APS
Speaker: Aratrika Pandey, IIT Bombay
Host: Ravi Raghunathan
Title: Simultaneous Khintchine theorem in local field of positive characteristic
Time, day and date: 11:45:00 AM – 12:45:00 PM, Wednesday, February 11
Venue: Ramanujan Hall
Abstract: In this talk, we focus on the convergence case of Khintchine's theorem for analytic nonplanar manifolds over local fields of positive characteristic, allowing general approximation functions $\psi$ that are not necessarily monotonic. Our approach is based on the method of counting rational points near manifolds developed by Beresnevich and Yang \cite{BY}. To address the scenario in which $\psi$ is not monotonic, we extend the function field by adjoining an appropriate root. Additionally, in the course of the proof, we establish several new results in the geometry of numbers over function fields, which we believe are of independent interest. If time permits, we will also briefly discuss the divergence case, which deals with lower bounds for counting rational points

Student Seminar
Speaker: Aditya Khambete, IIT Bombay
Host: Suman Kumar Sahoo
Title: Dependence modelling using copulas, and the extension to discrete random vectors.
Time, day and date: 2:00:00 PM – 3:00:00 PM, Wednesday, February 11
Venue: Room 215
Abstract: In this talk we will introduce the notion of copulas to model the dependence in multivariate distributions, discuss how the classical notion fails for discrete multivariate distributions, and then use ideas from Geenens (2020) to extend the idea to multivariate discrete distributions.

Mathematics Colloquium
Speaker: Girish Aras, IIT Bombay (Visiting Faculty)
Host: Radhendushka Srivastava
Title: Introduction to Causal Inference
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, February 11
Venue: Ramanujan Hall
Abstract: I will start with a few examples where confounders disrupt classical inference paradigm and motivate why a causal approach is needed. I will review the basic formalism and central ideas of causal inference such as Neyman’s potential outcomes (counterfactuals) and Don Rubin’s foundational assumptions under which causal inference is possible.

The presentation, though rigorous, should be accessible with minimal knowledge of statistics and probability theory.