In April of 1996 an array of mathematicians converged on Cambridge, Massachusetts, for the Rotafest and Umbral Calculus Workshop, two con ferences celebrating Gian-Carlo Rota's 64th birthday. It seemed appropriate when feting one of the world's great combinatorialists to have the anniversary be a power of 2 rather than the more mundane 65. The over seventy-five par ticipants included Rota's doctoral students, coauthors, and other colleagues from more than a dozen countries. As a further testament to the breadth and depth of his influence, the lectures ranged over a wide variety of topics from invariant theory to algebraic topology. This volume is a collection of articles written in Rota's honor. Some of them were presented at the Rotafest and Umbral Workshop while others were written especially for this Festschrift. We will say a little about each paper and point out how they are connected with the mathematical contributions of Rota himself."

In April of 1996 an array of mathematicians converged on Cambridge, Massachusetts, for the Rotafest and Umbral Calculus Workshop, two con ferences celebrating Gian-Carlo Rota's 64th birthday. It seemed appropriate when feting one of the world's great combinatorialists to have the anniversary be a power of 2 rather than the more mundane 65. The over seventy-five par ticipants included Rota's doctoral students, coauthors, and other colleagues from more than a dozen countries. As a further testament to the breadth and depth of his influence, the lectures ranged over a wide variety of topics from invariant theory to algebraic topology. This volume is a collection of articles written in Rota's honor. Some of them were presented at the Rotafest and Umbral Workshop while others were written especially for this Festschrift. We will say a little about each paper and point out how they are connected with the mathematical contributions of Rota himself."

This volume presents five papers based on selected lectures given at the Current Developments in Mathematics conference, held in November 2019 at Harvard University.

Papers based on selected lectures given at the Current Development Mathematics Conference, held in November 2017 at Harvard University.

Set in Chicago's immigrant neighborhoods west of Goose Island, these lighthearted coming-of-age adventures recount growing up on rough and tumble Division Street. Inspired by a series of short stories that morphed into something much more, Post delivers a warm and humorous coming-of-age memoir that captures an era of Americana with heart and honesty. As seen through the eyes of three young boys, Chicago becomes a sort of full-contact playground where the realities of life, the love of family, and a world of adventure wait around every corner. Marked by a keen eye for detail, West of Goose Island: A Chicago Story is a must-read for anyone, even those who didn't live in the Second City. Post's tales of life growing up in several Polish immigrant neighborhoods is part nostalgia, part history lesson, and an altogether invigorating journey to a simpler time. The streets and alleys of his neighborhood provided the adventure and life lessons we all experience. And in the tight-knit enclave just west of Goose Island where the phrase "It takes a village" operated in full force, the streets were safe because everyone looked out for one another. From swimming in the dank, bubbling darkness that was the North branch of the Chicago River surrounding Goose Island to the peculiarities of cultural assimilation, the 1940s and 1950s were a pretty great time to be a kid in his neighborhood, to learn about the value of hard work and education, and to truly understand the possibilities in a country where every dream could be realized We all remember moments of childhood that left indelible marks on our lives for one reason or another. Some are simple moments while others are more profound, but in every instance they leave behind an impression on our very beings, molding that we are from that moment forward. While they are not always positive, they set a foundation from which the rest of our lives are built. For Richard S. Post, those years were not only full of adventure but were also the beginning of an exciting life.

Americans sense that protection is the basic purpose of government-remember 9-11? Americans are also capitalists who seek private ownership and freedom. Culture wars have always been part of America. Remember the Civil War? Slogans and pamphlets helped cause our Revolutionary War. Words matter! Money is the plasma of politics, and each new freedom has cost us more in campaign costs. History is certainly humorous! Government's most important power is the power to tax-and boy, are politicians proficient at taxing! Since its early beginnings, public education in America has been decentralized and under local and popular control. It is therefore only natural that there are conflicting answers to the question, "Are the schools doing their job?" And, believe it or not, modern racism is an invention of the 19th Century's reaction to the international abolition movement. Hence, racism is curable! It's up to us!

Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of volume two covers the composition of generating functions, in particular the exponential formula and the Lagrange inversion formula, labelled and unlabelled trees, algebraic, D-finite, and noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course and focusing on combinatorics, especially the Robinson–Schensted–Knuth algorithm. An appendix by Sergey Fomin covers some deeper aspects of symmetric functions, including jeu de taquin and the Littlewood–Richardson rule. The exercises in the book play a vital role in developing the material, and this second edition features over 400 exercises, including 159 new exercises on symmetric functions, all with solutions or references to solutions.

This volume presents five papers based on selected lectures given at the Current Developments in Mathematics conference, held in November 2018 at Harvard University.

Papers based on selected lectures given at the Current Development Mathematics Conference, held in November 2015 at Harvard University.

Papers based on selected lectures given at the Current Development Mathematics Conference, held in November 2011 at Harvard University. Contents: The Laplacian on planar graphs and graphs on surfaces (Richard Kenyon); Hyperbolicity and stable polynomials in combinatorics and probability (Robin Pemantle); Introduction to KPZ (Jeremy Quastel)