BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Melvin Hochster (University of MIchigan)
DTSTART;VALUE=DATE-TIME:20200721T130000Z
DTEND;VALUE=DATE-TIME:20200721T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/1
DESCRIPTION:Title: Tight Closure\, lim Cohen-Maculay sequences\, content o
f local cohomology\, and related open questions - Part 1\nby Melvin Hochst
er (University of MIchigan) as part of Virtual commutative algebra seminar
\n\n\nAbstract\nThe talks will give multiple characterizations of tight cl
osure\, discuss some of its applications\, indicate connections with the
existence of big and small Cohen-Macaulay algebras and modules\, as well a
s variant notions\, and also explain connections with the theory of conte
nt. There will be some discussion of the many open questions in the area\
, including the very long standing problem of proving that Serre intersect
ion multiplicities have the behavior one expects.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hai Long Dao (The University of Kansas)
DTSTART;VALUE=DATE-TIME:20200724T130000Z
DTEND;VALUE=DATE-TIME:20200724T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/2
DESCRIPTION:Title: Reflexive modules over curve singularities\nby Hai Long
Dao (The University of Kansas) as part of Virtual commutative algebra sem
inar\n\n\nAbstract\nA finitely generated module $M$ over a commutative rin
g $R$ is called reflexive if the natural map from $M$ to $M^{**} = Hom(Hom
(M\,R)\, R)$ is an isomorphism. In understanding reflexive modules\, the c
ase of dimension one is crucial. If $R$ is Gorenstein\, then any maximal C
ohen-Macaulay module is reflexive\, but in general it is quite hard to und
erstand reflexive modules even over well-studied one-dimensional singulari
ties. In this work\, joint with Sarasij Maitra and Prashanth Sridhar\, we
will address this problem and give some partial answers.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melvin Hochster (University of Michigan)
DTSTART;VALUE=DATE-TIME:20200728T130000Z
DTEND;VALUE=DATE-TIME:20200728T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/3
DESCRIPTION:Title: Tight Closure\, lim Cohen-Maculay sequences\, content o
f local cohomology\, and related open questions - Part 2\nby Melvin Hochst
er (University of Michigan) as part of Virtual commutative algebra seminar
\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linquan Ma (Purdue University)
DTSTART;VALUE=DATE-TIME:20200804T130000Z
DTEND;VALUE=DATE-TIME:20200804T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/4
DESCRIPTION:Title: The deformation problem for $F$-injective singularities
\nby Linquan Ma (Purdue University) as part of Virtual commutative algebra
seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Polini (University of Notre Dame)
DTSTART;VALUE=DATE-TIME:20201103T130000Z
DTEND;VALUE=DATE-TIME:20201103T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/5
DESCRIPTION:Title: Core of ideals-I\nby Claudia Polini (University of Notr
e Dame) as part of Virtual commutative algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Polini (University of Notre Dame)
DTSTART;VALUE=DATE-TIME:20201106T130000Z
DTEND;VALUE=DATE-TIME:20201106T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/6
DESCRIPTION:Title: Core of ideals-II\nby Claudia Polini (University of Not
re Dame) as part of Virtual commutative algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jack Jeffries (University of Nebraska)
DTSTART;VALUE=DATE-TIME:20201023T130000Z
DTEND;VALUE=DATE-TIME:20201023T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/7
DESCRIPTION:by Jack Jeffries (University of Nebraska) as part of Virtual c
ommutative algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ken-Ichi Yoshida (Nihon University\, Japan)
DTSTART;VALUE=DATE-TIME:20201117T120000Z
DTEND;VALUE=DATE-TIME:20201117T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/8
DESCRIPTION:Title: Lower bound on Hilbert-Kunz multiplicities and some rel
ated results.\nby Ken-Ichi Yoshida (Nihon University\, Japan) as part of V
irtual commutative algebra seminar\n\n\nAbstract\nIn my talk\, we introduc
e some results of lower bounds on Hilbert-Kunz multiplicities\nfor non-reg
ular local rings. In the later half\, we will discuss the upper bound\non
F-signature.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro De Stefani\, (University of Genoa)
DTSTART;VALUE=DATE-TIME:20200811T120000Z
DTEND;VALUE=DATE-TIME:20200811T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/9
DESCRIPTION:Title: Deformation and stability of F-injective singularities\
nby Alessandro De Stefani\, (University of Genoa) as part of Virtual commu
tative algebra seminar\n\n\nAbstract\nPicking up from the talk given by Li
nquan Ma\, I will discuss some more cases where deformation of F-injectivi
ty is known to hold\, and I will discuss the related notion of m-adic stab
ility. The talk will be based on joint projects with Linquan Ma (deformati
on) and Ilya Smirnov (stability).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Núñez Betancourt (CIMAT\, Mexico)
DTSTART;VALUE=DATE-TIME:20200814T130000Z
DTEND;VALUE=DATE-TIME:20200814T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/10
DESCRIPTION:Title: Splittings and symbolic powers of Ideals\nby Luis Núñ
ez Betancourt (CIMAT\, Mexico) as part of Virtual commutative algebra semi
nar\n\n\nAbstract\nSplittings of Frobenius have been employed to study the
singularities\nand cohomology of rings. In this talk we will employ ideas
inspired by\nthis technique to obtain results of symbolic powers of monom
ial and\ndeterminantal ideals. This is joint work with Jonathan Montaño.\
n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pham Hung Quy (FPT University\, Hanoi -)
DTSTART;VALUE=DATE-TIME:20200818T120000Z
DTEND;VALUE=DATE-TIME:20200818T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/11
DESCRIPTION:Title: Frobenius closure of parameter ideals\nby Pham Hung Quy
(FPT University\, Hanoi -) as part of Virtual commutative algebra seminar
\n\n\nAbstract\nWe discuss recent results about Frobenius closure of param
eter ideals and $F$-singularities as well as the Frobenius test exponent o
f parameter ideals.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arindam Banerjee (RKM Vivekananda Institute\, Belur)
DTSTART;VALUE=DATE-TIME:20200821T120000Z
DTEND;VALUE=DATE-TIME:20200821T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/12
DESCRIPTION:Title: Lyubeznik numbers\nby Arindam Banerjee (RKM Vivekananda
Institute\, Belur) as part of Virtual commutative algebra seminar\n\n\nAb
stract\nLyubeznik numbers are certain Bass numbers of local cohomology mod
ules associated to local rings containing a field. This numerical invarian
ts are known to have many interesting homological\, geometric and topologi
cal properties and have been an active area of research. In this talk we p
lan to give a brief overview of these.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. V. Trung (Hanoi Institute of Mathematics)
DTSTART;VALUE=DATE-TIME:20201020T120000Z
DTEND;VALUE=DATE-TIME:20201020T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/13
DESCRIPTION:Title: Multiplicity sequence and integral dependence\nby N. V.
Trung (Hanoi Institute of Mathematics) as part of Virtual commutative alg
ebra seminar\n\n\nAbstract\nThe first numerical criterion for integral dep
endence was proved by Rees in 1961 which states that two m-primary ideals
$I \\subset J$ in an equidimensional and universally catenary local ring $
(R\, m)$ have the same integral closure if and only if they have the same
Hilbert-Samuel multiplicity. This result plays an important role in Teissi
er's work on the equisingularity of families of hypersurfaces with isolate
d singularities. For hypersurfaces with non-isolated singularities\, one
needs a similar numerical criterion for integral dependence of non-$m$-pri
mary ideals. Since the Hilbert-Samuel multiplicity is no longer defined fo
r non-$m$-primary ideals\, one has to use other notions of multiplicities
that can be used to check for integral dependence. A possibility is the mu
ltiplicity sequence which was introduced by Achilles and Manaresi in 1997
and has its origin in the intersection numbers of the Stuckrad-Vogel algor
ithm. It was conjectured that two arbitrary ideals $I \\subset J$ in an eq
uidimensional and universally catenary local ring have the same integral c
losure if and only if they have the same multiplicity sequence. This talk
will present a recent solution of this conjecture by Polini\, Trung\, Ulri
ch and Validashti.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neena Gupta (Indian Statistical Institute\, Kolkata)
DTSTART;VALUE=DATE-TIME:20200731T120000Z
DTEND;VALUE=DATE-TIME:20200731T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/14
DESCRIPTION:Title: On the triviality of the affine threefold $x^my = F(x\,
z\, t)$ - Part 2\nby Neena Gupta (Indian Statistical Institute\, Kolkata)
as part of Virtual commutative algebra seminar\n\n\nAbstract\nIn this tal
k we will discuss a theory for affine threefolds of the form $x^my = F(x\,
z\, t)$ which will yield several necessary and sufficient conditions for
the coordinate ring of such a threefold to be a polynomial ring. For inst
ance\, we will see that this problem of four variables reduces to the equi
valent but simpler two-variable question as to whether F(0\, z\, t) define
s an embedded line in the affine plane. As one immediate consequence\, on
e readily sees the non-triviality of the famous Russell-Koras threefold $
x^2y+x+z^2+t^3=0$ (which was an exciting open problem till the mid 1990s)
from the obvious fact that $z^2+t^3$ is not a coordinate. The theory on th
e above threefolds connects several central problems on Affine Algebraic G
eometry. It links the study of these threefolds with the famous Abhyankar
-Moh “Epimorphism Theorem” in characteristic zero and the Segre-Nagata
lines in positive characteristic. We will also see a simplified proof of
the triviality of most of the Asanuma threefolds (to be defined in the ta
lk) and an affirmative solution to a special case of the Abhyankar-Sathaye
Conjecture. Using the theory\, we will also give a recipe for constructin
g infinitely many counterexample to the Zariski Cancellation Problem (ZCP)
in positive characteristic. This will give a simplified proof of the spea
ker's earlier result on the negative solution for the ZCP.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vivek Mukundan (Indian Institute of Technoogy Delhi)
DTSTART;VALUE=DATE-TIME:20200825T120000Z
DTEND;VALUE=DATE-TIME:20200825T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/15
DESCRIPTION:Title: Reduction to characteristic $p$ - Part 1\nby Vivek Muku
ndan (Indian Institute of Technoogy Delhi) as part of Virtual commutative
algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vivek Mukundan (Indian Institute of Technoogy Delhi)
DTSTART;VALUE=DATE-TIME:20200828T120000Z
DTEND;VALUE=DATE-TIME:20200828T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/16
DESCRIPTION:Title: Reduction to characteristic $p$ - Part 2\nby Vivek Muku
ndan (Indian Institute of Technoogy Delhi) as part of Virtual commutative
algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matteo Varboro (University of Genoa)
DTSTART;VALUE=DATE-TIME:20200901T120000Z
DTEND;VALUE=DATE-TIME:20200901T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/17
DESCRIPTION:by Matteo Varboro (University of Genoa) as part of Virtual com
mutative algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mandira Mondal (Chennai Mathematical Institute)
DTSTART;VALUE=DATE-TIME:20200904T120000Z
DTEND;VALUE=DATE-TIME:20200904T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/18
DESCRIPTION:by Mandira Mondal (Chennai Mathematical Institute) as part of
Virtual commutative algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irena Swanson (Purdue University)
DTSTART;VALUE=DATE-TIME:20200908T130000Z
DTEND;VALUE=DATE-TIME:20200908T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/19
DESCRIPTION:by Irena Swanson (Purdue University) as part of Virtual commut
ative algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Puthenpurakal (IIT Bombay)
DTSTART;VALUE=DATE-TIME:20200911T120000Z
DTEND;VALUE=DATE-TIME:20200911T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/20
DESCRIPTION:Title: Homological algebra over complete intersections\nby Ton
y Puthenpurakal (IIT Bombay) as part of Virtual commutative algebra semina
r\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Briggs (University of Utah)
DTSTART;VALUE=DATE-TIME:20200915T130000Z
DTEND;VALUE=DATE-TIME:20200915T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/21
DESCRIPTION:Title: On a conjecture of Vasconcelos - Part 1\nby Ben Briggs
(University of Utah) as part of Virtual commutative algebra seminar\n\nAbs
tract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Briggs (Ben Briggs)
DTSTART;VALUE=DATE-TIME:20200918T130000Z
DTEND;VALUE=DATE-TIME:20200918T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/22
DESCRIPTION:Title: On a conjecture of Vasconcelos - Part 2\nby Ben Briggs
(Ben Briggs) as part of Virtual commutative algebra seminar\n\nAbstract: T
BA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunsuke Takagi (University of Tokyo)
DTSTART;VALUE=DATE-TIME:20200922T120000Z
DTEND;VALUE=DATE-TIME:20200922T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/23
DESCRIPTION:by Shunsuke Takagi (University of Tokyo) as part of Virtual co
mmutative algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunsuke Takagi (University of Tokyo)
DTSTART;VALUE=DATE-TIME:20200925T120000Z
DTEND;VALUE=DATE-TIME:20200925T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/24
DESCRIPTION:by Shunsuke Takagi (University of Tokyo) as part of Virtual co
mmutative algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:K. N. Raghavan (Institute of Mathematical Sciences\, Chennai)
DTSTART;VALUE=DATE-TIME:20200929T120000Z
DTEND;VALUE=DATE-TIME:20200929T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/25
DESCRIPTION:Title: Multiplicities of points on Schubert varieties in the G
rassmannian-I\nby K. N. Raghavan (Institute of Mathematical Sciences\, Che
nnai) as part of Virtual commutative algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:K. N. Raghavan (Institute of Mathematical Sciences\, Chennai)
DTSTART;VALUE=DATE-TIME:20201002T120000Z
DTEND;VALUE=DATE-TIME:20201002T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/26
DESCRIPTION:Title: Multiplicities of points on Schubert varieties in the G
rassmannian-II\nby K. N. Raghavan (Institute of Mathematical Sciences\, Ch
ennai) as part of Virtual commutative algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mrinal Das (ISI\, Kolkata)
DTSTART;VALUE=DATE-TIME:20201006T120000Z
DTEND;VALUE=DATE-TIME:20201006T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/27
DESCRIPTION:Title: Some open problems in projective modules and complete i
ntersections\nby Mrinal Das (ISI\, Kolkata) as part of Virtual commutative
algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarang Sane (IIT Madras)
DTSTART;VALUE=DATE-TIME:20201009T120000Z
DTEND;VALUE=DATE-TIME:20201009T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/28
DESCRIPTION:by Sarang Sane (IIT Madras) as part of Virtual commutative alg
ebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kamran Divaani Aazar (IPM\, Tehran)
DTSTART;VALUE=DATE-TIME:20201013T120000Z
DTEND;VALUE=DATE-TIME:20201013T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/29
DESCRIPTION:Title: A survey on the finiteness properties of local cohomolo
gy modules - Part 1\nby Kamran Divaani Aazar (IPM\, Tehran) as part of Vir
tual commutative algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kamran Divaani Aazar (IPM\, tehran)
DTSTART;VALUE=DATE-TIME:20201016T120000Z
DTEND;VALUE=DATE-TIME:20201016T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/30
DESCRIPTION:Title: A survey on the finiteness properties of local cohomolo
gy modules - Part 2\nby Kamran Divaani Aazar (IPM\, tehran) as part of Vir
tual commutative algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Satya Mandal (The University of Kansas)
DTSTART;VALUE=DATE-TIME:20201027T130000Z
DTEND;VALUE=DATE-TIME:20201027T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/31
DESCRIPTION:Title: Quillen $K$-Theory: A reclamation in Commutative Algebr
a - Part 1\nby Satya Mandal (The University of Kansas) as part of Virtual
commutative algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Satya Mandal (The University of Kansas)
DTSTART;VALUE=DATE-TIME:20201030T130000Z
DTEND;VALUE=DATE-TIME:20201030T140000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/32
DESCRIPTION:Title: Quillen $K$-Theory: A reclamation in Commutative Algebr
a - Part 2\nby Satya Mandal (The University of Kansas) as part of Virtual
commutative algebra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amartya Datta (ISI\, Kolkata)
DTSTART;VALUE=DATE-TIME:20201110T120000Z
DTEND;VALUE=DATE-TIME:20201110T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/33
DESCRIPTION:Title: G_a-actions on Affine Varieties: Some Applications - Pa
rt 1\nby Amartya Datta (ISI\, Kolkata) as part of Virtual commutative alge
bra seminar\n\n\nAbstract\nOne of the hardest problems that come up in aff
ine algebraic geometry is to decide whether a certain d-dimensional factor
ial affine domain is ``trivial''\, i.e.\, isomorphic to the polynomial r
ing in d variables. There are instances when the ring of invariants of a s
uitably chosen G_a-action has been able to distinguish between two rings (
i.e.\, to prove they are non-isomorphic)\, when all other known invariants
failed to make the distinction. It was using one such invariant that Mak
ar-Limanov proved the non-triviality of the Russell-Koras threefold\, lead
ing to the solution of the Linearization Problem\; and again\, it was usi
ng an invariant of G_a-actions that Neena Gupta proved the nontriviality o
f a large class of Asanuma threefolds leading to her solution of the Zari
ski Cancellation Problem in positive characteristic.\n\nG_a actions are al
so involved in the algebraic characterisation of the affine plane by M. Mi
yanishi and the algebraic characterisation of the affine 3-space.by Nikhi
lesh Dasgupta and Neena Gupta. Miyanishi's characterisation had led to the
solution of Zariski's Cancellation Problem for the affine plane. Using G
_a-actions\, a simple algebraic proof for this cancellation theorem was o
btained three decades later by Makar-Limanov.\n\nIn this talk (in two part
s)\, we will discuss the concept of G_a-actions along with the above appli
cations\, and the closely related theme of Invariant Theory. The concept o
f G_a-action can be reformulated in the convenient ring-theoretic language
of ``locally nilpotent derivation'' (in characteristic zero) and ``expone
ntial map'' (in arbitrary characteristic). The ring of invariants of a G_a
- action corresponds to the kernel of the corresponding locally nilpotent
derivation (in characteristic zero) and the ring of invariants of an expon
ential map. We will recall these concepts. We will also mention a theorem
on G_a actions on affine spaces (or polynomial rings) due to C.S. Seshad
ri. \n\nWe will also discuss the close alignment of the kernel of a loc
ally nilpotent derivation on a polynomial ring over a field of characteris
tic zero with Hilbert's fourteenth problem. While Hilbert Basis Theorem h
ad its genesis in a problem on Invariant Theory\, Hilbert's fourteenth pr
oblem seeks a further generalisation: Zariski generalises it still furthe
r. The connection with locally nilpotent derivations has helped construct
some low-dimensional counterexamples to Hilbert's problem. We will also me
ntion an open problem about the kernel of a locally nilpotent derivation o
n the polynomial ring in four variables\; and some partial results on it d
ue to Daigle-Freudenburg\, Bhatwadekar-Daigle\, Bhatwadekar-Gupta-Lokhan
de and Dasgupta-Gupta. Finally\, we will state a few technical results on
the ring of invariants of a G_a action on the polynomial ring over a Noeth
erian normal domain\, obtained by Bhatwadekar-Dutta and Chakrabarty-Dasgup
ta-Dutta-Gupta.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amartya Datta (ISI\, Kolkata)
DTSTART;VALUE=DATE-TIME:20201113T120000Z
DTEND;VALUE=DATE-TIME:20201113T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/34
DESCRIPTION:Title: G_a-actions on Affine Varieties: Some Applications - Pa
rt 2\nby Amartya Datta (ISI\, Kolkata) as part of Virtual commutative alge
bra seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shreedevi Masuti (IIT Dharwad)
DTSTART;VALUE=DATE-TIME:20200807T120000Z
DTEND;VALUE=DATE-TIME:20200807T130000Z
DTSTAMP;VALUE=DATE-TIME:20200812T064507Z
UID:VCAS/36
DESCRIPTION:Title: Normal Hilbert coefficients and blow-up algebras\nby Sh
reedevi Masuti (IIT Dharwad) as part of Virtual commutative algebra semina
r\n\n\nAbstract\nThe normal Hilbert coefficients are important numerical i
nvariants associated with an \nideal in an analytically unramified local
ring. They play an important role in determining \nthe homological propert
ies of the blow-up algebras. This will be an expository talk on the \nnorm
al Hilbert coefficients\, and its relation with blow-up algebras. We will
also discuss \nrecent developments on this topic.\n
END:VEVENT
END:VCALENDAR