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  • Topics in Algebraic K-theory 
    K, ARUN KUMAR (2016-05)
    The objective of this thesis is to study the algebraic K-theory of exact categories. In algebraic K-theory we construct a sequence of groups, called K n , which are invari- ants of a given exact category. We look at two ...
  • Homotopy Type Theory and The Univalent Foundations of Mathematics 
    PRASAD, VARUN (2017-03)
  • Gabber's Presentation Lemma 
    KULKARNI, GIRISH (Dept. of Mathematics, 2020-02)
    Gabber’s presentation lemma is a foundational result in A 1 -homotopy theory. This result can be thought of as an algebro-geometric analog of the tubular neighborhood theorem in differential geometry. Similar to tubular ...
  • Motives of Algebraic Stacks 
    DESHMUKH, NEERAJ (Dept. of Mathematics, 2021-09)
    The study of motives of algebriac stacks was initiated by Bertrand To\"{e}n for Deligne-Mumford stack, and subsequently, developed and extended by various authors to more general alegbraic stacks. There exists considerable ...
  • Infinity Categories 
    MAITY, DIPANKAR (2022-05)
    This text attempts to review and understand the fundamentals of ∞-categories via weak Kan complexes. We develop to some extent the construction of ∞ homs. We find a way to deal with 1-morphisms and equivalences and form ...
  • Topics in Motivic Homotopy Theory 
    YADAV, SURAJ PRAKASH (2022-10)
    In first half of the work we prove the \A^1 connectivity of moduli stack of vector bundles on a curve, as a consequence of which we classify projective bundles on curves upto their \A^1 homotopy type. Based on joint work ...

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