May 2021
Public Access Category: All |
2:30pm» Dipendra Prasad, IIT Bombay- Time:
- 2:30pm - 4:00pm
- Description:
- Title: Homological duality in representation theory.
Speaker: Dipendra Prasad, IIT Bombay.
Date: Sunday, May 2, 2021.
Time: 2.30 - 4:00 pm.
Abstract: The lecture will be an introduction to Grothendieck-Serre
duality in the abstract abelian category (typically modules over
non-commutative rings), due to Orloff and Bondal, and its application
to representation theory. The lecture will have no prerequisite except
knowledge of homological algebra in abelian categories, and the notion
of adjoint functors.
Join Zoom Meeting
https://iitgn-ac-in.zoom.us/j/93097173733?pwd=TE5OMHBjbVhicUJDYWR5Wkp4c1hEdz09
Meeting ID: 930 9717 3733
Passcode: 515959
- Time:
- 5:30pm
- Description:
- Speaker:* Indranath Sengupta, IIT Gandhinagar, Gujarat, India*
Date/Time: *7 May 2021, 5:30pm IST/ 12:00pm GMT / 8:00am EDT* (joining
time 5:15pm IST).
Google meet link: https://meet.google.com/kmy-ozko-jcq
Title: *Some Questions on bounds of Betti Numbers of Numerical Semigroup
Rings*
Abstract: J. Herzog proved in 1969 that the possible values of the first
Betti number (minimal number of generators of the defining ideal) of
numerical semigroup rings in embedding dimension 3 are 2 (complete
intersection and Gorenstein) and 3 (the almost complete intersection). In a
conversation about this work, O.Zariski indicated a possible relation
between Gorenstein rings and symmetric value semigroups. In response to
that, E.Kunz proved (in 1970) that a one-dimensional, local, Noetherian,
the reduced ring is Gorenstein if and only if its value semigroup is
symmetric. A question that remains open to date is whether the Betti
numbers (or at least the first Betti number) of every numerical semigroup
ring in embedding dimension e, are bounded above by a function of e.
In the years 1974 and 1975, two interesting classes of examples were given
by T. Moh and H. Bresinsky. Moh’s example was that of a family of algebroid
space curves and Bresinsky’s examples was about a family of numerical
semigroups in embedding dimension 4, with the common feature that there is
no upper bound on the Betti numbers. Therefore, for embedding dimension 4
and above, the Betti numbers (or at least the first Betti number) are not
bounded above by some “good” function of the embedding dimension e. A
question that emerges is the following: Is there a natural way to generate
such numerical semigroups in arbitrary embedding dimension? In this talk we
will discuss some recent observations in this direction, which is a joint
work of the author with his collaborators Joydip Saha and Ranjana Mehta.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar
- Time:
- 5:30pm
- Description:
- Speaker: Tim Roemer, University of Osnabrueck, Germany
Date/Time: 14 May 2021, 5:30pm IST/ 12:00pm GMT / 8:00am EDT (joining time
5:15pm IST).
Google meet link: https://meet.google.com/xpf-bjoz-waq
Title: Cut and related polytopes in commutative algebra
Abstract: The study of cuts in graphs is an interesting topic in discrete
mathematics and optimization with relations and applications to many other
fields such as algebraic geometry, algebraic statistics and commutative
algebra. Here we focus on cut algebras, which are toric algebras and each
ones is defined by all cuts of a given graph, and similar constructions.
We discuss known and new results as well as open questions related to
algebraic properties of such algebras and their defining ideals.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar
- Time:
- 6:30pm
- Description:
- Speaker: Ravi Rao, Narsee Monjee Institute of Management Studies, Mumbai.
Date/Time: 28 May 2021, 6:30pm IST/ 1:00pm GMT / 9:00am EDT (joining time
6:15pm IST).
Google meet link: https://meet.google.com/rqi-gpas-urn
Title: Some approaches to a question of Suslin
Abstract: In his Helsinki talk in `1978, Suslin asked if a stably free
module of rank d-1 over an affine algebra of dimension d over an
algebraically closed field is free, Here we discuss this question and
explain why it is true when the affine algebra is non-singular, and when
1/d! is in the base field. This is joint work with Jean Fasel and Richard
Swan.
Chairperson: Satya Mandal, University of Kansas, Lawrence, KS.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar.