Facets of Algebraic Geometry: Volume 1

Written to honor the 80th birthday of William Fulton, the articles collected in this volume (the first of a pair) present substantial contributions to algebraic geometry and related fields, with an emphasis on combinatorial algebraic geometry and intersection theory. Featured topics include commutative algebra, moduli spaces, quantum cohomology, representation theory, Schubert calculus, and toric and tropical geometry. The range of these contributions is a testament to the breadth and depth of Fulton's mathematical influence. The authors are all internationally recognized experts, and include well-established researchers as well as rising stars of a new generation of mathematicians. The text aims to stimulate progress and provide inspiration to graduate students and researchers in the field.

Paolo Aluffi is Professor of Mathematics at Florida State University. He earned a Ph.D. from Brown University with a dissertation on the enumerative geometry of cubic plane curves, under the supervision of William Fulton. His research interests are in algebraic geometry, particularly intersection theory and its application to the theory of singularities and connections with theoretical physics.

David Anderson is Associate Professor of Mathematics at The Ohio State University. He earned his Ph.D. from the University of Michigan, under the supervision of William Fulton. His research interests are in combinatorics and algebraic geometry, with a focus on Schubert calculus and its applications.

Milena Hering is Reader in the School of Mathematics at the University of Edinburgh. She earned a Ph.D. from the University of Michigan with a thesis on syzygies of toric varieties, under the supervision of William Fulton. Her research interests are in algebraic geometry, in particular toric varieties, Hilbert schemes, and connections to combinatorics and commutative algebra.

Mircea Mustaţă is Professor of Mathematics at the University of Michigan, where he has been a colleague of William Fulton for over 15 years. He received his Ph.D. from the University of California, Berkeley under the supervision of David Eisenbud. His work is in algebraic geometry, with a focus on the study of singularities of algebraic varieties.

Sam Payne is Professor in the Department of Mathematics at the University of Texas at Austin. He earned his Ph.D. at the University of Michigan, with a thesis on toric vector bundles, under the supervision of William Fulton. His research explores the geometry, topology, and combinatorics of algebraic varieties and their moduli spaces, often through relations to tropical and nonarchimedean analytic geometry.