Aug-Nov 2019 |
Jan-Apr 2020
Jan-Apr 2020
- Postponed
- Thursday, 2020-Mar-12, 15:30-16:45, Room LH-4
- Speaker: Neelarnab Raha, CMI
- Title: Test ideals for
Gorenstein rings
(continued.)
- Speaker: Nirmal Kotal, CMI
- Title: Briancon-Skoda
theorem, using tight
closure
- Thursday, 2020-Mar-05, 15:30-16:45, Room LH-4
- Speaker: Neelarnab Raha, CMI
- Title: Test ideals for
Gorenstein rings
(continued.)
- Thursday, 2020-Feb-27, 15:30-16:45, Room
LH-4 : No talk
- Thursday, 2020-Feb-27, 15:30-16:45, Room LH-4
- Speaker: Neelarnab Raha, CMI
- Title: Test ideals for
Gorenstein rings
(continued.)
- Thursday, 2020-Feb-20, 15:30-16:45, Room LH-4
- Speaker: Neelarnab Raha, CMI
- Title: Test ideals for
Gorenstein rings
- Thursday, 2020-Feb-13, 15:30-16:45, Room LH-4
- Speaker: Nirmal Kotal, CMI
- Title: Test ideals
(continued.)
- Thursday, 2020-Feb-06, 15:30-16:45, Room LH-4
- Speaker: Nirmal Kotal, CMI
- Title: Test ideals
(continued.)
- Thursday, 2020-Jan-30, 15:30-16:45, Room LH-4
- Speaker: Nirmal Kotal, CMI
- Title: Test elements and
test ideals: definition
and basic properties
- Thursday, 2020-Jan-23, 15:30-16:45, Room LH-4
- Speaker: Dharm Veer, CMI
- Title: Fedder's criterion
- Thursday, 2020-Jan-16, 15:30-16:45, Room LH-4
- Speaker: Dharm Veer, CMI
- Title: F-pure and F-split
rings
- Thursday, 2020-Jan-09, 15:30-16:45, Room LH-4
- Speaker: Dharm Veer, CMI
- Title: Flatness of the
Frobenius endomorphism
Aug-Nov 2019
These are listed reverse-chonologically.
- Monday, 2019-Nov-18, 15:45-16:45, Room
LH-6
- Speaker: Dharm Veer, CMI
- Title: Tate resolutions
(continued.)
- Thursday, 2019-Nov-14, 15:30-17:00, Room
LH-1
- Speaker: Dharm Veer, CMI
- Title: Tate resolutions
- Abstract: Following Tate's
paper 'Homology of
noetherian rings and
local rings (1957)' we
will look at
skew-commutative
differential graded
algebras (Such an
algebra is called an
R-algebra) over a
commutative noetherian
ring R. We will first
show that there always
exists a free resolution
X of the residue class
ring R/I which is an
R-algebra and we will
use these resolutions to
study the algebra
structure of
Tor^R(R/I,R/J).
- Thursday, 2019-Oct-24, 15:30-17:00, Room
LH-1
- Speaker: Kumari Saloni, CMI
- Title: Koszul algebras
(continued.)
- Thursday, 2019-Oct-17, 15:30-17:00, Room
LH-1
- Speaker: Kumari Saloni, CMI
- Title: Koszul algebras
(continued.)
- Thursday, 2019-Oct-10, 15:30-17:00, Room
LH-1
- Speaker: Kumari Saloni, CMI
- Title: Koszul algebras
- Abstract: Koszul algebra is
a graded K-algebra R
whose residue field K
has a linear free
resolution as an
R-module. From certain
point of views, Koszul
algebras behave
homologically as
polynomial rings. To
check that an algebra is
Koszul is usually a
difficult task. We will
discuss some methods in
this direction.
- Thursday, 2019-Sep-12, 15:30-17:00, Room
LH-1
- Speaker: Aditya Subramaniam, CMI
- Title: Newton-Okounkov
bodies
(continued.)
- Thursday, 2019-Sep-05, 15:30-17:00, Room
LH-1
- Speaker: Aditya Subramaniam, CMI
- Title: Newton-Okounkov
bodies
(continued.)
- Wednesday, 2019-Sep-04, 15:30-17:00, Room
LH-1
- Speaker: Aditya Subramaniam, CMI
- Title: Newton-Okounkov
bodies
(continued.)
- Thursday, 2019-Aug-29, postponed to
2019-Sep-04
- Thursday, 2019-Aug-22, 15:30-17:00, Room
LH-1
- Speaker: Aditya Subramaniam, CMI
- Title: Newton-Okounkov
bodies
(continued.)
- Thursday, 2019-Aug-08, 15:30-17:00, Room
LH-1
- Speaker: Aditya Subramaniam, CMI
- Title: Newton-Okounkov
bodies
(continued.)
- Thursday, 2019-Aug-01, 15:30-17:00, Room
801
- Speaker: Aditya Subramaniam, CMI
- Title: Newton-Okounkov
bodies
- Abstract:
The theory of
Newton-Okounkov bodies,
also called as Okounkov
bodies, is a
new connection between
algebraic geometry and
convex geometry.
Okounkov
bodies were first
introduced by Andrei
Okounkov, in a
construction
motivated by a question
of Khovanskii concerning
convex bodies governing
multiplicities of
representations.
Kaveh-Khovanskii and
Lazarsfeld-Mustata
have generalized and
systematically developed
Okounkov's
construction,
showing the existence of
convex bodies which
capture much of the
asymptotic
information about the
geometry of (X, D) where
X is an algebraic
variety
and D is a big divisor.
The main goal of these
lectures is to
understand Okounkov's
construction
given by
Lazarsfeld-Mustata and
give applications to
Seshadri Constants.
References:
- Robert
Lazarsfeld
and
Mircea
Mustata,
Convex
bodies
associated
to
linear
series,
Ann.
Sci. Ec.
Norm.Super.(4)
42
(2009),
no.5,
783-835.
- Kiumars Kaveh
and A.G.
Khovanskii,
Newton-Okounkov
bodies,
semigroups
of
integral
points,
graded
algebras
and
intersection
theory,
Ann. of
Math
(2)176
(2012),
no.2,
925-978.
- Alex Kuronya
and
Victor
Lozovanu,
Geometric
aspects
of
Newton-Okounkov
Bodies,
Phenomenological
approach
to
algebraic
geometry,
137-212,
Banach
Center
Publ.,116,
Polish
Acad.
Sci.
Inst.
Math.,
Warsaw,2018.