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A difference field is a field with a distinguished automorphism. Automorphisms of a finite field are powers of the Frobenius map. In this talk, I will discuss how to estimate the number of rational po...
Caporaso and Harris derive recursive formulas counting nodal plane curves of degree d and geometric genus g in the plane (through the appropriate number of xed general points). We rephrase their ar...
Abstract: In this paper we describe the characters of irreducible objects in category O for the rational Cherednik algebra associated to GL_2(F_p) over an algebraically closed field of positive charac...
Abstract: We study rational Cherednik algebras over an algebraically closed field of positive characteristic. We first prove several general results about category O, and then focus on rational Chered...
Over the years, finite automata have been used effectively in the theory of infinite groups to represent rational subsets.
In 2007, B. Poonen (unpublished) studied the p{adic closure of a subgroup of rational points on a commutative algebraic group. More recently, J. Bellache asked the same question for the special case...
In this paper, we describe the irreducible representations in category O of the rational Cherednik algebra H_c(G_12,h) associated to the complex reflection group G_12 with reflection representation h ...
We derive explicit formulas for the Mellin transform and the distribution of the exponential functional for Levy processes with rational Laplace exponent. This extends recent results by Cai and Kou o...
The asymptotic behavior (such as convergence to an equilibrium, convergence to a 2-cycle, and divergence to infinity) of solutions of the following multi-parameter, rational, second order difference e...
For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically recon- structs the true ...
In a classical work of the 1950’s, Lee and Yang proved that thezeros of the partition functions of a ferromagnetic Ising models always lie on the unit circle. Distribution of these zeros is physically...
We describe an algorithm for distinguishing hyperbolic compo-nents in the parameter space of quadratic rational maps with a periodic critical point. We then illustrate computer images of the hyperboli...
Let X be a Mori dream space together with an effective torus action of complexity one. In this note, we construct a polyhedral divisor DCox on a suitable finite covering of P1 which corresponds to the...
If G is a finite ℓ-group acting on an affine space An over a finite field K of cardinality prime to ℓ, Serre [29] shows that there exists a rational fixed point. We generalize this to the ...
We study the Dunkl-Opdam subalgebra of the rational Cherednik algebra for wreath products at t = 0, and use this to describe the block decomposition of restricted rational Cherednik algebras for G(m,...

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