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School of Mathematical Sciences

CeCANT - Prof Abhishek Shah

Number Theory, automorphic forms and representations, L-functions  

Supervisor: Prof Abhishek Shaha 

Research Interest:

Applications are welcome for topic related to Number Theory, automorphic forms and representations, L-functions.

This PhD is in the area of automorphic forms and number theory. Automorphic forms are central objects in the Langlands program, a vast web of theorems and conjectures that connects concepts coming from number theory, representation theory and geometry. The simplest examples of automorphic forms include Dirichlet characters and classical modular forms, both of which have proved to be of profound importance in modern mathematics. More generally, automorphic forms are complex valued functions that can be naturally viewed as vectors inside representations known as automorphic representations. From a different point of view, automorphic forms include (as special cases) eigenfunctions of Laplacians on arithmetic manifolds. This viewpoint allows one to bring in a whole range of additional perspectives coming from analysis, spectral theory and quantum mechanics. 

Automorphic forms and the L-functions attached to them have been key ingredients in the solutions of many famous and difficult problems, such as Wiles’ proof of Fermat’s last Theorem and Duke’s work on the representations of algebraic integers by ternary quadratic forms. There are many interestesting possibilities for PhD problems in this area, related to Siegel modular forms, L-functions, and analytic aspects of automorphic forms and representations

Further information: 
How to apply 
Entry requirements 
Fees and funding

Supervisor: Prof Abhishek Shaha 

Research Interest:

Applications are welcome for topic related to Number Theory, automorphic forms and representations, L-functions.

This PhD is in the area of automorphic forms and number theory. Automorphic forms are central objects in the Langlands program, a vast web of theorems and conjectures that connects concepts coming from number theory, representation theory and geometry. The simplest examples of automorphic forms include Dirichlet characters and classical modular forms, both of which have proved to be of profound importance in modern mathematics. More generally, automorphic forms are complex valued functions that can be naturally viewed as vectors inside representations known as automorphic representations. From a different point of view, automorphic forms include (as special cases) eigenfunctions of Laplacians on arithmetic manifolds. This viewpoint allows one to bring in a whole range of additional perspectives coming from analysis, spectral theory and quantum mechanics. 

 

Automorphic forms and the L-functions attached to them have been key ingredients in the solutions of many famous and difficult problems, such as Wiles’ proof of Fermat’s last Theorem and Duke’s work on the representations of algebraic integers by ternary quadratic forms. There are many interestesting possibilities for PhD problems in this area, related to Siegel modular forms, L-functions, and analytic aspects of automorphic forms and representations

Further information: 
How to apply 
Entry requirements 
Fees and funding

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