Number Theory seminar
Speaker: Dr. Sourabh Das, IIT Bombay
Host: Keshav Aggarwal
Title: An effective version of Chebotarev’s density theorem
Time, day and date: 11:30:00 AM – 12:30:00 PM, Monday, August 24
Venue: Ramanujan Hall
Abstract: Chebotarev’s density theorem asserts that the prime ideals are equidistributed among the conjugacy classes of the Galois group of any normal extension of number fields. An effective version of this theorem was first established by Lagarias and Odlyzko in 1977. In this talk, we present an explicit refinement of their statement that applies to all non-rational fields, with every implicit constant expressed explicitly in terms of the field invariants. Additionally, we provide a sharper bound for extensions of sufficiently small degree.

We describe the main analytic tools that lead to our results, including an explicit formula for a smoothed prime ideal counting function, zero-free regions for Dedekind zeta functions, and precise bounds for sums over the non trivial zeros of Dedekind zeta-functions. We further explain how these ingredients improve upon and differ from previous approaches in the literature.

This is joint work with Habiba Kadiri and Nathan Ng (University of Lethbridge, Canada). The preprint is available on arXiv at https://arxiv.org/abs/2508.09480.

Statistics/Probability Lecture Series
Speaker: Prof. Arindam Chatterjee, ISI Delhi
Host: Debraj Das
Title: Stein's method and its application to networks – Lecture 1
Time, day and date: 12:00:00 PM – 1:00:00 PM, Tuesday, August 25
Venue: Ramanujan Hall
Abstract: https://drive.google.com/file/d/1toQxgC_BAP_N0cVQ3FZkzD7Ta-f4D5U9/view?usp=sharing

Statistics/Probability Lecture Series
Speaker: Prof. Arindam Chatterjee, ISI Delhi
Host: Debraj Das
Title: Stein's method and its application to networks – Lecture 2
Time, day and date: 5:00:00 PM – 6:00:00 PM, Tuesday, August 25
Venue: Ramanujan Hall
Abstract: https://drive.google.com/file/d/1toQxgC_BAP_N0cVQ3FZkzD7Ta-f4D5U9/view?usp=sharing

Statistics/Probability Lecture Series
Speaker: Prof. Arindam Chatterjee, ISI Delhi
Host: Debraj Das
Title: Stein's method and its application to networks – Lecture 3
Time, day and date: 12:00:00 PM – 1:00:00 PM, Thursday, August 27
Venue: Ramanujan Hall
Abstract: https://drive.google.com/file/d/1toQxgC_BAP_N0cVQ3FZkzD7Ta-f4D5U9/view?usp=sharing

Talk
Speaker: Dr. Malavika
Host: Kummari Mallesham
Title: Distribution properties of some prime-indexed sequences, and exponential sums
Time, day and date: 3:00:00 PM – 4:00:00 PM, Thursday, August 27
Venue: Online (https://meet.google.com/csu-bknh-kkc)
Abstract: https://drive.google.com/file/d/1TlEUxi-1UOpnKF1Q_FfX645OJcIbjvnW/view?usp=sharing

Special Colloquium
Speaker: Jean-Marc Schlenker, University of Luxembourg
Host: Sanjoy Pusti
Title: Polyhedra inscribed in a quadric in Euclidean space
Time, day and date: 3:45:00 PM - 4:45:00 PM, Thursday, August 27
Venue: Ramanujan Hall
Abstract: Steiner asked in 1832: what are the possible combinatorial types of polyhedra with vertices on a quadric in R^3? We will review recent results on this question, as well as questions that are still open. The main results are based on the geometry of ideal polyhedra in the 3-dimensional hyperbolic or anti-de Sitter space, or in more exotic geometric spaces that we will also describe. Based on joint work with Hao Chen, Jeff Danciger and Sara Maloni.

Statistics/Probability Lecture Series
Speaker: Prof. Arindam Chatterjee, ISI Delhi
Host: Debraj Das
Title: Stein's method and its application to networks – Lecture 4
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, August 27
Venue: Ramanujan Hall
Abstract: https://drive.google.com/file/d/1toQxgC_BAP_N0cVQ3FZkzD7Ta-f4D5U9/view?usp=sharing

IPDF progress seminar
Speaker: Dr. Manabendra Giri, IIT Bombay
Host: Sutanu Roy
Title: Quantum Unitary Groups with Complex Deformation Parameters
Time, day and date: 4:30:00 PM – 5:30:00 PM, Friday, August 28
Venue: Ramanujan Hall
Abstract: In this talk, I want to discuss a family of quantum unitary groups associated with complex deformation parameters. I begin with the construction of the quantum unitary group $U_{q,\Phi}(n)$, extending the construction of Zhang and Zhao for $n=2$ to higher dimensions. I show that $U_{q,\Phi}(n)$ admits the structure of a compact quantum group in the sense of Woronowicz.

I then focus on the case $n=3$ and study the irreducible $*$-representations of the corresponding $C^*$ algebra $C(U_{q,\Phi}(3))$.It is possible to describe these representations in terms of irreducible representations of the rotational $C^*$-algebra generated by three unitaries.

Finally, I consider the crystalized algebra $C(U_{0,\Phi}(3))$ and investigate its $*$-irreducible representations.