• Machine Learning and Predicting Clinical Outcomes 

  Chandrani Kumari (IMSc, 2025)
• Pre- and Postselected Measurements, and Uncertainty Relations [HBNI Th258] 

  Sahil (The Institute of Mathematical Sciences, 2025)

  In this thesis, we focus on two well-connected topics: quantum measurement and quan- tum uncertainty relation. The first topic is the well-known “pre- and postselected mea- surements”. Aharonov, Bergmann, and Lebowitz ...
• On combinatorial models for q-Whittaker and modified Hall–Littlewood polynomials [HBNI Th257] 

  Ratheesh T V (The Institute of Mathematical Sciences, 2025)

  This thesis is structured into two distinct parts. The first part addresses two special cases of a conjecture proposed by Ayyer, Mandelshtam, and Martin concerning a bijection between two different combinatorial models for ...
• On holomorphy and special values of Artin L-functions [HBNI Th256] 

  Dhananjaya Sahu (The Institute of Mathematical Sciences, )

  In this thesis, we investigate holomorphy and special values of Artin L-functions. Let K/F be a Galois extension of number fields with Galois group G. Artin conjectured that Artin L-functions associated to non-trivial ...
• Rare events in cluster-cluster aggregation [HBNI Th255]  

  Subashri V (The Institute of Mathematical Sciences, 2024)

  To summarize, we developed a biased Monte Carlo algorithm to compute probabili- ties of rare events in irreversible cluster-cluster aggregation for an arbitrary collision kernel. In particular, the algorithm measures P (M, ...
• Cohomology of Generalized Dold Manifolds [HBNI Th254] 

  Manas Mandal (Institute of Mathematical Sciences, 2024)

  A Dold manifold is defined as the quotient space Sm × CP n /∼, where (s, L) ∼ (−s, L̄). These manifolds were first introduced by Albrecht Dold in 1956 to construct generators in odd dimensions for Thom’s unoriented cobordism ...
• Computational data-driven investigation of chemical exposome and its links to human and ecosystem health [HBNI Th253] 

  Ajaya Kumar Sahoo (Institute of Mathematical Sciences, 2024)

  Humans and ecosystems are frequently exposed to myriad of chemicals, including those found in consumer products, industrial pollutants, and pesticides, which collectively con- stitute the chemical exposome. These chemicals ...
• Effects of Charged Mutations and Phosphorylation on Binding Pocket Dynamics in Proteins [HBNI Th249] 

  T S Sreevidya (Institute of Mathematical Sciences, 2024)
• Poissonian Pair Correlation in Higher Dimensions [HBNI Th250] 

  Tanmoy Bera (The Institute of Mathematical Sciences, 2024)
• Evolution and its Role in DNA, Centromeres and Speciation [HBNI Th251] 

  S Pavitra (The Institute of Mathematical Sciences, 2024)

• Machine Learning and Predicting Clinical Outcomes 

  Chandrani Kumari (IMSc, 2025)
• Pre- and Postselected Measurements, and Uncertainty Relations [HBNI Th258] 

  Sahil (The Institute of Mathematical Sciences, 2025)

  In this thesis, we focus on two well-connected topics: quantum measurement and quan- tum uncertainty relation. The first topic is the well-known “pre- and postselected mea- surements”. Aharonov, Bergmann, and Lebowitz ...
• On combinatorial models for q-Whittaker and modified Hall–Littlewood polynomials [HBNI Th257] 

  Ratheesh T V (The Institute of Mathematical Sciences, 2025)

  This thesis is structured into two distinct parts. The first part addresses two special cases of a conjecture proposed by Ayyer, Mandelshtam, and Martin concerning a bijection between two different combinatorial models for ...
• On holomorphy and special values of Artin L-functions [HBNI Th256] 

  Dhananjaya Sahu (The Institute of Mathematical Sciences, )

  In this thesis, we investigate holomorphy and special values of Artin L-functions. Let K/F be a Galois extension of number fields with Galois group G. Artin conjectured that Artin L-functions associated to non-trivial ...
• Rare events in cluster-cluster aggregation [HBNI Th255]  

  Subashri V (The Institute of Mathematical Sciences, 2024)

  To summarize, we developed a biased Monte Carlo algorithm to compute probabili- ties of rare events in irreversible cluster-cluster aggregation for an arbitrary collision kernel. In particular, the algorithm measures P (M, ...
• Cohomology of Generalized Dold Manifolds [HBNI Th254] 

  Manas Mandal (Institute of Mathematical Sciences, 2024)

  A Dold manifold is defined as the quotient space Sm × CP n /∼, where (s, L) ∼ (−s, L̄). These manifolds were first introduced by Albrecht Dold in 1956 to construct generators in odd dimensions for Thom’s unoriented cobordism ...
• Computational data-driven investigation of chemical exposome and its links to human and ecosystem health [HBNI Th253] 

  Ajaya Kumar Sahoo (Institute of Mathematical Sciences, 2024)

  Humans and ecosystems are frequently exposed to myriad of chemicals, including those found in consumer products, industrial pollutants, and pesticides, which collectively con- stitute the chemical exposome. These chemicals ...
• Effects of Charged Mutations and Phosphorylation on Binding Pocket Dynamics in Proteins [HBNI Th249] 

  T S Sreevidya (Institute of Mathematical Sciences, 2024)
• Poissonian Pair Correlation in Higher Dimensions [HBNI Th250] 

  Tanmoy Bera (The Institute of Mathematical Sciences, 2024)
• Evolution and its Role in DNA, Centromeres and Speciation [HBNI Th251] 

  S Pavitra (The Institute of Mathematical Sciences, 2024)
• On Multi-Parameter CCR Flows [HBNI Th252] 

  Piyasa Sarkar (The Institute of Mathematical Sciences, 2024)

  An E 0 -semigroup is a semigroup of normal, unital §-endomorphisms of B(H ), where H is an infinite-dimensional separable Hilbert space. Though initially considered only in the one-parameter context, multiparameter E 0 ...
• Demazure Crystal Structure for Flagged Skew Tableaux and Flagged Reverse Plane Partitions [HBNI Th248] 

  Siddheswar Kundu (The Institute of Mathematical Sciences, 2024)

  This thesis is divided into two parts. The first part includes the Demazure crystal structure for flagged reverse plane partitions and flagged skew semi-standard tableaux. The second part addresses the saturation property ...
• Applications of Renormalisation Group in Holography [HBNI Th247] 

  Pavan Dharanipragada (The Institute of Mathematical Sciences, 2024)

  The renormalisation group is a powerful set of ideas that relate physical theories at different length scales. The Polchinski’s exact renormalisation group (ERG) equation is a differential equation that enables us to perform ...
• Elucidating and leveraging design principles towards realistic Boolean models of gene regulatory networks [HBNI Th246] 

  Subbaroyan Ajay (The Institute of Mathematical Sciences, 2024)

  Cells make decisions based on underlying gene regulatory networks (GRNs). GRNs may be modeled as a Boolean network (BN) in which nodes and directed edges represent genes or proteins and their interactions respectively. In ...
• Studies in disease dynamics [HBNI Th244] 

  Farhina Mozaffer (The Institute of Mathematical Sciences, 2023)

  Infectious disease are transmitted by pathogens such as bacteria, viruses and parasites. This thesis describes modeling work on two different diseases: COVID-19 and Malaria. The first wave of COVID-19 reached India at ...
• Exploring Size Complexity and Randomness in the Query Model [HBNI Th245] 

  Yogesh Dahiya (The Institute of Mathematical Sciences, 2024)

  A central goal of computer science is to understand the capabilities and limitations of various computational devices. To understand various computational devices we formalize them using mathematical models called "models ...
• On factorization results for tensor products and twisted characters [HBNI Th243] 

  V Sathish Kumar (The Institute of Mathematical Sciences, 2024)

  1. Let A n⇥n be a symmetrizable generalized Cartan matrix (GCM) and let g be the associated symmetrizable Kac-Moody Lie algebra with a fixed Cartan subalgebra h. Parabolic Verma modules are highest weight modules for g ...
• Aspects of Chiral Symmetries in Holography [HBNI Th242] 

  Nishant Gupta (The Institute of Mathematical Sciences, 2024)

  This thesis explores the derivation of chiral current algebras from different gravita- tional theories, including R1,3 gravity, AdS4 gravity, and 3d conformal gravity. We propose chiral boundary conditions consistent ...
• Haglund’s conjecture and Clebsch-Gordan rule for Macdonald polynomials [HBNI Th241] 

  Aritra Bhattacharya (The Institute of Mathematical Sciences, 2024)

  This thesis is divided in two parts. The rst part is about a conjecture of J. Haglund on expansion of the (normalized) integral form Macdonald symmetric functions in terms of the Schur basis. The second part of the thesis ...
• Arithmetic and analytic aspects of values of L-functions [HBNI Th240] 

  Rashi Sanjay Lunia (The Institute of Mathematical Sciences, 2024)

  The central theme of this thesis is to study some analytic and arithmetic properties of values of L-functions at “special points”. The values of L-functions encode a lot of arithmetic data and are at the heart of several ...

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