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Giuseppe Nozzi, University of L'Aquila, October 9, 2025 h 17:30-Aula Biancofiore, Coppito 1
Iterated Wreath Products in Odd and Zero Characteristic
Abstract: Let p > 2 be a prime and let W_n be the Sylow p-subgroup of Sym(p^n). This group can be realized as the iterated wreath product W_n = \wreath_{i=1}^n Z_p, where Z_p is the cyclic group of order p. We compute both the upper and lower central series of W_n, providing a proof that these two series coincide. We introduce the graded Lie algebra associated with the lower central series of W_n and define a map establishing a correspondence between the group and the Lie algebra, intertwining central series and a special class of normal subgroups with ideals. Next, we investigate the normal subgroups N of W_n. In particular, we prove that if N is contained within the last n-k base subgroups of W_n, then N contains a term of the lower central series with bounded index depending only on k.
Finally, we will show how this construction can be extended to iterated wreath products of domains of characteristic zero.
Giulia Pallotta, University of L'Aquila, October 21, 2025 h 16:30 Aula A1.4, Coppito 0
Freidlin-Wentzell solutions of discrete Hamilton Jacobi equations
Abstract: We study finite irreducible Markov chains on a fixed directed graph with transition rates decaying exponentially in a parameter N. At the exponential scale, as N goes to infinity, the invariant measure satisfies a discrete Hamilton-Jacobi equation, which may admit multiple solutions. We define a notion of discrete viscosity solutions and characterize them geometrically via Lipschitz functions. A distinguished "vanishing viscosity" solution, selected through the matrix tree theorem, provides a combinatorial realization of the minimal action principle from Freidlin and Wentzell’s theory of large deviations, paralleling the weak KAM framework in the discrete setting.
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