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ArticleKatz, Daniel J.Consider the Weil sum , where is a finite field of characteristic , is the canonical additive character of , is coprime to , and . We say that is threevalued when it assumes precisely three distinct values as runs through : this is the minimum number . . .

ArticleFuller, TerryWe show that there are homeomorphisms of closed oriented genus surfaces which are fiberpreserving with respect to an irregular branched covering and isotopic to the identity, but which are not fiberisotopic to the identity.

ArticleSivic, KlemenWe show that for all $ k\ge 1$ there exists an integer $ N(k)$ such that for all $ n\ge N(k)$ the $ k$th order jet scheme over the commuting $ n\times n$ matrix pairs scheme is reducible. At the other end of the spectrum, it is known that for all $ k . . .

ArticleStevenson, Katherine F.Recently, it has been shown by Harbater and Stevenson that a profinite group G is free profinite of infinite rank m if and only if G is projective and mquasifree. The latter condition requires the existence of m distinct solutions to certain embeddin . . .

ArticleHarbater, DavidWe study the properties of the fundamental group of an affine curve over an algebraically closed field of characteristic p from the point of view of embedding problems. In characteristic zero the fundamental group is free, but in characteristic p it i . . .

ArticleSethuraman, BharathLet n = pab ,w here pis a prime, and g.c.d. (p;b )=1 . In P n 2 1 , let Xr be the variety dened by rank ((xi;j)) n r. We show that any subvariety of Xr of codimension less than par must have degree a multiple of p. We also show that the bounds on the . . .

ArticleCandel, AlbertoThis paper gives an upper bound for the first eigenvalue of the universal cover of a complete, stable minimal surface in hyperbolic space, and a sharper one for least area disks.

ArticleD'Orsogna, MariaRita R.We introduce a twovariable lattice model to describe conflict within communities. Our model includes polarization and radicalization of individuals, each of which harbors a continuous belief variable and a discrete radicalization level describing the . . .

ArticleLi, Yi LiFor a class of twopoint boundary value problems we prove exactness of an Sshaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities like for [formula].

Conference paper or proceedingsLi, Yi LiWe study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities. We obtain sharp bounds for h such that the equation has exactly three ordered Tperiodic solutions. Moreover, when h is within these . . .