Topology Seminar
Speaker: Dr. Sumanta Das, IIT Bombay
Host: Rekha Santhanam
Title: Proper Homology in the Spirit of Brown’s Proper Homotopy Theory
Time, day and date: 11:45:00 AM – 12:30:00 PM, Monday, October 06
Venue: Ramanujan Hall
Abstract: We construct a proper homology theory for non-compact spaces, inspired by Brown’s proper homotopy theory. This theory satisfies analogues of the Eilenberg–Steenrod axioms in the proper setting and is functorial with respect to proper maps. It captures the behavior of spaces at infinity and aligns naturally with Brown’s proper homotopy groups. This is ongoing joint work with Rekha Santhanam.

Student Seminar
Speaker: Manish Prasad, IIT Bombay
Host: Santanu Dey
Title: Some Correspondence Results
Time, day and date: 2:00:00 PM – 2:45:00 PM, Monday, October 06
Venue: Room 113
Abstract: We will discuss some Correspondence Results-
             i) Between Algebraic sets and Ideals.
             ii) Between morphism and k -algebra homomorphism.

Student Seminar
Speaker: Rohit Jana, IIT Bombay
Host: Santanu Dey
Title: TBA
Time, day and date: 2:45:00 PM, Monday, October 06
Venue: Room 113
Abstract: TBA

Seminar
Speaker: Dr. Divya Kappara, Mathematics Department, IIT Bombay
Host: Siuli Mukhopadhyay
Title: Spatial prediction and risk mapping: a generalized linear model approach with applications to disease modeling
Time, day and date: 4:00:00 PM - 5:00:00 PM, Monday, October 06
Venue: Ramanujan Hall
Abstract: Epidemiological data typically appear as overdispersed count observations sampled from limited spatial locations. This sparsity motivates the use of spatial statistical methods to predict disease burden in unsampled regions while handling non-normality. A central task in disease modeling is to identify high-risk areas where disease counts exceed critical thresholds. Such events can signal conditions under which outbreaks are more likely or sustained transmission may occur. We propose using a generalized linear model approach for predicting spatially referenced count data. The response variable is assumed to be conditioned on a weakly stationary latent spatial process accounting for both overdispersion and spatial correlation structure. The Model estimates are used to generate predictions at new locations, quantify prediction uncertainty, and estimate the odds of threshold exceedance. The uncertainty around the predictions and odds of an outbreak are quantified using resampling methods adapted for spatial data under a GLM setup. We illustrate the proposed method through real data analysis, also studying the effect of varying sampling procedures.