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 self-normalizing 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 well-known 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 infinite-sheeted 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: Boij-Soderberg Theory over Standard-Graded Rings

Abstract:  The Boij-Soderberg 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 k-algebras, 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