


Geometry and topology Seminar
Thursday, 6 April, 2023 at 11.30 am
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Venue: Ramanujan Hall
Host: Rekha Santhanam
Speaker: Kashyap Rajeevsarathy
Affiliation: IISER, Bhopal
Title: Generating the liftable mapping class groups of regular cyclic covers
Abstract: Let $\mathrm{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g \geq 1$. We show that the liftable mapping class group $\mathrm{LMod}_k(S_g)$ of the $k$sheeted regular cyclic cover of $S_g$ is selfnormalizing in $\mathrm{Mod}(S_g)$ and that $\mathrm{LMod}_k(S_g)$ is maximal in $\mathrm{Mod}(S_g)$ when $k$ is prime. Moreover, we establish the existence of a normal series of $\mathrm{LMod}_k(S_g)$ that generalizes a wellknown normal series of congruence subgroups in $\mathrm{SL}(2,\mathbb{Z})$. Furthermore, we give an explicit finite generating set for $\mathrm{LMod}_k{S_g)$ for $g \geq 3$ and $k \geq 2$, and when $(g,k) = (2,2)$. As an application, we provide a finite generating set for the liftable mapping class group of the infinitesheeted regular cyclic covering of $S_g$ for $g \geq 3$ by the infinite ladder surface.
Commutative algebra seminar
Thursday, 6 April 2023 at 4 pm
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Venue: Ramanujan Hall
Host: Tony Puthenpurakal
Speaker: H. Ananthnarayan
Affiliation: IIT Bombay
Title: BoijSoderberg Theory over StandardGraded Rings
Abstract: The BoijSoderberg conjectures, which appeared in 2008, signified a paradigm shift in the study of Betti numbers of graded modules over polynomial rings. In this talk, we identify questions arising from these conjectures, that are relevant over standard graded kalgebras, and some attempts to resolve them.
IPDF extension seminar
Date: 6 April, 5 pm
Venue: Ramanujan Hall
Host: J. K. Verma
Speaker: Suprajo Das, IIT Bombay
Title: Toward Computing the Epsilon Multiplicity