Prof. Sneha Chaubey (IIIT Delhi) will be visiting IIT Bombay on Monday,

28th July. She will deliver a number theory seminar on Monday, 28th July

at 4pm in the Ramanujan Hall. Further details below:

Title: On the distribution of polynomial Farey fractions

Abstract: The notion of classical visibility from the origin has been

generalised by viewing lattice points through curved lines of sight. This

generalisation motivates us to define polynomial Farey fractions. For a

positive integer $Q$, and polynomial $P(x)\in\mathbb{Z}[X]$ with $P(0)=0$,

we define polynomial Farey fractions as

\[\mathcal{F}_{Q,P}:=\left\{\frac{a}{q}: 1\leq a\leq q\leq Q,\ \gcd

(P(a),q)=1\right\}.\] The classical Farey fractions are obtained by

considering $P(x)=x$. In this talk, we will look at the global and local

distribution of the sequence of polynomial Farey fractions via discrepancy

and pair correlation measure, respectively. In particular, restricting the

polynomial Farey denominators to certain subsets of primes yields explicit

estimates of the pair correlation measure.

Statistics and Probability Seminar
Speaker: Dr. Sagnik Nandy (Ohio State University)
Host: Parthanil Roy
Title: Orchestrated Approximate Message Passing: A new way of information integration from multimodal data
Time, day and date: 4:00:00 PM – 5:00:00 PM, Wednesday, July 30
Venue: Ramanujan Hall
Abstract: Integrating information across correlated datasets is a central challenge in many contemporary data analysis problems. Despite numerous methods available for this purpose, the lack of clarity regarding their statistical properties poses significant hurdles to achieving robust statistical inference. In this talk, I shall introduce a novel method
called Orchestrated Approximate Message Passing for integrating information across multiple correlated datasets. This method is both computationally efficient and statistically optimal under a stylized model, and its asymptotic properties enable users to construct asymptotically valid prediction sets. Subsequently, I shall describe how to use the technique to construct cell atlases using multi-modal single-cell data and querying these atlases
with partial molecular features. Finally, I shall present a technique for constructing prediction sets of the multi-modal spectral embeddings from new cells with only one observed modality, utilizing the atlas. (This talk is based on a joint work with Zongming Ma.)

Combinatorics Seminar
Speaker: Himanshu Gupta (University of Regina, SK, Canada)
Host: Krishnan Sivasubramanian
Title: On the eigenvalues of the graphs D(5, q)
Time, day and date: 11:00:00 AM – 12:00:00 PM, Friday, August 1
Venue: Ramanujan Hall
Abstract: In 1995, Lazebnik and Ustimenko introduced the family of q-regular graphs D(k, q), which is defined for any positive integer k and prime power q. The connected components of the graph D(k, q) have provided the bestknown general lower bound on the size of a graph
for any given order and girth to this day. Furthermore, Ustimenko conjectured that the second largest eigenvalue of D(k, q) is always less than or equal to 2√q, indicating that the graphs D(k, q) are almost Ramanujan graphs. In this talk, we will discuss some recent progress on this conjecture. This includes the result that the second largest eigenvalue of D(5, q) is less than or equal to 2√q when q is an odd prime power. This is joint work with Vladislav Taranchuk.