Resume

• Definable Combinatorics (Ph.D. Course Project)
  Mentor: Dr. Amit Shekhar Kuber, Department of Mathematics, IIT Kanpur
  - Characterisation of first-order structures exhibiting certain elementary combinatorial properties such as the pigeon hole principle or the counting principles.
  - Defining the Grothendieck ring of a first-order structure in that regard.
  
  

• Higher Topological K-theory (Ph.D. Course Project)
  Mentor: Dr. Amit Shekhar Kuber, Department of Mathematics, IIT Kanpur
  - Defining the K-groups KO(X)and KU(X)of a topological space X and then defining the higher K-groups.
  -Showing that the topological K-theory is a generalised cohomology theory.
  
  

• A Study on Three-Valued Logic (M.Sc. Thesis)
  Mentor: Dr. Mohua Banerjee, Department of Mathematics, IIT Kanpur

–Presentation of a logic system that includes a third value undecidability(1/2) along with truth(1) and falsity(0).
–Discussion of algebra, axiomatisation, semantics along with completeness theorems.

• Sahlqvist Formulas (M.Sc. Course Project)
  Mentor: Dr. Mohua Banerjee, Department of Mathematics, IIT Kanpur
  – Explored a particular class of modal formulae called “Sahlqvist formulas” which has first-order frame correspondents.
  
  

• Elementary and Grothendieck Topos (Joint Project) (M.Sc. Course Project)

Mentor: Dr. Amit Shekhar Kuber, Department of Mathematics, IIT Kanpur
– First explored the concept of sheaves in a topological space X and ultimately defined the category of sheaves on a new type of space called the Grothendieck site.
–Using sub-object classifiers on site and associated sheaf functor concluded that a Grothendieck Topos is an elementary topos, but the converse is not generally true.

• Accessing Inaccessibles (B.Sc. Thesis)
  Mentor: Dr. Sourav Tarafder, Department of Mathematics, St. Xavier’s College (Autonomous), Kolkata
  –Understood the definition of cardinal and ordinal numbers.
  –Understood what inaccessible cardinals are.
  –Showed that the existence of inaccessible cardinals is not provable in ZFC.

–Showed the consistency of ZFC by assuming that there exists an inaccessible cardinal.

• Organising Committee Member of Indian School of Logic and its Applications (ISLA) (Part-I), 2022.

• Students Editorial Body Member of Beacon Volume 6 published at the event 'Analytica' which is a 2-3 day long departmental seminar organised by the Department of Mathematics, St. Xavier's College (Autonomous), Kolkata.

Coding

• Fluent at programming languages like Java, C, C++.

• Quick learner of new programming languages.

• Runners up in a coding event “Exabyte” organized by Dept. of Computer Science of St. Xavier’s College, Kolkata.

Music

• Completed 6th year in 'Sugam Sangeet'.

• Completed 1st year in 'Classical Music'.

• Self-taught cajon and ukulele player.