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.

Speaker: Sumit Chandra Mishra, Department of Mathematics, IIT Indore

Host: Sandip Singh

Title: Ruled residue theorem for function fields

Time, day and date: 4:00 PM - 5:00:00 PM, Tuesday, October 07

Venue: Room No. 215, Mathematics Department

Abstract: Let E be a field with a valuation v. In 1983, Ohm proved that for any extension of v to the rational function field E(X)  in one variable, the corresponding residue field extension is either algebraic or ruled, i.e., it is the rational function field in one variable over a finite extension of the residue field of E. This is called the Ruled Residue Theorem. More generally, one can consider the function field F of a curve over E and ask if for all extensions of v to F, the corresponding residue field extension is either algebraic or ruled? If not, is there any bound on the number of extensions of v to F where this fails? I will mention known results for the function fields of conics. Later on, I will discuss the case of function fields of elliptic curves and hyperelliptic curves( joint work with Prof. Karim J. Becher and Dr. Parul Gupta, and joint work with Dr Parul Gupta, respectively).

All are welcome to attend the seminar.

Mathematics Colloquium
Speaker: Sundaram Thangavelu, Indian Institute of Science, Bangalore
Host: Sanjoy Pusti
Title: On points of contention between two families of operators
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, October 08
Venue: Ramanujan Hall
Abstract: Let $ \mathcal{H} $ be a Hilbert space and $ \mathcal{F}_j, j =1,2 $ two families of bounded linear operators acting on $ \mathcal{H}.$ We say that a vector $ u \in \mathcal{H} $ is a point of contention between $ \mathcal{F}_1$ and $ \mathcal{F}_2 $ if for any $ T \in \mathcal{F}_1 $ and $ S \in \mathcal{F}_2, $ the condition $ Tu = Su $ forces both $ T $ and $ S $ to be contstant multiple of the identity operator. We explain this phenomenon when $ \mathcal{H} $ is either the Labesgue space $ L^2(\R^n) $ or the Fock space $ \mathcal{F}(\C^n).$

Student Seminar
Speaker: Garima Khetawat, IIT Bombay
Host: Santanu Dey
Title: Independence attractors of graphs
Time, day and date: 2:00:00 PM – 2:45:00 PM, Thursday, October 09
Venue: Room 113
Abstract: By an independent set in a simple graph G, we mean a set of pairwise non-adjacent vertices in G. The independence polynomial of G is defined as IG(z) = a0+a1z+a2z 2+ · · · + aβz β , where ai is the number of independent sets in G with cardinality i and β denotes the cardinality of a largest independent set in G, known as the independence number of G. Let Gm denote the m-times lexicographic product of G with itself. The independence attractor of G, denoted by A (G), is defined as A (G) = limm→∞{z : IGm(z) = 0}, where the limit is taken with respect to the Hausdorff metric on the space of all compact subsets of the plane. In this talk, we discuss some results (without proofs) regarding the possibility of independence attractors being circles or line segments.

Student Seminar
Speaker: Aditya Dwivedi, IIT Bombay
Host: Santanu Dey
Title: TBA
Time, day and date: 2:45:00 PM – 3:30:00 PM, Thursday, October 09
Venue: Room 113
Abstract: TBA

Seminar
Speaker: Professor Ori Davidov (Department of Statistics, The University of Haifa)
Host: Siuli Mukhopadhyay
Title: Safe hypotheses testing with application to order restricted inference
Time, day and date: 3:00:00 PM – 4:00:00 PM, Thursday, October 09
Venue: Ramanujan Hall
Abstract: Hypothesis testing problems are fundamental to the theory and practice of statistics. It is well known that when the union of the null and the alternative does not encompass the full parameter space the possibility of a Type III error arises, i.e., the null hypothesis may be rejected when neither the null nor the alternative are true. In such situations, common in the context of order restricted inference, the validity of our inferences may be severely compromised. The study of the geometry of the distance test, a test widely used in constrained inference, illuminates circumstances in which Type III errors arise and motivates the introduction of \emph{safe tests}. Heuristically, a safe test is a test that is free of Type III errors at least asymptotically. A novel safe test is proposed and studied. The new testing procedure is associated with a \emph{certificate of validity}, a pre--test indicating whether the original hypotheses are consistent with the data. Consequently, Type III errors can be addressed in a principled way, and constrained tests can be carried out without fear of systematically incorrect inferences. Although we focus on testing problems arising in order restricted inference, the underlying ideas are more broadly applicable. The benefits associated with the proposed methodology are demonstrated through simulations and analysis of illustrative examples

Commutative Algebra seminar
Speaker: Prof. R. V. Gurjar, TIFR Bombay (Retd.)
Host: Tony Puthenpurakal
Title: Resolution of singularities of algebraic or analytic varieties.
Time, day and date: 4:00:00 PM - 5:00:00 PM, Thursday, October 09
Venue: Ramanujan Hall
Abstract: First I will show how to resolve curve singularities (this must be well-known to many). Then discuss Jung-Hirzebruch argument to get the equation of a surface in three variables in a very simple form, and then resolve its singularities. This will complete the proof of resolution of singularitiies of surfaces. Next I will discuss some easy but useful results about resolution type results (resolution of indeterminacies, principalization, general notion of resolution of singularities, and their relations to each other).