February 2021
Public Access Category: All |
5:30pm» Vijaylaxmi Trivedi, TIFR, Mumbai, India- Time:
- 5:30pm
- Description:
- Speaker:* Vijaylaxmi Trivedi, TIFR, Mumbai, India*.
Date/Time: *5 February 2021, 5:30pm IST/ 12:00pm GMT/ 7:00am EST* (joining
time: 5:15 pm IST - 5:30 pm IST).
Google meet link: https://meet.google.com/vnc-vhqp-axj.
Title: *Hilbert-Kunz density function and its applications*.
Abstract: In this talk, we recall the notion of Hilbert-Kunz density
function for graded rings. This function was introduced to understand the
Hilbert-Kunz multiplicity which is a difficult characteristic $p$
invariant
to compute and to make speculation about its properties. It turns out the
HK density function is also related to another characteristic
$p$-invariant
namely $F$-threshold. Here we describe its properties and give its
applications to HK multiplicity, $F$-thershold and to a conjecture of
Watanabe-Yoshida. The talk is partly based on a joint work with K.I.
Watanabe.
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: Graham Leuschke, Syracuse University, New York, USA.
Date/Time: 12 February 2021, 6:30pm IST/ 1:00pm GMT/ 8:00am EST (joining
time: 6:15 pm IST - 6:30 pm IST).
Google meet link: https://meet.google.com/mkx-gcmp-axf.
Title: Matrix Factorizations and Knörrer Periodicity.
Abstract: A matrix factorization of a ring element $f$ is a pair of square
matrices so that the product (in either order) is diagonal with $f$ in
each diagonal entry. These were introduced by Eisenbud in 1980. When the
ring is regular, matrix factorizations of $f$ correspond to maximal
Cohen-Macaulay modules over the hypersurface defined by $f$. This talk
will give an overview of the theory of matrix factorizations, ending with
some recent generalizations to factorizations by more than two matrices.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar.
- Time:
- 2:00pm
- Description:
- Date and Time: Wednesday, 17th February 2021 at 2 PM
Google Meet Link: https://meet.google.com/zif-jpge-ybc?hs=122&authuser=1
Speaker: Sagar Kalane, IISER Pune
Title: Classification of pairs of quaternionic and complex hyperbolic
isometries
Abstract:
Consider the Lie groups G=SU(n, 1) and Sp(n, 1) that act as isometries
of the complex and the quaternionic hyperbolic spaces respectively. In
this talk, we will classify pairs of semisimple elements in Sp(n, 1) and
SU(n, 1) up to conjugacy. This gives local parametrization of the
representations ρ in deformation space Hom(F2, G)/G such that both
ρ(x) and ρ(y) are semisimple elements in G, where F2 =
- Time:
- 6:30pm
- Description:
- Speaker:* Bernd Ulrich, Purdue University, West Lafayette, IN, USA*
Date/Time: *19 February 2021, 6:30pm IST/ 1:00pm GMT/ 8:00am EST* (joining
time: 6:15 pm IST - 6:30 pm IST)
Google meet link: https://meet.google.com/kav-pjey-rir
Title:* Generalized multiplicities and integral dependence*
Abstract: The talks will give a survey about multiplicity based criteria
for the integral dependence of ideals. This subject has close connections
with equisingularity theory and intersection theory, which will be
discussed as well. The first numerical criterion for integral dependence
was proved in the 1960s by Rees who treated the case of zero-dimensional
ideals using the Hilbert-Samuel multiplicity. Criteria for arbitrary
ideals require generalized notions of multiplicities. We will discuss
various such
notions and talk about how they are used to detect integral dependence. The
most recent results are from joint work with Claudia Polini, Ngo Viet
Trung, and Javid Validashti.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar.