Preface This volume contains a selection of papers stemming from the conference Hodge Theory and Classical Algebraic Geometry, held on the campus of The Ohio State University in Columbus, Ohio, from May 13 to 15, 2013. The conference web page is still accessible at Most of the conference talks were captured on video, which may be viewed by following the appropriate links. A program and abstracts are also available there. In some instances the paper in this volume closely adheres to the conference lecture in other instances there is a great difference. The idea of the conference was to offer young researchers a global view of recent developments and to have the speakers share their vision of the future. The papers in this proceeding follow essentially a similar idea there are a few survey papers while others contain original research. The topics range from more classical aspects of Hodge theory to modern developments in compactifications of period domains, applications of Saito’s theory of mixed Hodge modules, and connections with derived category theory and non-commutative motives. The reader may note an odd feature: although there is no dedication on the title page, each paper in our volume is dedicated to Professor Herb Clemens. This is because our conference inadvertently used the venerable sales technique known as “bait and switch,” with Clemens as our bait. That is to say: we announced that he was retiring, and that we were organizing a conference in his honor. But it turned out after all that he was not in fact retiring, but instead beginning yet another chapter in his distinguished career. In view of this history, we tried to enforce the following rule at our confer- ence: you are forbidden to say anything nice about Herb. Of course the rule was skirted repeatedly. One speaker tried to evade it by praising not Herb but rather his basement, where he had stayed as a houseguest while learning to ski in the mountains of Utah. Others broke the rule quite brazenly. For example, it would be violating this rule to remark how much energy he has brought to the Ohio State Mathematics Department and in particular to those who work in algebraic geom- etry. And again it would be against the rule to note the awe with which we seem to observe at least two or three different people doing full-time jobs, each one of them named Herb Clemens. One of us once had the opportunity to speak to Robert Moses, a civil rights pioneer and the founder of the Algebra Project, who told us of his admiration for Herb’s work in mathematics education, and Moses seemed genuinely astonished to learn that Herb was also famous for a conjecture named after him in pure mathematics. We are very glad to report that his efforts on behalf of mathematics research, education, and infrastructure continue unceasingly. vii
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