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  • Inverse Galois Problem 
    SHUKLA, ABHISHEK (2016-04)
    In this thesis, motivated by the Inverse Galois Problem, we prove the occurence of Sn as Galois group over any global field. While Hilbert’s Irreducibility Theorem, the main ingredient of this proof, can be proved(for ...
  • Spinorial representations of Lie Groups 
    JOSHI, ROHIT (Dept. of Mathematics, 2016-08)
    We solve the question: which finite-dimensional irreducible orthogonal representations of connected reductive complex Lie groups lift to the spin group? We have found a criterion in terms of the highest weight of the ...
  • Determinants of Representations of Hyperoctahedral Groups 
    GHOSH, DEBARUN (2017-04)
  • Spinorial Representations of Symmetric and Alternating Groups 
    GANGULY, JYOTIRMOY (Dept. of Mathematics, 2019-02)
    Representations of the symmetric groups can be thought of as homomorphisms to the orthogonal group. We give criteria for whether such a representation lifts to the Pin group, which is a two-fold cover of the orthogonal ...
  • Stiefel-Whitney classes of representations of dihedral and symmetric groups 
    BHALERAO, SUJEET (2020-04)
    We compute Stiefel-Whitney classes of irreducible representations of dihedral groups and symmetric groups $S_4$ and $S_5$. We give character formulas for all Stiefel-Whitney classes of representations of the cyclic group ...
  • How many irreducibles are prime? 
    JAIN, YASHI (2022-05)
    In the first course in ring theory, we learn about primes and irreducible elements. An easy proof tells us that if an element is prime then it is irreducible. It is, therefore, very natural to ask the question “How many ...
  • Counting Cores and Bar Cores: From Modular Forms to McKay numbers 
    KHANNA, ADITYA (2022-05)
    In this thesis, we delve into the theory of cores of partitions and tackle two main problems: the enumeration of t-cores and t-bar cores, and the computation of McKay numbers for the symmetric and alternating groups. For ...
  • Stiefel-Whitney Classes of Representations of Some Finite Groups of Lie Type 
    MALIK, NEHA (Dept. of Mathematics, 2022-09)
    Orthogonal representations \pi of a finite group G have invariants w_i(\pi), living in the ith degree cohomology group H^i(G, Z/2Z), called Stiefel-Whitney Classes (SWCs). Their sum is known as the total SWC of \pi. There ...
  • Fibrations over Topological Groups 
    VASISHT, KARTHIK (2023-05)
    This thesis serves three purposes. First, we define Wu classes of representations and compute them for orthogonal representations of cyclic groups. Next, we provide an exposition to simplicial homotopy theory and discuss ...
  • An Excursion in Chern Groups 
    DATTA, SUTIRTHA (2024-05)
    We start with a manifold B. In this project, we are interested in figuring out the multiplicative group generated by the total Chern Classes of all complex vector bundles over B. We call it the "Chern Group" of B and denote ...

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