundamental Sciences
(IPM))
DTSTART;VALUE=DATE-TIME:20220125T130000Z
DTEND;VALUE=DATE-TIME:20220125T143000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/6
DESCRIPTION:Title: Rapoport-Zink spaces for local ℙ-shtukas\nby Esmail Arasteh Rad (
Institute for Research in Fundamental Sciences (IPM)) as part of IPM Algeb
raic Geometry Seminar\n\n\nAbstract\nRapoport-Zink spaces for p-divisible
groups are local counterparts for Shimura varieties. According to the dict
ionary between function fields and number fields\, they correspond to the
RZ-spaces for local P-shtukas. We review the construction of these moduli
spaces and then discuss our approach for computing the semi-simple trace o
f Frobenius on their (nearby-cycles) cohomology.\n\nhttps://zoom.us/join\n
\nMeeting ID: 9086116889\n\nPasscode: 13440 $\\times$ the number of lines
on a cubic surface\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Nasr (Institute for Research in Fundamental Sciences (IPM))
DTSTART;VALUE=DATE-TIME:20220208T103000Z
DTEND;VALUE=DATE-TIME:20220208T120000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/7
DESCRIPTION:Title: Toric quiver varieties\nby Amir Nasr (Institute for Research in Fun
damental Sciences (IPM)) as part of IPM Algebraic Geometry Seminar\n\n\nAb
stract\nWe discuss the smoothness of toric quiver varieties. When a quiver
$Q$ is defined with the identity dimension vector\, the corresponding qu
iver variety is also a toric variety. So it has a fan representation and a
quiver representation. I consider only quivers with canonical weight and
we classify smooth such toric quiver varieties. I show that a variety corr
esponding to a quiver with the identity dimension vector and the canonical
weight is smooth if and only if it is a product of projective spaces or t
heir blowups.\n\nhttps://zoom.us/join\n\nMeeting ID: 9086116889\n\nPasscod
e: 13440 $\\times$ the number of lines on a cubic surface\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Bajravani (Azarbaijan Shahid Madani University)
DTSTART;VALUE=DATE-TIME:20220222T130000Z
DTEND;VALUE=DATE-TIME:20220222T143000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/8
DESCRIPTION:Title: Stable vector bundles on curves and their Brill-Noether theory\nby
Ali Bajravani (Azarbaijan Shahid Madani University) as part of IPM Algebra
ic Geometry Seminar\n\n\nAbstract\nWe discuss some stricking properties of
stable vector bundles over curves\, which are frequently used in moduli a
nd Brill-Noether arguments of these bundles. Then\, after a quick historic
al surf in the topic\, we give an upper bound for dimensions of Brill-Noet
her schemes of rank 2 stable vector bundles.\n\nhttps://zoom.us/join\n\nMe
eting ID: 9086116889\n\nPasscode: 13440 $\\times$ the number of lines on a
cubic surface\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hassan Haghighi (K. N. Toosi University of Technology)
DTSTART;VALUE=DATE-TIME:20220308T130000Z
DTEND;VALUE=DATE-TIME:20220308T143000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/9
DESCRIPTION:Title: Unexpected hypersurfaces: some examples\, a few constructions\nby H
assan Haghighi (K. N. Toosi University of Technology) as part of IPM Algeb
raic Geometry Seminar\n\n\nAbstract\nIn recent years\, a novel attitude to
the classical problem of identifying and classifying special linear syst
ems in projective $n$ space\, has been emerged.\nFor a subvariety $Z$ of
the projective $n$ space with defining ideal $I$\, let $P_1\,\\dots\,P_s$
be general distinct points in this space and let $m_1\,\\dots\,m_s$ be pos
itive integers which at least\none of them is greater than one. On the sub
space of those elements of degree $d$ part of the homogeneous ideal $I$ wh
ich vanish at $P_i$ with multiplicity at least $m_i$\, each fat point $m_i
P_i$ defines a specific number of linear relations on this subspace. For a
given set of points $P_i$ with multiplicity $m_i$\, $1\\le i \\le s$\, it
is expected that these linear equations to be linearly independent. If it
is not the case\, then one says that the variety $Z$ admits an unexpected
hypersurface with respect to fat point subscheme defined by these fat poi
nts\, and this linear subspace is called a special linear system on the va
riety $Z$. Each element of this subspace\, defines a hypersurface\, known
as unexpected hypersurface.\nIn this talk\, we review some interesting exa
mples which brought into the scene with this new approach and explain some
existing methods to construct unexpected hypersurfaces.\n\nhttps://zoom.u
s/join\n\nMeeting ID: 9086116889\n\nPasscode: 13440 $\\times$ the number o
f lines on a cubic surface\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takuya Murata (Institute for Research in Fundamental Sciences (IPM
))
DTSTART;VALUE=DATE-TIME:20220412T120000Z
DTEND;VALUE=DATE-TIME:20220412T133000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/10
DESCRIPTION:Title: A map to a toric variety and construction of a toric degeneration\
nby Takuya Murata (Institute for Research in Fundamental Sciences (IPM)) a
s part of IPM Algebraic Geometry Seminar\n\n\nAbstract\nIn the first part
of the talk\, I consider a map to a toric\nvariety\, a generalization of a
map to a projective space (also known\nas a linear system). A torus embed
ding is a special case of such a map\nand thus the notion can be thought o
f as a generalization of a torus\nembedding or\, when the map is flat\, a
generalization of a vector\nbundle on or a covering map of a toric variety
. The work on this part\nis a joint work with Lara Bossinger.\nIn the seco
nd part\, I consider a toric degeneration (= degeneration to\na toric vari
ety) with the focus on a construction of it. Instead of a\ngeneral constru
ction\, I will discuss illustrative examples. Depending\non time\, I will
also discuss some applications of toric degenerations.\n\nhttps://zoom.us/
join\n\nMeeting ID: 9086116889\n\nPasscode: 13440 $\\times$ the number of
lines on a cubic surface\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamid Abban (Loughborough University)
DTSTART;VALUE=DATE-TIME:20220426T120000Z
DTEND;VALUE=DATE-TIME:20220426T133000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/11
DESCRIPTION:Title: What is K-stability?\nby Hamid Abban (Loughborough University) as
part of IPM Algebraic Geometry Seminar\n\n\nAbstract\nK-stability is an al
gebraic notion introduced by Tian and Donaldson to characterise which Fano
manifolds admit a Kähler-Einstein metric. There are various equivalent d
efinitions for K-stability\, amongst them the more recent ones are based o
n valuative criteria and are more useful from a birational point of view.
In this talk\, I will give an introduction to the subject\, from a biratio
nal viewpoint\, and explain some key questions and developments in the fie
ld\, mostly around methods of verifying K-stability. This is based on join
t work with Ziquan Zhuang.\n\nhttps://zoom.us/join\n\nMeeting ID: 90861168
89\n\nPasscode: 13440 $\\times$ the number of lines on a cubic surface\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ciro Ciliberto (University of Rome Tor Vergata)
DTSTART;VALUE=DATE-TIME:20220510T120000Z
DTEND;VALUE=DATE-TIME:20220510T133000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/12
DESCRIPTION:Title: Enumeration in geometry\nby Ciro Ciliberto (University of Rome Tor
Vergata) as part of IPM Algebraic Geometry Seminar\n\n\nAbstract\nEnumera
tion of geometric objects verifying some specific properties is an old and
venerable subject. In this talk I will start by briefly reviewing some
of its history and problems. In the last decades\, enumerative geometry sa
w the flourishing of new problems and underwent a tremendous change of per
spective and a spectacular progress\, with the introduction of extremely r
efined new mathematical ideas and tools which launched unexpected bridges
between different parts of mathematics. This has been due also\, sometimes
mainly\, to the input of questions coming from physics. New insights have
also been provided by discretization methods in algebraic geometry introd
uced by the so--called tropical mathematics\, which\, by the way\, has qui
te interesting applications in phylogenetics. Being impossible to present
all this material in a one hour talk\, I will limit myself to give general
information on some aspects of these topics\, the ones which are closer t
o my own research and (limited) knowledge.\n\nhttps://zoom.us/join\n\nMee
ting ID: 9086116889\n\nPasscode: 13440 $\\times$ the number of lines on a
cubic surface\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Chiantini (University of Siena)
DTSTART;VALUE=DATE-TIME:20220524T120000Z
DTEND;VALUE=DATE-TIME:20220524T133000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/13
DESCRIPTION:Title: Configurations of points and tensor analysis\nby Luca Chiantini (U
niversity of Siena) as part of IPM Algebraic Geometry Seminar\n\n\nAbstrac
t\nI will make an overview on the theory of secant varieties to projective
varieties\,\nstarting with fundamental motivations and basic tools\, and
focusing on\nsome recent developments of the theory. The general pattern
shows that properties of secant varieties\nto X are intimately related wit
h the geometry of its configurations of points\, thus\nwith the intrinsic
geometry of the variety X. The recent awareness of strong connections\nbet
ween the theory of secant varieties and multilinear algebra\nsuggests seve
ral lines of investigations which involve highly sophisticated geometric t
ools\,\nand poses questions on projective loci that represent a challenge
for the\ndevelopment of Algebraic Geometry.\n\nhttps://zoom.us/join\n\nMee
ting ID: 9086116889\n\nPasscode: 13440 $\\times$ the number of lines on a
cubic surface\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hossein Movasati (IMPA)
DTSTART;VALUE=DATE-TIME:20220607T120000Z
DTEND;VALUE=DATE-TIME:20220607T133000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/14
DESCRIPTION:Title: Hodge conjecture\nby Hossein Movasati (IMPA) as part of IPM Algebr
aic Geometry Seminar\n\n\nAbstract\nHodge conjecture is one of the major c
onjectures in complex algebraic geometry which is\n still unsolved. In thi
s talk I will tell my own experience with this conjecture\, why it is hard
even in very \n special cases and what are the implications of this conje
cture. The talk is mainly based on my book: \n A Course in Hodge Theory:
With Emphasis on Multiple Integrals\, Somerville\, MA: International Pres
s Boston\, 2021.\n\nhttps://zoom.us/join\n\nMeeting ID: 9086116889\n\nPass
code: 13440 $\\times$ the number of lines on a cubic surface\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandra Di Rocco (KTH\, Sweden)
DTSTART;VALUE=DATE-TIME:20221018T130000Z
DTEND;VALUE=DATE-TIME:20221018T143000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/15
DESCRIPTION:Title: Geometry of algebraic data\nby Sandra Di Rocco (KTH\, Sweden) as p
art of IPM Algebraic Geometry Seminar\n\n\nAbstract\nIt is often convenien
t to visualize algebraic varieties (and hence systems of polynomial equati
ons) by sampling. The key challenge is to have the right distribution and
density in order to recover the shape\, i.e the topology of the variety. B
ottlenecks are pairs of points on the variety joined by a line which is no
rmal to the variety at both points. These points play a special role in de
termining the appropriate density of a point-sample. Under suitable generi
city assumptions the number of bottlenecks of an affine variety is finite
and is called the bottleneck degree. Estimations of the bottleneck degree
and certain generalizations lead to efficient sampling techniques. We will
show how classical projective algebraic geometry has proven very useful i
n this analysis. The talk is based on joint work with D. Eklund\, P. Edwar
ds\, O. Gäfvert\, J Hauenstein\, M. Weinstein.\n\nhttps://zoom.us/join\n\
nMeeting ID: 9086116889\n\nPasscode: 362880\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farbod Shokrieh (University of Washington\, USA)
DTSTART;VALUE=DATE-TIME:20221101T130000Z
DTEND;VALUE=DATE-TIME:20221101T143000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/16
DESCRIPTION:Title: Heights and moments of abelian varieties\nby Farbod Shokrieh (Univ
ersity of Washington\, USA) as part of IPM Algebraic Geometry Seminar\n\n\
nAbstract\nWe give a formula which\, for a principally polarized abelian v
ariety $(A\, \\lambda)$ over a number field (or a function field)\, relate
s the stable Faltings height of $A$ with the N\\'eron--Tate height of a sy
mmetric theta divisor on $A$. Our formula involves invariants arising from
tropical geometry. We also discuss the case of Jacobians in some detail\,
where graphs and electrical networks will play a key role. (Based on join
t works with Robin de Jong.)\n\nhttps://zoom.us/join\n\nMeeting ID: 908611
6889\n\nPasscode: 362880\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giorgio Ottaviani (University of Florence\, Italy)
DTSTART;VALUE=DATE-TIME:20221115T110000Z
DTEND;VALUE=DATE-TIME:20221115T123000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/17
DESCRIPTION:Title: The Hessian map\nby Giorgio Ottaviani (University of Florence\, It
aly) as part of IPM Algebraic Geometry Seminar\n\n\nAbstract\nIn a joint w
ork with C. Ciliberto we study the Hessian map h_{d\,r} which associates t
o any hypersurface of degree d>=3 in P^r its Hessian hypersurface\, which
is the determinant of the Hessian matrix. We prove that h_{d\,r} is generi
cally finite unless h_{3\,1}\, and in the binary case h_{d\,1} is biration
al onto its image if d>=5\, which is sharp. We conjecture that h_{d\,r} is
birational onto its image unless h_{3\,1}\, h_{4\,1} and h_{3\,2}\, these
exceptional cases were well known in classical geometry.\n\nThe first evi
dence for our conjecture is given by h_{3\,3} (the case of cubic surfaces)
which is again birational onto its image.\n\nhttps://zoom.us/join\n\nMeet
ing ID: 9086116889\n\nPasscode: 362880\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Prokhorov (Steklov Mathematical Institute\, Moscow State Univ
ersity\, Russia)
DTSTART;VALUE=DATE-TIME:20221129T130000Z
DTEND;VALUE=DATE-TIME:20221129T143000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/18
DESCRIPTION:Title: Finite groups of birational transformations\nby Yuri Prokhorov (St
eklov Mathematical Institute\, Moscow State University\, Russia) as part o
f IPM Algebraic Geometry Seminar\n\n\nAbstract\nFirst\, I survey know resu
lts on finite groups of birational transformations of higher-dimensional a
lgebraic varieties. This theory has been significantly developed during th
e last 10 years due to the success of the minimal model program. \nThen
I will talk about finite groups of birational transformations of surface
s\nover fields of positive characteristic.\nIn particular\, I will discuss
a recent result on Jordan property of Cremona groups over finite fields (
joint with Constantin Shramov).\n\nhttps://zoom.us/join\n\nMeeting ID: 908
6116889\n\nPasscode: 362880\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Azizeh Nozad (IPM\, Iran)
DTSTART;VALUE=DATE-TIME:20221220T110000Z
DTEND;VALUE=DATE-TIME:20221220T123000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/20
DESCRIPTION:Title: Serre polynomials and geometry of character varieties\nby Azizeh N
ozad (IPM\, Iran) as part of IPM Algebraic Geometry Seminar\n\n\nAbstract\
nWith G a complex reductive group\, let XrG denote the G-character varieti
es of free group Fr\, of rank r\, and XirrG ⊂ XrG be the locus of irredu
cible representation conjugacy classes. In this talk we shall present a re
sult showing that the mixed Hodge structures on the cohomology groups of X
rSLn and of XrPGLn\, and on the compactly supported cohomology groups of t
he irreducible loci XirrSLn and XirrPGLn are isomorphic\, for any n\,r ∈
N. The proof uses a natural stratification of XrG by polystable type comi
ng from affine GIT and the combinatorics of partitions. In particular\, th
is result would imply their E-polynomials coincide\, settling the question
raised by Lawton-Muñoz. This is based on joint work with Carlos Florent
ino and Alfonso Zamora.\n\nhttps://zoom.us/join\n\nMeeting ID: 9086116889\
n\nPasscode: 362880\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Laface (University of Concepción (Chile))
DTSTART;VALUE=DATE-TIME:20230215T140000Z
DTEND;VALUE=DATE-TIME:20230215T153000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/21
DESCRIPTION:Title: On effective cones of algebraic surfaces\nby Antonio Laface (Unive
rsity of Concepción (Chile)) as part of IPM Algebraic Geometry Seminar\n\
n\nAbstract\nIt is an open problem to describe the shape of the effective
cone of\nan algebraic surface. Nagata conjecture predicts part of this sha
pe\nwhen the surface is the blow-up of the projective plane at general\npo
ints. More recently Ciliberto and Kouvidakis proved that Nagata\nconjectur
e implies that the two-dimensional effective cone of the\nsymmetric produc
t C_2 of a general\, genus g > 9\, curve C is open on\none side whenever g
is not a square.\nIn this talk I will show that the effective cone of the
blow-up of C_2\nat a general point is non-polyhedral for a general positi
ve genus\ncurve C. This result generalizes previous statements of J.F. Gar
cía\nand G. McGrat about the genus 1 case. To prove the statement we firs
t\nshow that having polyhedral effective cone is a closed property for\nfa
milies of surfaces having the same Picard group and then we prove it\nin t
he hyperelliptic case.\nThis is joint work with Luca Ugaglia.\n\nhttps://z
oom.us/join\n\nMeeting ID: 9086116889\n\nPasscode: 362880\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Hashemi (Isfahan University of Technology (Iran))
DTSTART;VALUE=DATE-TIME:20230301T140000Z
DTEND;VALUE=DATE-TIME:20230301T153000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/22
DESCRIPTION:Title: On the computation of staggered linear bases\nby Amir Hashemi (Isf
ahan University of Technology (Iran)) as part of IPM Algebraic Geometry Se
minar\n\n\nAbstract\nGrobner bases are a powerful tool in polynomial ideal
theory with many applications in various areas of science and engineering
. A Grobner basis is a particular generating set for a given ideal which
represents many useful properties of the ideal. The general theory of Grob
ner bases along with the first algorithm for constructing them were introd
uced by Buchberger in 1965 in his Ph.D. thesis. An staggered linear basis
is indeed a linear basis containing a Grobner basis for a given ideal. Thi
s notion was first introduced by Gebauer and Moller in 1988\, however the
algorithm that they described for computing these bases was not complete.
In this talk\, we first give a brief overview on the theory of Grobner bas
es (as well as of staggered linear bases) and then present a simple algori
thm for computing staggered linear bases.\n\nhttps://zoom.us/join\n\nMeeti
ng ID: 9086116889\n\nPasscode: 362880\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Araujo (IMPA (Brazil))
DTSTART;VALUE=DATE-TIME:20230426T140000Z
DTEND;VALUE=DATE-TIME:20230426T153000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/23
DESCRIPTION:Title: The Calabi problem for Fano threefolds\nby Carolina Araujo (IMPA (
Brazil)) as part of IPM Algebraic Geometry Seminar\n\n\nAbstract\nThe Cala
bi Problem is a formidable problem in the confluence of differential and a
lgebraic geometry. It asks which compact complex manifolds admit a Kähler
-Einstein metric. A necessary condition for the existence of such a metric
is that the canonical class of the manifold has a definite sign. For mani
folds with zero or positive canonical class\, the Calabi problem was solve
d by Yau and Aubin/Yau in the 1970s. They confirmed Calabi's prediction\,
showing that these manifolds always admit a Kähler-Einstein metric. On th
e other hand\, for projective manifolds with negative canonical class\, ca
lled “Fano manifolds”\, the problem is much more subtle: Fano manifold
s may or may not admit a Kähler-Einstein metric. The Calabi problem for F
ano manifolds has attracted much attention in the last decades\, resulting
in the famous Yau-Tian-Donaldson conjecture. The conjecture\, which is no
w a theorem\, states that a Fano manifold admits a Kähler-Einstein metric
if and only if it satisfies a sophisticated algebro-geometric condition\,
called “K-polystability”. In the last few years\, tools from biration
al geometry have been used with great success to investigate K-polystabili
ty. In this talk\, I will present an overview of the Calabi problem\, the
recent connections with birational geometry\, and the current state of the
art in dimension 3.\n\nhttps://zoom.us/join\n\nMeeting ID: 9086116889\n\n
Passcode: 362880\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Cascini (Imperial College London (UK))
DTSTART;VALUE=DATE-TIME:20230524T140000Z
DTEND;VALUE=DATE-TIME:20230524T153000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/24
DESCRIPTION:Title: On the Minimal Model Program for complex foliated varieties\nby Pa
olo Cascini (Imperial College London (UK)) as part of IPM Algebraic Geomet
ry Seminar\n\n\nAbstract\nI will survey some recent developments regarding
the minimal model program for foliations defined over a complex algebraic
variety\, together with some applications towards the study of fibrations
in birational geometry.\n\nzoom.us/join\n\nMeeting ID: 9086116889\n\nPass
code: 362880\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jihun Park (IBS Center for Geometry and Physics\, POSTECH (Korea))
DTSTART;VALUE=DATE-TIME:20230607T100000Z
DTEND;VALUE=DATE-TIME:20230607T113000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/25
DESCRIPTION:Title: Sasaki-Einstein 5-manifolds and del Pezzo surfaces\nby Jihun Park
(IBS Center for Geometry and Physics\, POSTECH (Korea)) as part of IPM Alg
ebraic Geometry Seminar\n\n\nAbstract\nThis talk briefly explains how to f
ind closed simply connected Sasaki-Einstein 5-manifolds from K-stable log
del Pezzo surfaces. It then lists closed simply connected 5-manifolds that
are known so far to admit Sasaki-Einstein metrics. It also presents possi
ble candidates for Sasaki-Einstein 5- manifolds to complete the classifica
tion of closed simply connected Sasaki-Einstein 5-manifolds.\n\nzoom.us/jo
in\n\nMeeting ID: 9086116889\n\nPasscode: 362880\n
LOCATION:https://researchseminars.org/talk/IPMAlgGeom/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lutz Hille (University of Münster (Germany))
DTSTART;VALUE=DATE-TIME:20230510T140000Z
DTEND;VALUE=DATE-TIME:20230510T153000Z
DTSTAMP;VALUE=DATE-TIME:20230921T152524Z
UID:IPMAlgGeom/26
DESCRIPTION:Title: Polynomial invariants for triangulated categories with full exceptiona
l sequences\nby Lutz Hille (University of Münster (Germany)) as part
of IPM Algebraic Geometry Seminar\n\n\nAbstract\nFor a full exceptional se
quence of vector bundles on the projective plane there is a remarkable equ
ation\, the so-called Markov equation\, in terms of the ranks of the three
vector bundles. This equation\, slightly modified\, has been used in a jo
int work with Beineke and Brüstle for cluster mutations for quivers with
three vertices. The aim of this talk is to define the natural generalizati
on for full exceptional sequences with n members. This leads to the notion
of a polynomial invariant\, that is a polynomial in indeterminants x(i\,j
) for i