Billerafest Celebrates Birthday of Math and ORIE Faculty Member Louis Billera

Many of Louis Billera's Ph.D. students and professional colleagues gathered in  Ithaca in June to celebrate his 65th birthday with a three day conference of scholarly papers and social events.

Billera, who joined ORIE in 1968, did early research in game theory, including a seminal 1978 paper, Internal Telephone Billing Rates: a Novel Application of Nonatomic Game Theory, written with his colleague David Heath and.ORIE Ph.D. student Joseph Raanan. The paper applied the game-theoretic concept of the Shapley Value to cost allocation, and was motivated in part by the problem of allocating the costs of the shared Cornell telephone system among its users. It remains one of the more heavily cited of his more than 65 publications. 

Billera eventually moved to the Cornell Department of Mathematics, where his current research is concerned with using algebraic techniques to solve combinatorial problems, most often arising in discrete and convex geometry of the sort that underlies linear and integer programming, for example. According to Billera, "one problem which has attracted the interest of mathematicians for hundreds of years is that of enumerating the faces of convex polytopes" such as the region, traversed by the Simplex Method, of feasible solutions to a linear programming problem. The insights and methods developed through his research have been applied to methods of solving partial differential equations, to generating surfaces for computer-graphic display, and to understanding the structure of the polytope underlying the classical Traveling Salesman problem. 

The talks at Billerafest generally dealt with topics related to Billera's more mathematical research, although Shmuel Onn, a student of Leslie Trotter who also worked with Billera, discussed an algebraic theory of nonlinear discrete optimization. Among the nearly two dozen Ph.D.'s whose work Billera supervised are five who were in ORIE: Fernando Garagorry, with the Brazilian Agricultural Research Corporation EMBRAPA; Robert Bixby, founder of CPLEX; Scott Provan, Professor of Operations Research at the University of  North Carolina; Joseph Raanan, at the College of Management in Israel; and Ruth Haas, Professor of Mathematics and Engineering and Director of the Center for Women in Mathematics at Smith College. (Provan's son Chris is currently an ORIE Ph.D. student.)

Bixby, who delivered the D. R. Fulkerson Lectures at Cornell in April, commented that "the memory of working with Lou as a student is still vivid in my mind to this day, after all these years. Lou somehow in his own special way conveyed to me a sense of the importance of scholarship -- that's how I view him, as a true scholar." Garagorry, who was Billera's first Ph.D. student, echoed Bixby's comment and notes that Billera provided him with "several ideas and counter-examples which were crucial to clarifying some difficult points" in his thesis research. Haas (right) found him a "great person to work with. He has mathematical breadth and the ability to find interesting problems."   Bixby and Haas both attended the conference. Haas commented that Billera's concluding talk, called Mistakes I Didn't Make, "showed us again his humor and humility." Bixby "enjoyed most of all that [the conference] happened, and that Lou had the good sense to just enjoy it." 

Billera said that "I was extremely fortunate to have been hired straight out of graduate school 40 years ago by Cornell's OR Department (as it was then known). The department and the College of Engineering provided support at crucial points in my early career, while Cornell's flexible graduate field structure gave me access to talented students in three graduate fields. Taken together, they had a lot to do with getting my career on the track that led to this conference."