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## Research: Number Theory

Number theory is the study of all mathematics arising from the arithmetic of the ordinary integers. It is at once one of the most ancient disciplines, with integral Pythagorean triples appearing on ancient cuneiform tablets which are thousands of years old, and at the same time one of the most active and modern areas of study including the most famous problems of mathematics such as Fermat's Last Theorem, the Twin Primes Conjecture, the Riemann Hypothesis, and the grand system of conjectures known as the Langlands Program. Modern number theory is now also involved in vital applications throughout society including digital communications and security systems.

Research Interests | |
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Mahdi AsgariAssociate Professor |
Ph.D., Purdue, 2000. Number Theory, Automorphic Forms, and L-functions. |

Kwangho ChoiyVisiting Assistant Professor |
Ph.D., Purdue, 2012. Number Theory, Automorphic Forms and Representation Theory. |

Amit GhoshFull Professor |
B.Sc., Imperial College of London; Ph.D., Nottingham, 1981. Analytic number theory, L-functions. |

Anthony KableFull Professor |
B.Sc. (Hon), Australian National University, 1986; M.Sc., Oxford University, 1989; Ph.D., Oklahoma State, 1997. Representation Theory, Number Theory, and Invariant Theory. |

Igor PritskerFull Professor |
B.A., M.S. Donetsk State University, USSR, 1990, Ph.D. University of South Florida, Tampa, FL, 1995. Complex Analysis, Approximation Theory, Potential Theory, Analytic Number Theory and Numerical Analysis. |

A. RaghuramNone |
B.Tech., Indian Institute of Technology at Kanpur, India, 1992. Ph.D., Tata Institute of Fundamental Research, University of Mumbai, India, 2001. Number Theory, Representation Theory and Automorphic Forms. He is interested in the special values of automorphic L-functions. He uses the results and techniques of the Langlands program to prove theorems about special values of various L-functions; these values encode within them a lot of number theoretic infromation. He is also interested in the representation theory and harmonic analysis of p-adic groups. |

David WrightFull Professor |
A.B., Cornell U., 1977; Part III, Cambridge U., 1978; A.M./Ph.D., Harvard, 1982. His primary interest is the study of the properties of algebraic number fields, in particular, those properties (discriminants, class-numbers, regulators) that can be studied with tools from the theory of algebraic matrix groups. This theory dates back to the work of Gauss on the theory of equivalence of binary integral quadratic forms. He also studies the theory of Riemann surfaces and Kleinian groups, a subfield of complex analysis. Surprisingly, many concepts in algebraic number theory have very precise analogues in the theory of surfaces. He is particularly interested in the properties of limit sets of Kleinian groups and in the shape of Teichmuller space, which is a kind of parameter space for Riemann surfaces. SeeIndra's Pearls, (Mumford, Series, Wright). |