We investigate a free energy functional that arises in aggregation-diffusion phenomena modelled by nonlocal interactions and local repulsion on the hyperbolic space ${\mathbb H}^n$. The free energy consists of two competing terms: an entropy, corresponding to slow nonlinear diffusion, that favours spreading, and an attractive interaction potential energy that favours aggregation. We establish necessary and sufficient conditions on the interaction potential for ground states to exist on the hyperbolic space ${\mathbb H}^n$. To prove our results, we derived several Hardy–Littlewood–Sobolev (HLS)-type inequalities on general Cartan–Hadamard manifolds of bounded curvature, which have an interest in their own.

In the present notes, we study a generalization of the Peterson subalgebra to an oriented (generalized) cohomology theory which we call the formal Peterson subalgebra. Observe that by recent results of Zhong the dual of the formal Peterson algebra provides an algebraic model for the oriented cohomology of the affine Grassmannian.

Our first result shows that the centre of the formal affine Demazure algebra (FADA) generates the formal Peterson subalgebra. Our second observation is motivated by the Peterson conjecture. We show that a certain localization of the formal Peterson subalgebra for the extended Dynkin diagram of type $\hat A_1$ provides an algebraic model for “quantum” oriented cohomology of the projective line. Our last result can be viewed as an extension of the previous results on Hopf algebroids of structure algebras of moment graphs to the case of affine root systems. We prove that the dual of the formal Peterson subalgebra (an oriented cohomology of the affine Grassmannian) is the zeroth Hochschild homology of the FADA.

Northwestern University's interest in Africa South of the Sahara dates back to 1927 and was originally centered in the field of Anthropology. By 1948 the need for greater knowledge of Africa and its inhabitants had become so increasingly apparent that the Anthropology Department announced the establishment of an African research program to be guided by an interdisciplinary committee. At approximately the same time, the University Library acquired a large collection of African newspapers, periodicals, pamphlets, and monographs as a gift from the University Museum of the University of Pennsylvania. The report in the Northwestern Library News for December 17, 1948describing the gift concluded with these words:

Africana - works about Africa and publications issued in Africa - is dispersed widely among the general collections of The Library of Congress. As these collections at the latest reckoning number more than eleven million books and pamphlets, and for all forms of material amount to over thirty-six million pieces, and as the Library policy has for many years been to acquire all worthwhile works published anywhere in the world, the holdings relating to the second largest continent may be presumed to be very substantial. The Africana is not under any separate, unifying control. Consequently it is impossible to give even approximate estimates of a total figure, but scholars working in the African field will usually find a visit to the Library of Congress richly rewarding.

The Library acquires Africana as it does its materials in general, by copyright, purchase, gift, exchange, and transfer. It thus achieves broad coverage in all subject fields except technical agriculture and clinical medicine, which are the provinces respectively of the Department of Agriculture Library and the National Library of Medicine.

When Carl Rosberg, the chairman of our program committee, asked me to deliver a presidential address at tonight's banquet, I agreed to do soonly if I couldnot find a better speaker for the occasion. Happily for you, I found him. Moreover, if you'll forgive a commercial, you can read all my potential presidential addresses anyway — in my bookAfrica in World Politics which Harper's is publishing next month. So you can have the best of both worlds.

Governor Williams has shown in many ways that he is a good friend of our association. In introducing him to you, therefore, I want to take a few minutes to pay him a special tribute by giving you my assessment of his achievements during the nearly two years he has been in charge of African affairs.

When President-elect Kennedy began to select his advisers late in 1960, many of us were surprised to find him putting the cart before the horse. That is to say, he appointed the Governor to be Assistant Secretary of State for African Affairs, even before he designated Dean Rusk as Secretary of State. The Williams appointment suggested to me, however, that the President considered African problems second to none in importance. He chose a man of stature, already baptized in the fire of Michigan politics on political, racial and social issues — a man with direct access to the President and a seasoned politician and administrator who is more than a match for the Assistant Secretaries for Europe and other areas in the State Department. At this point, I hasten to add that my remarks have not been cleared either by the State Department, or by the Fellows of the African Studies Association!