Abstract: Resonances of Riemannian manifolds are often studied with tools
of microlocal analysis. I will discuss some recent results on upper
fractal Weyl bounds for certain hyperbolic surfaces of infinite area,
obtained with transfer operator techniques, which are tools complementary
to microlocal analysis. This is joint work with F. Naud and L. Soares.
Google Meet joining info
Video call link: https://meet.google.com/oua-zdfd-oib
Or dial: (US) +1 406-686-2004 PIN: 869 293 958#
Time:
5:30pm
Description:
Speaker: Dharm Veer, Chennai Mathematical Institute, India.
Date/Time: 25 March 2022, 5:30pm IST/ 12:00pm GMT / 8:00am ET (joining
time 5:15pm IST).
Gmeet link: meet.google.com/uht-oqmy-awd
Title: On Green-Lazarsfeld property $N_p$ for Hibi rings/
Abstract: Let $L$ be a finite distributive lattice. By Birkhoff's
fundamental structure theorem, $L$ is the ideal lattice of its subposet
$P$ of join-irreducible elements. Write $P=\{p_1,\ldots,p_n\}$ and let
$K[t,z_1,\ldots,z_n]$ be a polynomial ring in $n+1$ variables over a field
$K.$ The {\em Hibi ring} associated with $L$ is the subring of
$K[t,z_1,\ldots,z_n]$ generated by the monomials
$u_{\alpha}=t\prod_{p_i\in \alpha}z_i$ where $\alpha\in L$. In this talk,
we show that a Hibi ring satisfies property $N_4$ if and only if it is a
polynomial ring or it has a linear resolution. We also discuss a few
results about the property $N_p$ of Hibi rings for $p=2$ and 3. For
example, we show that if a Hibi ring satisfies property $N_2$, then its
Segre product with a polynomial ring in finitely many variables also
satisfies property $N_2$.
For more information and links to previous seminars, visit the website of
VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar