August 2021
Public Access Category: All |
4pm» Mathematics Colloquium: Sriknath Srinivasan (Department of Mathematics, IIT Bombay and Department of Computer Science, Aarhus University)- Time:
- 4:00pm
- Description:
- Speaker: Sriknath Srinivasan (Department of Mathematics, IIT Bombay and
Department of Computer Science, Aarhus University)
Title: A Recent Result in Algebraic Complexity Theory
Time, Day and Date: 16:00, Wednesday, August 4.
Abstract: Given a multivariate polynomial P from C[x_1,...,x_n], one
can always write it as a sum of monomials, i.e. a sum of products of
variables. However, for most polynomials, such an expression is very
verbose, and one can ask if more complicated but succinct expressions
can be found. Such expressions can take the form of a sum of products
of sums of variables, or a sum of products of sums of products, and so
on.
The main result here is negative, showing that for some interesting
families of polynomials (e.g. the Determinant), there are no such
"small" expressions.
The aim of the talk is to present the formal statement of the above
result and the motivation behind it, which stems from an algebraic
analogue of the P vs. NP question (due to Valiant). If there is time,
I might even present (part of) the proof, which is short and
elementary, needing only some combinatorial and linear-algebraic
arguments.
Joint work with Nutan Limaye (IITB CSE) and Sébastien Tavenas (Univ.
Grenoble Alpes, Univ. Savoie Mont Blanc).
Join Zoom Meeting
https://zoom.us/j/96441833399?pwd=OWlIcnFabHIzL1Y3ajhlbzhZalhYdz09
Meeting ID: 964 4183 3399
Passcode: 313170
- Time:
- 6:30pm
- Description:
- Speaker: Purna Bangere, University of Kansas, Lawrence, KS, USA.
Date/Time: 6 August 2021, 6:30pm IST/ 1:00pm GMT / 9:00am EDT (joining
time 6:15pm IST).
Google meet link: https://meet.google.com/ffu-vhwk-mjd
Title: Syzygies and Gonality
Abstract: In this talk we will deal with recent results on the so-called
property N_p and M_p. These concern the structure of free resolutions
associated with a very ample line bundle on a projective variety. There
are interesting conjectures and ideas related to the structure of free
resolutions and the intrinsic geometry connected with properties N_p and
M_p. A lot of attention has been paid of property N_p, not so much for
property M_p. In this talk we will describe some new results about
properties M_p for an algebraic surface, some higher dimensional
varieties, and even interesting everywhere non reduced schemes called
carpets.
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: K.-i. Watanabe, Nihon University, Tokyo, Japan.
Date/Time: 13 August 2021, 5:30pm IST/ 12:00pm GMT / 8:00am EDT (joining
time 5:15pm IST)
Google meet link: https://meet.google.com/uxn-zmfu-efa
Title: Inverse polynomials of symmetric numerical semigroups.
Abstract: This is a joint work with Kazufumi Eto (Nippon Institute of
Technology). This work was inspired by the talk of M.E. Rossi (Univ.
Genova) at VCAS on Dec. 1, 2020. Let H be a numerical semigroup and K[H]
be its semigroup ring over any field K. If $H = (n_1,...,n_e)$, we express
$K[H]$ as $K[x_1,...,x_e]/I_H$ and we want to express $K[H]/(t^h)$ by
"Inverse polynomials" of Macaulay. We study the defining ideal of a
numerical semigroup ring K[H] using the inverse polynomial attached to the
Artinian ring $K[H]/(t^h)$ for $h \in H_+.$ I believe this method to
express by inverse polynomials is very powerful and can be used for many
purposes. At present, we apply this method for the following cases. (1) To
give a criterion for H to be symmetric or almost symmetric. (2)
Characterization of symmetric numerical semigroups of small multiplicity.
(3) A new proof of Bresinsky’s Theorem for symmetric semigroups generated
by 4 elements.
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: Mousumi Mandal, IIT Kharagpur, West Bengal, India
Date/Time: 20 August 2021, 5:30pm IST/ 12:00pm GMT / 8:00am EDT (joining
time 5:15pm IST)
Google meet link: https://meet.google.com/dzc-vkzz-iey
Title: Symbolic powers of edge ideals
Abstract: In this talk we discuss about the symbolic powers of edge
ideals of graphs and prove Minh's conjecture for certain classes of
graphs.
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: Jai Laxmi, TIFR, Mumbai, India.
Date/Time: 27 August 2021, 5:30pm IST/ 12:00pm GMT / 8:00am EDT (joining
time 5:15pm IST).
Google meet link: meet.google.com/rtf-kzcg-mmg
Title: Gorenstein ideals of codimension four.
Abstract: We explore spinor coordinates on free resolutions of
codimension four Gorenstein ideals. Our analysis of spinor coordinate
examples shows notable differences between Gorenstein ideals with 4, 6, 7,
and 8 generators compared to those with more generators. Also, we discuss
the codimension four Gorenstein ideals resulting from doubling codimension
three perfect ideals. We see, in particular, the construction of generic
doublings of almost complete intersection perfect ideals of codimension
three.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar