June 25, 2018 - June 29, 2018
Public Access Category: All |
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- Time:
- 11:30am-12:30pm
- Location:
- Room A1-A2, Ground floor, Mathematics Department
- Description:
- Algebra-Geometry Seminar
Speaker: Prof. Manoj Kummini, CMI Chennai
Title: Singularities of conormal varieties.
VENUE: Room A1-A2, Ground floor, Mathematics Department
Tea: 11.15 am
Seminar time: 11.30-12.30
Date: 27 June, 2018
Abstract: Let X be a complex variety, in the complex affine n-space. The
conormal variety of X can be described using the Jacobian matrix associated
to any finite generating set of the ideal of X. We use this description to
explore some necessary and sufficient conditions for the conormal variety
to have rational singularities.
- Time:
- 3:00pm
- Location:
- Room No. 216, Department of Mathematics
- Description:
- Title: Degree of a boolean symmetric function
Speaker: Rajat Mittal (IITK)
Date-Time: Thursday, June 27, 2018, 3 PM.
Venue: 216, Dept. of Mathematics, IITB
Abstract: Every boolean function $f:{0,1}^n -->{0,1}$ can be represented by a multi-linear polynomial of degree less than or equal to $n$. A boolean function is symmetric if it is invariant under any permutation of the input. We consider the natural question, what is minimum possible degree of a symmetric boolean function on
$n$ variables? Gathen et.al. were able to show that any symmetric boolean function will have degree at least $n-O(n^{.525})$.
We will give a somewhat simplified proof of the result above and show some other consequences of this proof. We will also discuss possible approaches to tackle this question.