Physical Sciences and Mathematics Commons^™

Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna Tymoczko

Department of Math & Statistics Faculty Publications

Springer varieties are studied because their cohomology carries a natural action of the symmetric group S_n and their top-dimensional cohomology is irreducible. In his work on tangle invariants, Khovanov constructed a family of Springer varieties X_n as subvarieties of the product of spheres (S²)ⁿ. We show that if X_n is embedded antipodally in (S²)ⁿ then the natural S_n-action on (S²)ⁿ induces an Sn-representation on the image of H_*(X_n). This representation is the Springer representation. Our construction admits an elementary (and geometrically …

Problems With And Without … Problems!, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This book is addressed to College honor students, researchers, and professors. It contains 136 original problems published by the author in various scientific journals around the world. The problems could be used to preparing for courses, exams, and Olympiads in mathematics. Many of these have a generalized form. For each problem we provide a detailed solution.

I was a professeur coopérant between 1982-1984, teaching mathematics in French language at Lycée Sidi EL Hassan Lyoussi in Sefrou, Province de Fès, Morocco. I used many of these problems for selecting and training, together with other Moroccan professors, in Rabat city, of the …