Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size

We construct affinization of the algebra $gl_{\lambda}$ of ``complex size'' matrices, that contains the algebras $\hat{gl_n}$ for integral values of the parameter. The Drinfeld--Sokolov Hamiltonian reduction of the algebra $\hat{gl_{\lambda}}$ results in the quadratic Gelfand--Dickey structure on the Poisson--Lie group of all pseudodifferential operators of fractional order. This construction is extended to the simultaneous deformation of orthogonal and simplectic algebras that produces self-adjoint operators, and it has a counterpart for the Toda lattices with fractional number of particles.Comment: 29 pages, no figure

Homological Type of Geometric Transitions

The present paper gives an account and quantifies the change in topology induced by small and type II geometric transitions, by introducing the notion of the \emph{homological type} of a geometric transition. The obtained results agree with, and go further than, most results and estimates, given to date by several authors, both in mathematical and physical literature.Comment: 36 pages. Minor changes: A reference and a related comment in Remark 3.2 were added. This is the final version accepted for publication in the journal Geometriae Dedicat

Pasquale del Pezzo, Duke of Caianello, Neapolitan mathematician

This article is dedicated to a reconstruction of some events and achievements, both personal and scientific, in the life of the Neapolitan mathematician Pasquale del Pezzo, Duke of Caianello

Interacting Preformed Cooper Pairs in Resonant Fermi Gases

We consider the normal phase of a strongly interacting Fermi gas, which can have either an equal or an unequal number of atoms in its two accessible spin states. Due to the unitarity-limited attractive interaction between particles with different spin, noncondensed Cooper pairs are formed. The starting point in treating preformed pairs is the Nozi\`{e}res-Schmitt-Rink (NSR) theory, which approximates the pairs as being noninteracting. Here, we consider the effects of the interactions between the Cooper pairs in a Wilsonian renormalization-group scheme. Starting from the exact bosonic action for the pairs, we calculate the Cooper-pair self-energy by combining the NSR formalism with the Wilsonian approach. We compare our findings with the recent experiments by Harikoshi {\it et al.} [Science {\bf 327}, 442 (2010)] and Nascimb\`{e}ne {\it et al.} [Nature {\bf 463}, 1057 (2010)], and find very good agreement. We also make predictions for the population-imbalanced case, that can be tested in experiments.Comment: 10 pages, 6 figures, accepted version for PRA, discussion of the imbalanced Fermi gas added, new figure and references adde

Four lectures on secant varieties

This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications. Several references and solved exercises are also included.Comment: Lectures notes to appear in PROMS (Springer Proceedings in Mathematics & Statistics), Springer/Birkhause

Venture capital-backed firms, unavoidable value-destroying trade sales, and fair value protections

This paper investigates the implications of the fair value protections contemplated by the standard corporate contract (i.e., the standard contract form for which corporate law provides) for the entrepreneur–venture capitalist relationship, focusing, in particular, on unavoidable value-destroying trade sales. First, it demonstrates that the typical entrepreneur–venture capitalist contract does institutionalize the venture capitalist’s liquidity needs, allowing, under some circumstances, for counterintuitive instances of contractually-compliant value destruction. Unavoidable value-destroying trade sales are the most tangible example. Next, it argues that fair value protections can prevent the entrepreneur and venture capitalist from allocating the value that these transactions generate as they would want. Then, it shows that the reality of venture capital-backed firms calls for a process of adaptation of the standard corporate contract that has one major step in the deactivation or re-shaping of fair value protections. Finally, it argues that a standard corporate contract aiming to promote social welfare through venture capital should feature flexible fair value protections.info:eu-repo/semantics/publishedVersio

Contextualizing legal norms: a multi-dimensional view of the 2014 legal capital reform in China

This paper intends to shed light on the contentious theme of the reception of legal transplantation in the host environment, by examining the 2014 legislative reform of legal capital in China, which at least on paper imitates the enabling settings of US Revised Model Business Corporation Act (RMBCA). The paper looks at the interconnections between national-specific contextual elements, the resultant complexities, and the spillover effects of transplanted configurations in the unique Chinese socio-cultural setting, implicating the discrepancy between the ‘law in practice’ and the borrowed words ‘on the books’, and suggesting the importance of gaining a holistic understanding of ‘law’ involving the legal traditions in both the donor country and the recipient nation

the italian didactic tradition

Starting with a historic overview highlighting the increasing interest and involvement of the community of mathematicians in educational issues, the chapter outlines some of the crucial features that shaped Italian didactics and, more specifically, the emergence of research studies on mathematics education. Some of these features are related to local conditions, for instance, the high degree of freedom left to the teacher in the design and realization of didactic interventions. The specificity of the Italian case can also be highlighted through a comparison with the reality of other countries. The fruitfulness of this comparison is presented by reporting on collective and personal collaboration experiences between the French and Italian research communities. A final contribution, coming from East Asia, puts the Italian tradition under the lens of a completely new eye, and invites reflection upon historical and institutional aspects of the Italian tradition

Foreign ownership, bank information environments, and the international mobility of corporate governance

This paper investigates how foreign ownership shapes bank information environments. Using a sample of listed banks from 60 countries over 1997–2012, we show that foreign ownership is significantly associated with greater (lower) informativeness (synchronicity) in bank stock prices. We also find that stock returns of foreign-owned banks reflect more information about future earnings. In addition, the positive association between price informativeness and foreign ownership is stronger for foreign-owned banks in countries with stronger governance, stronger banking supervision, and lower monitoring costs. Overall, our evidence suggests that foreign ownership reduces bank opacity by exporting governance, yielding important implications for regulators and governments