#### Overview

We are organizing a weekly seminar, Meet-in-the-Middle, from 18th August 2021. This seminar is held on each Wednesday from 16:00. The aim of this seminar is to create the diversification of the knowledge and to share and explore new research ideas in Computer Science and Mathematics among the researchers and the students. Each week, a designated speaker from IAI (Faculties and Students) or from other institutes will be delivering the talk. A prior notice about the topic is intimated a week before the talk.

Co-ordinator: Dr. Avijit Dutta (avijit.dutta@tcgcrest.org).

https://us06web.zoom.us/j/81203195437?pwd=eEY1V0szZmpxWHo0czlPTERHcWxrdz09

Meeting ID: 823 6262 7024
Passcode: 502333

#### Upcoming Talk (on 29/03/2023)

• Affiliation: Postdoctoral Fellow at Ben-Gurion University of the Negev, Israel
• Title: Towards a noncommutative theory of Cowen-Douglas class of noncommuting operators
• Abstract: The classical Cowen-Douglas class of (commuting tuples of) operators possessing an open set of (joint) eigenvalues of finite constant multiplicity was introduced by Cowen and Douglas generalizing the backward shifts. Their unitary equivalence classes are determined by equivalence classes of certain hermitian holomorphic vector bundles associated to them on this set, and as emphasized in the work of Curto and Salinas, they are modelled by the adjoints of the multiplication operators by the independent variable(s) on a reproducing kernel Hilbert space. Our goal is to develop a free noncommutative analogue of the Cowen-Douglas theory aiming to understand the notion of noncommutative vector bundles. We define the noncommutative Cowen–Douglas class using matrix joint eigenvalues as envisioned by Taylor and use the Taylor-Taylor series of free noncommutative function theory to show that the joint eigenspaces together constitute — in a natural sense — a noncommutative hermitian holomorphic vector bundle. If time permits, we also discuss noncommutative reproducing kernel Hilbert space models and the noncommutative Gleason problems.

#### All Previous Talks

• Speaker: Sagnik Nandy
Affiliation: University of Pennsylvania
Date: 11/01/2023
Title: Orchestrated AMP: A novel way of Data Integration
Abstract: In modern-day data science, we are faced with the dilemma of integrating data carrying information about the same latent parameters but coming from multiple sources. In this talk, we shall see how a novel technique called the Orchestrated Approximate Message Passing introduced by Ma and Nandy (2021) can be leveraged to perform such data integration optimally. We shall consider two different settings. In the first setting, we shall consider the task of recovering a latent community assignment of $n$ vertices from $m$ different interaction networks between them with different connectivity patterns and a set of correlated Gaussian feature vectors for each of the vertex. We shall see how our Orchestrated Approximate Message Passing algorithm can be used to perform this task of recovering the communities, optimally. Next, we shall explore a linear regression problem where the feature vectors are indexed by an undirected network. The smoothness of the regression parameters is characterized by the connectivity pattern of the observed network. Such data is common in several biological applications (Li and Li (2010)). The traditional approach to combine the linear model with such network side information is to use penalized least squares with a penalty on the Laplacian of the observed network (Li and Li (2010), Tran et. al. (2022)). However, such methods are extremely slow in high dimensions and not provably optimal. We apply the Orchestrated Approximate Message Passing algorithm to this problem and the resulting solution is shown to vastly outperform the traditional penalized estimators in terms of the reconstruction error. Our method is also extremely fast compared to the existing methods and provably Bayes optimal in the proportional asymptotic regime when $n/p \rightarrow c \in (0,1)$. This talk is based on two joint projects with Zongming Ma and Subhabrata Sen.

• Speaker: Debsoumya Chakraborti
Affiliation: Post Doctoral Fellow at Institute for Basic Sciences (IBS), South Korea
Title: Colorful combinatorics
Abstract: There have been extensive studies on the following question: given $k$ graphs $G_1,\dots, G_k$ over a common vertex set of size $n$, what conditions on $G_i$ ensure a \textit{rainbow} copy of $H$, i.e., a copy of $H$ with at most one edge from each $G_i$? In the first half of this talk, we will survey some results on this topic. Joos and Kim showed that for $k=n$, the condition that each $G_i$ has minimum degree at least $n/2$ confirms a rainbow Hamiltonian cycle. This generalizes the classical Dirac’s theorem. In the second half, we will discuss our recent rainbow generalizations of some results on embedding oriented Hamiltonian cycles in tournaments.

• Speaker: Prof. Mridul Nandi
Affiliation: Professor, ISI Kolkata
Date: 09/11/2022
Title: A Brief Overview of Streaming Algorithm

Affiliation: Post Doctoral Fellow, IAI, TCG CREST
Date: 02/11/2022
Title: Random Walk-steered Majority Undersampling

Abstract: This paper proposes Random Walk-steered Majority Undersampling (RWMaU), an undersampling approach to address the class imbalance problem for binary classifiers. RWMaU is focused to find the majority points which lie at the overlapped region of the minority and the majority classes. Such points meddle with the learning and detection of the minority points. RWMaU uses random walks to mark the majority points satisfying the above characteristic in a non-parametric fashion. For each majority point, a proximity score is calculated on the basis of — their visit frequencies and the order of visits of the majority points in the random walks. This score is used to perceive the closeness of the majority class points to the minority class. The majority points lying close to the minority class are subsequently undersampled. Empirical evaluations on 21 datasets using 3 classifiers demonstrate substantial improvement in the performance of RWMaU over existing methods for addressing class imbalance and show that it is an efficient and effective way to address class imbalance in binary classification problems.

• Speaker: Dr. Arun Maiti
Affiliation: Post Doctoral Fellow, IIT Bombay
Date: 12/10/2022
Title: Cohomology of unordered flag manifolds
Abstract: The (complex and real) complete flag manifolds are important objects in algebraic topology and geometry. The cohomology of these spaces is well known. Viewing complete flags as ordered bases, we obtain unordered complete flag manifolds by forgetting the ordering of the bases. Motivated by questions arising in algebraic topology and Banach geometry, we (jointly with Lorenzo Guerra) study the cohomology of the later spaces. In this talk, I will present a method for computing the mod-2 cohomology and obtain a complete description of the cohomology of these spaces in lower orders. A few of the important applications of our work will also be discussed.

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• Speaker: Dr. Navnath Daundkar
Affiliation: Post Doctoral Fellow, IIT Bombay
Date: 28/09/2022
Title: Moduli spaces of polygonal linkages via cellular surgery
Abstract: The planar polygon space (or the moduli space of a polygonal linkage) with generic side lengths is a smooth, closed manifold. It is known that these spaces contain the real points of the moduli space of genus-zero curves as a dense subset; hence are a compactification. Kapranov showed that the real points of the Deligne-Mumford-Knudson compactification can be obtained from the projective Coxeter complex of type A by blowing up along the minimal building set. In this talk, we show that the planar polygon spaces can also be obtained from the projective Coxeter complex of type A, but, by performing iterative cellular surgery along a subcollection of the minimal building set. Interestingly, this sub-collection is encoded by a combinatorial data associated with the length vector called its genetic code. This is a joint work with Priyavrat Deshpande.

• Speaker: Dr. Mrinal Nandi
Affiliation: Assistant Professor, Department of Statistics, West Bengal State University
Date: 21/09/2022
Title: Some Applications of Algebra and the concept of Symmetry

• Speaker: Dr. Avisek Gupta
Affiliation: Post Doctoral Fellow, IAI – TCG CREST
Date: 10/08/2022
Title: Machine Learning under Weak Supervision: Reducing the cost of labelling data

Affiliation: Post Doctoral Fellow, EIMI and SPbU, Saint Petersburg.
Date: 27/07/2022
Title: Crossings in Geometric Hypergraphs

• Speaker: Dr. Aranya Lahiri
Affiliation: SEW Visiting Assistant Professor at UC San Diego
Date: 06/07/2022
Title: Irreducibility of rigid analytic vectors in p-adic principal series representations.
Abstract: For the $L$-rational points $G:=\mathbb{G}(L)$ of a p-adic reductive group, let  $Ind^G_B(\chi)$  be the continuous p-adic principal series representations. Here $L$ is a finite extension of $\mathbb{Q}_p$,  $B$ is the borel subgroup corresponding to a maximal torus $T$ and $\chi$ is a character of $T$. We will consider the globally analytic vectors of the pro-p Iwahori group  $I$ in the principal series representations.  This is done by endowing the pro-p Iwahori with a $p$-valuation and subsequently giving it structure of a rigid analytic group. We will talk about topological irreducibility of these globally analytic vectors under certain assumptions on $\chi$. This is a generalization of works of Clozel ($GL_2$ case) and Ray in the case of $G:= GL_n(L)$ . This is joint work with Claus Sorensen.

• Speaker: Dr. Benjamin Wesolowski
Affiliation: CNRS researcher (Chargé de Recherche), Institut de Mathématiques de Bordeaux (IMB), France
Date: 22/06/2022
Title: Hard Problems for Isogeny-based Cryptography
Abstract: Isogeny-based cryptography is one of the few branches of public-key cryptography that promises to resist quantum attacks. The security of these cryptosystems relates to the (presumed) hardness of a variety of computational problems: finding paths in large “isogeny graphs”, computing endomorphisms of elliptic curves, or inverting group actions. We present these problems, and analyse how they relate to each other: which are equivalent, easier, or harder, and how they relate to cryptosystems.

• Speaker: Dr. Tanmay Basu
Affiliation: Assistant Professor, IISER Bhopal
Date: 15/06/2022
Topic: Role of NLP for Information Extraction from Unstructured Biomedical Text
Abstract: Natural Language Processing (NLP) is the process of using computer algorithms to identify, analyze and derive key elements in unstructured text in a smart and effective way. With the widespread use of online social media and electronic health records (EHRs), unstructured text is a veritable gold mine, and NLP is the best way to extract value from these resources. Some recent research works and scopes of further works regarding the potential of NLP for information extraction from the unstructured biomedical text will be discussed.

• Speaker: Daniel Vallieres
Affiliation: Assistant Professor, California State University Chico
Date: 01/06/2022
Title: Iwasawa theory and graph theory
Abstract: In the 1950s, Iwasawa proved his celebrated theorem on the growth of the p-part of the class number in Zp-extensions of number fields, and this discovery sparked the study of various arithmetic objects such as class groups and selmer groups in infinite towers of number fields.  Recently, similar phenomena have emerged in the context of graph theory where infinite towers of number fields are replaced with infinite towers of graphs.  In this talk, I will explain the basic objects of study in this area and depending on the time I will present some results obtained in this direction in collaboration with either Kevin McGown, or Antonio Lei, or still Sage DuBose.

• Speaker: Dr. Luca De Feo
Affiliation: Research Staff Member, IBM Research Europe
Date: 25/05/2022
Title: Isogeny graphs for cryptography
• Speaker: Prof. Steven Galbraith
Affiliation: Head, Mathematics Department, Cyber Security Foundry, University of Auckland
Date: 18/05/2022
Title:  Isogeny based cryptography and zero-knowledge proofs of isogeny

• Speaker: Mr. Cédric Dion
Affiliation: Ph.D. student at Université Laval
Date: 11/05/2022
Title: Arithmetic statistics for 2-bridge links

• Speaker: Dr. Debanjana Kundu
Affiliation: PIMS Postdoctoral Fellow at UBC, Vancouver
Date: 04/05/2022
Title: Introduction to the theory of elliptic curves and Iwasawa theory

• Speaker: Dr Angsuman Das
Affiliation: Assistant Professor, Presidency University, Kolkata
Date: 27/04/2022
Title: Groups and Graphs

• Speaker: Dr. Apratim Chakraborty
Affiliation: Post Doctoral Fellow, IAI TCG CREST
Date: 06/04/2022
Title: Elsers conjecture and the topology of U-nucleus complex

• Speaker: Prof. Prasant Mohapatra
Affiliation: Professor, Vice Chancellor for Research at University of California, Davis (UC Davis)
Date: 04/04/2022
Title: Vulnerabilities in Federated Learning Networks

Affiliation: Professor, Head of Mathematics Department, Presidency University
Date: 17/03/2022
Title: Practical Attacks on a Class of Secret Image Sharing Schemes: Few Open Issues

• Speaker: Dr. Angshul Majumdar
Affiliation: Associate Professor, IIIT Delhi
Date: 16/03/2022
Title: Deep Learning based Clustering

• Speaker: Dr. Debolina Ghatak
Affiliation: Post-Doctoral Fellow at IAI, TCG CREST
Date: 09/03/2022
Title: Inference from Private Microdata

• Speaker: Mr. Arka Banerjee
Affiliation: Final year Ph.D. student at the University of Wisconsin-Milwaukee
Date: 02/03/2022
Title: Obstruction to coarse embedding

• Speaker: Dr. Avik Chakraborti
Affiliation: Lecturer in Computer Science (E&R), University of Exeter.
Date: 23/02/2022
Title: A Brief Introduction to White-box Cryptography

• Speaker: Dr. Ruhul Amin
Affiliation: Assistant Professor, Computer and Information Sciences Department, Fordham University
Date: 16/02/2022
Title: Homology Based Sequence Annotation Algorithms

• Speaker: Bibhas Chandra Das
Affiliation: Research Scholar, IAI – TCG CREST
Date: 09/02/2021
Title: Dynamic Symmetric Searchable Encryption for Conjunctive Queries

• Speaker: Dr. Dipayan Das
Affiliation: Post Doctoral Fellow, CISPA-Helmholtz Center for Information Security
Date: 29th December 2021
Title: Digital Signatures from ID scheme: Lattice Challenges & Open Problems

• Speaker: Dr. Satrajit Ghosh
Affiliation: Assistant Professor, IIT Kharagpur
Date: 22nd December 2021
Title: In search for sub-linear PSI protocols

• Speaker: Mr. Anirban Sanyal
Affiliation: Department of Economics, UCSC
Date: 17th December 2021
Title: Forecasting with Real Time Information

• Speaker: Dr. Kuldeep Saha
Affiliation: Post Doctoral Fellow, IAI TCG CREST, Kolkata
Date: 08th December 2021
Title: Persistent Homolgy and Data Analysis
Abstract:  In recent times, various tools from algebraic topology are  being heavily applied to tackle problems in data analysis. Persistent homology, for the past two decades, has been one of the main tools. We shall  talk about the basics of persistent homology and some of its applications.

• Speaker: Prof. Mridul Nandi
Affiliation: Professor, Indian Statistical Institute, Kolkata
Date: 01st December 2021
Title: Some Indifferentiable Attacks on Cryptographic Designs

• Speaker: Dr. Kaushik Chakraborty
Affiliation: Senior Research Associate, University of Edinburgh, UK
Date: 24th November 2021
Title: How to Secure your Cryptosystem with Key-Recycling even if P=NP

Affiliation: Post Doctoral Fellow, IAI, TCG CREST
Date: 17th November 2021
Title of the talk: Open set classification – when you predict more than what you learn

Affiliation: Professor, IAI, TCG CREST
Date: 10th November 2021
Title of the talk: A Learning Experience in Performance Improvement of High Throughput Wireless Access Networks

• Speaker: Mr. Arijit Shaw
Affiliation: Junior Research Fellow, IAI, TCG CREST
Date: 22nd October 2021
Title of the talk: CrystallBall: Gazing in the Black Box of SAT Solving

• Speaker: Prof. Rana Barua
Affiliation: Visiting Scientist, IAI, TCG CREST
Date: 22nd September 2021
Title of the talk: On the equation $RX^2+SY^2\equiv 1\bmod N$ and its application to Cryptography
Abstract: We shall look at attempts at solving the congruence and how it has been used in constructing certain cryptographic primitives.

Affiliation: Professor at Indian Statistical Institute, Bangalore
Date: 15th September 2021
Title of the talk: Quantum Mechanics- Looking back after 100 years

• Speaker: Dr. Prasenjit Majumder
Affiliation: Professor at DAIICT, Gandhinagar and Visiting Scientist at IAI, TCG-CREST.
Date: 8th September 2021
Title of the talk: Natural Language Processing: Miles to go