APS
Speaker: Lal Bahadur Sahu, IIT Bombay
Host: Sandip Singh
Title: Some infinite families of arithmetic symplectic hypergeometric groups.
Time, day and date: 10:00:00 AM – 11:00:00 AM, Tuesday, September 29
Venue: Room 215
Abstract: In this talk, we construct some of the very first examples of infinite families of arithmetic symplectic hypergeometric groups that do NOT satisfy the arithmeticity criterion of Singh and Venkataramana.
For example, we show that the hypergeometric groups associated to the pairs of polynomials $(x-1)^4P_m(x^{9})$ and $(x^4+x^3+2x^2+x+1)Q_m(x^{9})$, where $P_m$ and $Q_m$ are integral polynomials of degree $2m$ such that the corresponding pair determines a Zariski dense symplectic hypergeometric group, are arithmetic in $\Sp(18m+4)$ for any integer $m\in\N$.

APS
Speaker: Adarsh Gupta, IIT Bombay
Host: Sudarshan R. Gurjar
Title: Line bundle restrictions to Hyperplane sections and their connections to first homology on Affine Varieties.
Time, day and date: 12:30:00 PM – 1:30:00 PM, Tuesday, September 29
Venue: Room 105
Abstract: The broad aim of the talk is to understand line bundles on affine varieties and their restrictions to hyperplane sections. We examine connections between torsion line bundles and units in the coordinate ring and also make connections of these objects with the first homology groups.

APS
Speaker: Amal Das, IIT Bombay
Host: Saikat Mazumdar
Title: Compactness and Stability for the Hardy-Sobolev equation.
Time, day and date: 2:30:00 PM – 3:30:00 PM, Tuesday, September 29
Venue: Ramanujan Hall
Abstract: We will study the Hardy-Sobolev equation with full boundary singularities and critical growth. We will show that blow-up solutions concentrate at a finite number of points on the boundary of the domain, and also show the compactness and stability of the solutions.

APS
Speaker: Amanpreet Singh, IIT Bombay
Host: Saurav Bhaumik
Title: Moduli Field Vs. Field of Definition of projective schemes over $\mathb{C}$
Time, day and date: 4:00:00 PM – 5:00:00 PM, Tuesday, September 29
Venue: Ramanujan Hall
Abstract: In this seminar, we study the moduli field $M(X)$ of projective schemes $X$ and the question of when a projective scheme can be defined over a finite extension of its moduli field.
we study this question for projective schemes whose canonical sheaf is ample or anti-ample, and prove the following main theorem: Let $X$  be a smooth, irreducible projective scheme of finite type over $\mathbb{C}$ and the canonical sheaf $\omega_X$ or the anti-canonical sheaf $\omega_X^{-1}$ is ample, then X can be defined over a finite extension of its moduli field M(X). 
As an immediate consequence, we recover the theorem of Hammer and Herrlich: a smooth projective curve over $\mathbb{C}$ of genus $g \geq  2$ can be defined over a finite extension of its moduli field.

APS
Speaker: Pallab Kumar Sinha, IIT Bombay
Host: Siuli Mukhopadhyay
Title: Discrete Time Chain Binomial Model for Infectious Disease Transmission.
Time, day and date: 4:00:00 PM – 5:00:00 PM, Tuesday, September 29
Venue: Conference Room
Abstract: -