October 5, 2020 - October 9, 2020
Public Access Category: All |
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- Time:
- 4:00pm-5:00pm
- Description:
- Speaker: Mainak Poddar, IISER Pune
Time: Monday 5th October 4 to 5pm (joining time 3.50pm IST)
Google Meet Link: https://meet.google.com/qvo-kduy-yco
Title: Equivariant splitting of toric principal bundles over projective
spaces.
Abstract: I will describe a classification of torus equivariant principal
G-bundles over a complex nonsingular toric variety where G is a complex
linear algebraic group. I will discuss a connection between their
equivariant automorphisms and equivariant reduction of structure group.
Using this we will show the existence of a torus equivariant splitting of
such a bundle over the projective space of dimension n when G is a
reductive subgroup of GL(r) for r < n. This generalizes a theorem of
Kaneyama on the existence of equivariant splitting of any torus
equivariant vector bundle of rank r < n over a projective space of
dimension n. The talk is based on joint works with Indranil Biswas, Jyoti
Dasgupta, Arijit Dey and Bivas Khan.
- Time:
- 5:30pm
- Description:
- Date/Time: 6 October 2020, 5:30pm IST/ 12:00GMT / 08:00am EDT (joining
time: 5:15 pm IST - 5:30 pm IST)
Google meet link: meet.google.com/wif-eiof-jvd
Speaker: Mrinal Das, ISI Kolkata
Title: Some open problems in projective modules and complete intersections
Abstract: Consider a surjective $k$-algebra ($k$ field) morphism from a
polynomial ring of $n$ variables to a polynomial ring of $m$ variables
over $k.$ Is the kernel generated by $n - m$ elements? Our discussion will
primarily be around this question and its variants.
- Time:
- 7:00pm
- Description:
- Title: Matrix orbit closures and their Hilbert functions.
Speaker: Alex Fink, Queen Mary University of London.
Time: 7pm IST (gate opens 6:45 pm IST).
Google Meet Link: meet.google.com/upg-tmyo-ekw.
Phone: (US) +1 929-266-1977 PIN: 832 926 004#.
Abstract: If an ordered point configuration in projective space is
represented
by a matrix of coordinates, the resulting matrix is determined up to
the action of the general linear group on one side and the torus of
diagonal matrices on the other. We study orbits of matrices under the
action of the product of these groups. The main question is what
properties of closures of these orbits, or quotients in other ambient
spaces, are determined by the matroid of the point configuration. The
main result is that the finely-graded Hilbert function is so
determined in characteristic 0 (we think also in general).
The results of mine in this talk are mostly joint with Andy Berget.
- Time:
- 5:30pm
- Description:
- Date/Time: 9 October 2020, 5:30pm IST/ 12:00GMT / 08:00am EDT (joining
time: 5:15 pm IST - 5:30 pm IST)
Google meet link: meet.google.com/wif-eiof-jvd
Speaker: Sarang Sane, IIT Madras
Title: $K_0$ and ideals
Abstract: We begin by discussing $K_0$ and defining $K_1$ for a ring $R$
and the exact sequence connecting them on localization with respect to a
multiplicative set $S$. More generally, there is a similar localization
exact sequence for an open set $V(I)^c$ of Spec(R) connecting $K_0$ and
$K_1$, and we relate the properties of the ideal $I$ with the intermediate
term in the sequence.