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Ramin Takloo-Bighash

Publications and source records attributed to Ramin Takloo-Bighash.

24 records · Page 2Linked to original sources
arXiv2010

An invitation to model-theoretic Galois theory

We carry out some of Galois's work in the setting of an arbitrary first-order theory T. We replace the ambient algebraically closed field by a large model M of T, replace fields by definably closed subsets of M, assume that T codes finite sets, and obtain the fundamental duality of Galois theory matching subgroups of the Galois group of L over F with intermediate extensions. This exposition of a special case of Poizat's "Une théorie de Galois imaginaire." (1983) has the advantage of requiring almost no background beyond familiarity with fields, polynomials, first-order formulae, and automorphisms.

math.LO↗
arXiv2007

Bessel models for $GSp(4)$

Methods of theta correspondence are used to analyze local and global Bessel models for $GSp(4)$ proving a conjecture of Gross and Prasad which describes these models in terms of local epsilon factors in the local case, and the non-vanishing of central critical $L$-value in the global case.

math.NT↗
arXiv2006

Rational points on compactifications of semi-simple algebraic groups

We prove Manin's conjecture concerning the distribution of rational points of bounded height, and its refinement by Peyre, for wonderful compactifications of semi-simple algebraic groups over number fields. The proof proceeds via the study of the associated height zeta function and its spectral expansion.

math.NT↗