In this paper we present a new and elementary approach for proving the main results of Katz (1996) using the Jordan-Pochhammer matrices of Takano and Bannai (1976) and Haraoka (1994). We nd an… (More)

Using the middle convolution functor MCχ which was introduced by N. Katz we prove the existence of rigid local systems whose monodromy is dense in the simple algebraic group G2. We derive the… (More)

In [6], a purely algebraic analogon of Katz’ middle convolution functor (see [10]) is given. In this paper, we find an explicit Riemann-Hilbert correspondence for this functor. This leads to a… (More)

In [9], a purely algebraic analogon of Katz’ middle convolution functor (see [12]) is given. It is denoted by MCλ. In this paper, we present a cohomological interpretation of MCλ and find an explicit… (More)

We study 4-dimensional Galois representations attached to Siegel modular forms. In some cases we determine the images of the absolute Galois group. This yields Galois realizations over Qfor… (More)

We relate the theory of the middle convolution functor MCλ to the study of algebraic solutions of the sixth Painlevé equation PVI. We interprete some recently found algebraic solutions by Boalch in… (More)

We give a list of Heun equations which are Picard-Fuchs associated to families of algebraic varieties. Our list is based on the classification of families of elliptic curves with four singular fibers… (More)

In this article we find connections between the values of Gauss hypergeometric functions and the dimension of the vector space of Hodge cycles of four dimensional cubic hypersurfaces. Since the Hodge… (More)

Let G be a reductive algebraic group over C and let X be a smooth quasiprojective complex variety. Let us call a representation ρ : π1(X) → G to be G-rigid, if the set theoretic orbit of the… (More)