June 15, 2020 - June 19, 2020
Public Access Category: All |
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- Time:
- 11:00am
- Description:
- Speaker: Debraj Das.
Affiliation: IIT Kanpur.
Title of the talk: Bootstrap Inference in Regression.
Abstract of the talk:
https://drive.google.com/file/d/1DH3CM3_mqVMGlEu90lt9giDP6Qy4XLls/view
Date and Time: Tuesday 16 June 2020, 11.00am.
Meeting link:
https://iitbombay.webex.com/iitbombay/j.php?MTID=me8a0b222c39e84e489a4bf137b3b33d0
Meeting number:
166 274 8342
Password:
X4VgsQCJu44
- Time:
- 3:30pm
- Description:
- 16 June 2020 (Tuesday), 15:30 GMT
Speaker: Nikolaos Tziolas (Cyprus).
Title: Vector fields on canonically polarized surfaces
Abstract: In this talk I will present some results about the geometry of
canonically polarized surfaces defined over a field of positive
characteristic which have a nontrivial global vector field, equivalently
non reduced automorphism scheme, and the implications that the existence
of such surfaces has in the moduli problem of canonically polarized
surfaces.
Zoom link:
https://us02web.zoom.us/j/9918493831?pwd=NzJNWmd5Y2h2eXFqbGpiN3Fva1pYQT09
- Time:
- 6:30pm-7:30pm
- Description:
- Date and Time: 16 June 2020, 6:30 pm IST - 7:30 pm IST (joining time :
6:15 pm IST - 6:30 pm IST)
Google meet link: https://meet.google.com/gkc-hydx-fkn
Speaker: Madhusudan Manjunath, IIT Bombay.
Title: Frobenius numbers.
Abstract: For a natural number $k$, the $k$-th (generalised) Frobenius
number of relatively prime natural numbers $(a_1, \dots, a_n)$ is the
largest natural number that cannot be written as a non-negative integral
combination of $(a_1, \dots, a_n)$ in $k$ distinct ways. We study the
$k$-th Frobenius number from a commutative algebraic perspective. We
interpret the $k$-th Frobenius number in terms of the Castelnuovo-Mumford
regularity of certain modules associated to $(a_1, \dots, a_n)$. We study
these modules in detail and using this study, show that the sequence of
generalised Frobenius numbers form a finite difference progression, i.e. a
sequence whose set of successive differences form a finite set. This talk
is based on a joint work with Ben Smith.
- Time:
- 2:00pm
- Description:
- 18 June 2020 (Thursday), 14:00 GMT
Speaker: Claire Voisin (Paris, France)
Title: Triangle varieties and surface decomposition of hyper-Kahler manifolds
Abstract: In recent years, new constructions of complete families of
polarized hyper-Kahler manifolds have been found starting from Fano
geometry. These hyper-Kahler manifolds also appear as general deformations
of Hilbert schemes of K3 surfaces or O'Grady manifolds. I will introduce
the notion of surface decomposition for a variety X with a nontrivial
Hodge structure on degree 2 cohomology. I will show that this notion is
restrictive topologically, as it implies Beauville-Fujiki type relations.
I will also show the existence of such a surface decomposition for the
general hyper-Kahler manifolds mentioned above. This has interesting
consequences on Beauville's conjecture on the Chow ring of hyper-Kahler
manifolds.
Zoom link:
https://us02web.zoom.us/j/9918493831?pwd=NzJNWmd5Y2h2eXFqbGpiN3Fva1pYQT09
- Time:
- 6:00pm
- Description:
- Speaker: Vivek Mukundan (Unversity of Virginia, USA)
Day and Time: 6:00 p.m. (18:00 hours), Thursday, June 18, 2020
Title: Two themes on Rees Algebra of Ideals.
Abstract: The talk discusses two problems, namely, the Implicitization
problem and the stable Harbourne problem which uses Rees Algebra of ideals
in an essential way. Implicitization problem seeks the equations defining
the closed image of certain rational map. The rational map is defined by a
height two perfect ideals satisfying certain conditions. This translates
to finding the equations defining the special fiber ring.
The second problem relates to finding optimal solution to the containment
problem. The containment problem is about finding the best values of n and
b such that I^{(b)}\subseteq I^n. We discuss the Harbourne conjecture and
various aspects of the containment problem. We then introduce the stable
Harbourne problem and prove classes of ideals giving credence to it.
Videoconferencing will be via webex.
Meeting link:
https://iitbombay.webex.com/iitbombay/j.php?MTID=m982006e853c9c6d003858b79e7767d37
Meeting number: 166 383 6958
Password: pK39MPtDfe3
- Time:
- 6:30pm-7:30pm
- Description:
- Date and Time: 19 June 2020, 6:30 pm IST - 7:30 pm IST (joining time :
6:15 pm IST - 6:30 pm IST)
Google meet link: https://meet.google.com/gkc-hydx-fkn
Speaker: Madhav Nori, University of Chicago.
Title: Intersection multiplicities.
Abstract: Bezout's theorem states that projective curves of degrees a and
b meet in ab points if ''counted properly''. The correct number to count
at a point of intersection is the intersection-multiplicity defined in
Serre's book ''Local Algebra and Intersection-Multiplicity''. The talk,
meant for graduate students, will be an introduction to the subject. The
definitions will be looked at from various angles. This will be followed
by a report on the progress towards Serre's conjectures.