8:00am 


9:00am 


10:00am 


11:00am 
[11:30am] Ramya Dutta : TIFRCAM
 Description:
Speaker: Ramya Dutta (TIFRCAM)
Time: October 14, Friday, 11:30 am
Venue: Room 216
Title: Apriori decay estimates for HardySobolevMaz'ya equations and
application to a BrezisNirenberg problem.
Abstract: In this talk we will discuss some qualitative properties and
sharp decay estimates of solutions to the EulerLagrange equation
corresponding to HardySobolevMazya inequality with cylindrical weight.
Using these sharp asymptotics we will establish a BrezisNirenberg type
existence result for class of $C^1$ sublinear perturbations of the
pHardySobolev equation with cylindrical weight in a bounded domain in
dimensions $n > p^2$ and an appropriate notion of positivity for these
perturbations.


12:00pm 


1:00pm 


2:00pm 


3:00pm 


4:00pm 


5:00pm 
[5:30pm] Parnashree Ghosh, Indian Statistical Institute Kolkata, India
 Description:
Virtual Commutative Algebra Seminar
Speaker: Parnashree Ghosh, Indian Statistical Institute Kolkata, India
Date/Time: 14 October 2022, 5:30pm IST/ 12:00pm GMT /8:00am ET (joining
time 5:20 pm IST)
Gmeet link: meet.google.com/eapqswgxvg [1]
Title: On the triviality of a family of linear hyperplanes
Abstract: Let k be a field, m a positive integer, V an affine
subvariety of $A^{m+3}$ defined by a linear relation of the form $x_1^{
r_1} · · · x_r^{r_m} y = F(x_1, . . . , x_m, z, t),$ A the coordinate
ring of V and $G = X_1^{ r_1} · · · X_r^{r_m} Y  F(X_1, . . . , X_m, Z,
T).$ We exhibit several necessary and sufficient conditions for V to be
isomorphic $A^{m+2}$ and G to be a coordinate in $k[X_1, . . . , X_m, Y,
Z, T],$ under a certain hypothesis on F. Our main result immediately
yields a family of higherdimensional linear hyperplanes for which the
AbhyankarSathaye Conjecture holds.
We also describe the isomorphism classes and automorphisms of integral
domains of type A under certain conditions. These results show that for
each integer d ⩾ 3, there is a family of infinitely many pairwise
nonisomorphic rings which are counterexamples to the Zariski
Cancellation Problem for dimension d in positive characteristic.
This is joint work with Neena Gupta.
For more information and links to previous seminars,
visit the website of VCAS:
https://sites.google.com/view/virtualcommalgebraseminar [2]
Links:

[1] http://meet.google.com/eapqswgxvg
[2] https://sites.google.com/view/virtualcommalgebraseminar


6:00pm 

