Coding Theory Seminar
Speaker: Birenjith Sasidharan (IIT Palakkad)
Host: Sudhir R. Ghorpade
Title: Block circulant codes with application to blockchain networks
Time, day and date: 11:00:00 AM - 12:00:00 PM, Monday, July 7
Venue: Ramanujan Hall
Abstract: In this talk, we present a family of [n,k,d] block circulant codes composed of many [n0 << n, k0 << k, d0 < d] local codes and that satisfy two properties: (1) the global code supports distributed decoding of up to (d-1) erasures without a central coordinator, and (2) the local codes support cryptographic verification of code symbols using a commitment scheme. These properties make the code ideal for use in a blockchain protocol that ensures data availability by random sampling - an emerging application of block codes. Compared to the currently used 2D Reed-Solomon (RS) code, the block circulant code achieves a larger fractional distance (d/n), as desired in the protocol, for the same rate (k/n) in the high-rate regime. We will discuss the code's topology, its instantiation using RS codes as local codes, and provide a proof of its minimum distance.

Thesis Defence
Speaker: Utkarsh Tripathi (IIT Bombay)
Host: Srikanth Srinivasan
Title: On the AC0[⊕] Circuit Complexity of the Coin Problem and Variants
Time, day and date: 11:00:00 AM, Wednesday, July 9
Venue: Ramanujan Hall
Abstract: -

Date: 9th July 2025
Venue: Ramanujan Hall
Time: 4:00 pm to 5:00 pm
Host Radhendushka Srivastava

Title: Signal-to-noise ratio aware minimax analysis of sparse linear
regression
Speaker: Shubhangi Ghosh ( Columbia University)

Abstract:

We consider parameter estimation under sparse linear regression – an
extensively studied problem in high-dimensional statistics and compressed
sensing. While the minimax framework has been one of the most fundamental
approaches for studying statistical optimality in this problem, we
identify two important issues that the existing minimax analyses face: (i)
The signal-to-noise ratio appears to have no effect on the minimax
optimality, while it shows a major impact in numerical simulations. (ii)
Estimators such as best subset selection and Lasso are shown to be minimax
optimal, yet they exhibit significantly different performances in
simulations. In this paper, we tackle the two issues by employing a
minimax framework that accounts for variations in the signal-to-noise
ratio (SNR), termed the SNR-aware minimax framework. We adopt a delicate
higher-order asymptotic analysis technique to obtain the SNR-aware minimax
risk. Our theoretical findings determine three distinct SNR regimes:
low-SNR, medium-SNR, and high-SNR, wherein minimax optimal estimators
exhibit markedly different behaviors. The new theory not only offers much
better elaborations for empirical results, but also brings new insights to
the estimation of sparse signals in noisy data.

Commutative Algebra seminar
Speaker: Kabeer Manali Rahul (Australian National University)
Host: Ananthnarayan Hariharan
Title: Metric techniques for triangulated categories
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, July 16
Venue: Ramanujan Hall
Abstract: Neeman has recently introduced certain techniques for triangulated categories which are analogous to notions related to a metric space. These techniques have been used to prove many interesting results in algebraic geometry, including settling several conjectures. In this talk, I will try to give some motivation, and an overview of these techniques. If time permits, I will also talk about some new representability theorems which have been proven using them.

Mathematics Colloquium
Speaker: Amalendu Krishna (Department of Mathematics, UCSB)
Host: Preeti Raman
Title: Some remarks on Kato's ramification theory and applications
Time, day and date: 4:00:00 PM - 5:00:00 PM, Friday, July 18
Venue: Ramanujan Hall
Abstract: Kazuya Kato developed a theory of ramification for henselian discrete valuation fields with arbitrary residue fields which extended the classical ramification theory with perfect residue fields. Kato's definition of his ramification filtration is in general complicated and is often difficult to work with. In a joint work with Subhadip Mazumder, I recently provided a new description of this filtration using sheaf theory. This description has several applications. In this talk, I shall explain this description and show some applications to Brauer groups.

Speaker: Dr. Harsita Srivastava (NIT-J)

Date and Time: Tuesday, 22/07/2025 from 11:00 AM to 12:00 PM

Mode: Online

Google Meet link: https://meet.google.com/bas-tfye-crn

Title:  ANALYSIS OF INITIAL AND BOUNDARY VALUE PROBLEMS FOR NON-IDEAL COMPRESSIBLE FLOWS

Abstract: The talk will explore nonlinear wave phenomena in hyperbolic systems of conservation laws, with a focus on the two-dimensional Riemann problem and transonic flow problem in non-ideal gas models such as the Noble-Abel and van der Waals gases. I will discuss the structure and interaction of elementary waves in 2-D Riemann problems, the impact of real gas effects on wave patterns, and the behavior of sonic-supersonic transitions in steady compressible flows. A significant part of the talk will be devoted to magnetohydrodynamics (MHD) flow with van der Waals gas, where I construct special solutions (e.g., circulatory and spiral flows) and analyze the existence and regularity of sonic-supersonic solutions via hodograph and characteristic decomposition methods. The results provide new insights into flow structures influenced by real gas dynamics and magnetic fields, with implications for theoretical and applied fluid dynamics.

Combinatorics Seminar
Spreaker: Samir Mondal (University of Regina)
Host: Krishnan Sivasubramanian
Title: P-matrix Powers
Time, day and date: 11:00:00 AM – 12:00:00 PM, Tuesday, July 22
Venue: Ramanuajan Hall
Abstract: A P-matrix is a matrix all of whose principal minors are positive. We demonstrate that the fractional powers of a P-matrix are also P-matrices. This insight allows us to affirmatively address a longstanding conjecture raised in [D. Hershkowitz and C.R. Johnson, Spectra of matrices with P-matrix powers, Linear Algebra Appl., 80:159–171, 1986]: It is shown that if Ak is a P-matrix for all positive integers k, then the eigenvalues of A are positive. [In order to study (fractional and integer) powers of a matrix, we will make use of some classical aspects of the theory of matrix functions. Definition 0.1 Let f(z) be a complex function defined and analytic on a domain containing all the eigenvalues of a matrix A ∈ Mn (C). The function of A induced by f, denoted by f[A], is defined by the Cauchy integral formula

,

where Γ is any simple closed curve surrounding all eigenvalues of A and contained in the given domain. If time permits, we will explore this topic in a bit more detail.]

Speaker: Prof Jeff Adler, from American University, USA

Title:  Representations of p-adic groups: Reducing general problems to depth-zero problems.

Abstract:  Suppose that G is a connected reductive group over a nonarchmidean local field F.  The Bernstein decomposition expresses the category of smooth representations of G(F) has a (usually infinite) product of subcategories.  It has long been known that each of these subcategories is equivalent to the category of modules over some algebra.  We will show that, up to isomorphism, only finitely many algebras arise, and will describe their structure.  As a corollary, each such subcategory is equivalent to a category of “depth-zero” representations of a smaller group.  I will not assume that the audience already knows what “depth-zero” means, or why it matters.
 

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.)