8:00am 


9:00am 


10:00am 


11:00am 


12:00pm 


1:00pm 


2:00pm 


3:00pm 


4:00pm 


5:00pm 
[5:30pm] Matteo Varbaro, University of Genoa
 Description:
 Date and Time: Tuesday 1st September 2020, 5:30 pm IST  6:30 pm IST
(joining time : 5:15 pm IST  5:30 pm IST)
Google Meet link: https://meet.google.com/yqumvvyjrs
Speaker: Matteo Varbaro, University of Genoa
Title: Fsplittings of the polynomial ring and compatibly split
homogeneous ideals
Abstract: A polynomial ring R in n variables over a field K of positive
characteristic is Fsplit. It has many Fsplittings. When K is a perfect
field every Fsplitting is given by a polynomial g in R with the monomial
u^{p1} in its support (where u is the product of all the variables)
occurring with coefficient 1, plus a further condition, which is not
needed if g is homogeneous (w.r.t. any positive grading). Fixed an
Fsplitting s : R > R, an ideal I of R such that s(I) is contained in I
is said compatibly split (w.r.t. the Fsplittings). In this case R/I is
Fsplit. Furthermore, by Fedder’s criterion when I is a homogeneous ideal
of R, R/I is Fsplit if and only if I is compatibly split for some
Fsplitting s : R > R. If, moreover, u^{p1} is the initial monomial of
the associated polynomial g of s w.r.t. some monomial order, then in(I) is
a squarefree monomial ideal… In this talk I will survey these facts (some
of them classical, some not so classical), and make some examples,
focusing especially on determinantal ideals.


6:00pm 

7:00pm 
[7:00pm] Amritanshu Prasad: IMSc, Chennai
 Description:
 The speaker is
Prof. Amritanshu Prasad from IMSc, Chennai. The following are the
details.
Title: Polynomials as Characters of Symmetric Groups.
Time: 7pm, Tuesday, September 1, 2020 (gate opens at 6:45pm).
Google meet link: meet.google.com/prmfeowzwm.
Phone: (US) +1 7402393129 PIN: 706 683 026#
Abstract: Treating the variable $X_i$ as the number of $i$cycles in a
permutation allows a polynomial in $X_1, X_2,\dotsc$ to be regarded as a
class function of the symmetric group $S_n$ for any positive integer $n$.
We present a simple formula for computing the average and signed average
of such a class function over the symmetric group. We use this formula to
investigate the dimension of $S_n$invariant and $S_n$signequivariant
vectors in polynomial representations of general linear groups.
This talk is based on joint work with Sridhar P Narayanan, Digjoy Paul,
and Shraddha Srivastava. Some of these results are available in the
preprint available at: http://arxiv.org/abs/2001.04112.

