November 16, 2020 - November 20, 2020
Public Access Category: All |
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- Time:
- 4:00pm-5:00pm
- Description:
- Speaker: Roy Skjelnes, KTH, Stockholm
Time: Monday 16th November 4 to 5pm (joining time 3.45 pm IST)
Google Meet Link: https://meet.google.com/qvo-kduy-yco
Title: Classification of smooth Hilbert schemes.
Abstract: The Hilbert scheme parametrizing closed subschemes in a fixed
projective n-space having Hilbert polynomial p is a projective scheme.
Each such polynomial p can be described in terms of an integer partition,
and this can then be used to classify which Hilbert schemes are smooth.
The corresponding subschemes parametrized are described by a
generalization of partial flags. I will try to explain the classification
result and the underlying geometry. These new results are based on a joint
work with Greg Smith.
- Time:
- 6:30pm
- Description:
- Date/Time: 17 November 2020, 6:30pm IST/ 1:00pm GMT/ 8:00am EDT (joining
time: 6:15 pm IST - 6:30 pm IST)
Speaker: Giulio Caviglia, Purdue University, USA
Google meet link: meet.google.com/gyc-baih-xas
Title: The Eisenbud-Green-Harris Conjecture
Abstract: The $f$-vector of a simplicial complex is a finite sequence of
integers defined by the number of $i$-dimensional faces of the complex.
All possible such vectors are completely characterized thanks to a
classical theorem by Kruskal and Katona. This result, when rephrased in
terms of Hilbert functions of certain quotients of polynomial rings by
monomial ideals, extends the celebrated theorem of Macaulay on
lexicographic ideals.
The Eisenbud-Green-Harris conjecture is a further generalization of both
the Kruskal-Katona theorem and the well-known Cayley–Bacharach theorem for
plane curves. I will survey the known results on this conjecture including
a recent joint work with Alessandro De Stefani.
- Time:
- 4:00pm
- Description:
- Date and Time: Wednesday, 18 November, 04.00pm
Speaker: Anik Roy
Title: Testing Independence among random vectors based on Univariate Test
Abstract: The problem of testing independence of random vectors has
received increased attention in recent years. There are lots of method for
testing independence among univariate random variables and also random
vectors. In this presentation we carry out a test of Independence for
random vectors
based on univariate test.
Google Meet Link: https://meet.google.com/rxi-ebqz-qhy
- Time:
- 5:30pm
- Description:
- Date/Time: 20 November 2020, 5:30pm IST/ 12:00 GMT/ 7:00am EDT (joining
time: 5:15 pm IST - 5:30 pm IST)
Speaker: Parangama Sarkar, IIT Palakkad, India
Google meet link: meet.google.com/gyc-baih-xas
Title: Frobenius Betti numbers of finite length modules
Abstract: Let $(R, m)$ be a Noetherian local ring of dimension $d > 0$ and
$M$ be a finitely generated $R$-module of finite length. Suppose char R =
$p > 0$ and $d = 1.$ De Stefani, Huneke and Núńez-Betancourt explored the
question: what vanishing conditions on the Frobenius Betti numbers force
projective dimension of $M$ to be finite. In this talk we will discuss the
question for $d ≥ 1.$ This is joint work with Ian Aberbach.