Leonardo of Pisa (a.k.a Fibonacci) has a remarkable connection with Bucknell, and to celebrate this fact we are holding an interdisciplinary conference on October 14. Featured speakers include:

Mario Livio – an astrophysicist and author of popular science books,

Keith Devlin – NPR’s “Math Guy” and the author of numerous popular mathematics books,

William Goetzmann – Director of the International Center for Finance, Yale University

This event will be in the Langone Center from 10:00 a.m. until 2:30 p.m.

Lunch tickets are available in Olin 380, or by writing to math@bucknell.edu

]]>**Title:** Efficiency Of Non-Compliance Chargeback Mechanisms In Retail Supply Chains

**Abstract:** In practice, suppliers fill retailers’ purchase orders to the fill-rate targets to avoid the non-compliance financial penalty, or chargeback, in the presence of service level agreement. Two chargeback mechanisms – flat-fee and linear – have been proven to effectively coordinate the supply chain in a single-period setting. However, the mechanisms’ efficiency, the incurred penalty costs necessary to coordinate the supply chain, have not been studied yet. Since retailers are often accused of treating chargeback as an additional source of revenue, this study compares the expected penalties resulted from the flat-fee or linear chargeback to shed light on the retailers’ choice of mechanisms. Using experimental scenarios consisting of various demand functions, demand variabilities, and fill-rate targets, the simulation results offer counter-evidence to the accusation.

**Title:** What Do You Mean, It’s Hard?

**Abstract:** Suppose someone gives you a computer and asks you to perform one of the following tasks:

- solve a 17 × 17 × 17 Rubik’s cube, or
- decide if a given list of 100 integers can be broken into two parts having equal sums.

If your life depended on it, which task would you choose? Which is harder, computationally?

In 1971, Stephen Cook proposed a strong measure of efficiency – *polynomial time, or simply P – *as a desirable standard to which we should hold solutions to computational problems. Task A is an instance of a problem with such a solution. He also identified a seemingly less stringent measure – *nondeterministic polynomial time, or simply NP* – in which one merely has to check, efficiently, that a given solution is correct. Tasks A and B are both instances of problems satisfying this condition. The big question raised by Cook is whether these two measures of computational efficiency are actually distinct.

One can argue that the “P ≠ NP Problem,” as it is now known, is the most important open problem in all of mathematics and computer science. Certainly, it has far-reaching implications both within these two fields and beyond. Cook showed in his 1971 paper that there are NP problems that seem *really hard*: remarkably, if you can solve **any one** of these problems efficiently, then you can solve **every** NP problem efficiently. Problem B is an instance of one of these “NP-complete” problems. To solve P ≠ NP, one could look for NP problems that are unlikely to be hard in this sense and try to show that they’re also not easy. We have yet to find such a problem, but in this talk I will try to persuade you that there are some candidates worthy of further scrutiny!

**Title: **Fluid Flow Around Slender Bodies in Viscous Fluids: From Swimming Worms to Bacterial Carpets

**Abstract: **There are many biologically relevant situations which involve long slender bodies (e.g. worms, flagella, bacterial bodies, etc.) where it is important to understand the dynamic interactions of the body and the low Reynolds number fluid in which it moves. In this presentation, I will be discussing applications of the method of regularized stokeslets to periodically moving bodies in fluids. These models have applications to the study of locomotion as well as fluid mixing.

**Title:** Proofs (not) from the Book

**Abstract: **The eminent mathematician of the 20th century, Paul Erdos, often mention “The Book” in which God keeps the most elegant proof of every mathematical theorem. So, attending a mathematical talk, he would say: “This is a proof from The Book”, or “This is a correct proof, but not from The Book”. M. Aigner and G. Ziegler authored the highly successful “Proofs from THE BOOK” (translated into 13 languages). In this talk, I shall present several proofs that are not included in the Aigner-Ziegler book but that, in my opinion, could belong to “The Book”

**Title:** What can topology tell us about the neural code?

**Abstract:** Cracking the neural code is one of the central challenges of neuroscience. Neural codes allow the brain to represent, process, and store information about the outside world. Unlike other types of codes, they must also reflect relationships between stimuli, such as proximity between locations in an environment. In this talk, I will explain why algebraic topology provides natural tools for understanding the structure and function of neural codes.

**Title:** The Mathematics of Soap Films

**Abstract: **Every child knows that when you blow bubbles the surface that results is a sphere. But why? We’ll talk about this, more exotic examples, and a little bit about the group of Princeton mathematicians that became obsessed with soap films in the 1960s.

**Title: **Quasinormality and weak quasinormality of operators

Abstract: There are two notions to define the quasinormality of unbounded operators by Kaufman and Stochel-Szafraniec respectively. Our results show that Kaufman’s definition of an unbounded quasinormal operator coincides with that given by Stochel-Szafraniec. In this talk we discuss various characterizations of unbounded quasinormal operators. Examples demonstrating the sharpness of our results are constructed. An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. This approach establishes a new definition to be called weakly quasinormal operators. Some characterizations concerning to the weakly quasinormal operators are discussed. In addition, various examples and counterexamples illustrating the concepts of this work are constructed by using weighted shifts on directed trees.

]]>**Title: ** Weighted shifts on directed trees

**Abstract: **The main goal of this research is to implement some methods of graph theory into operator theory. We do it by introducing a new class of Hilbert space operators, which we propose to call weighted shifts on directed trees. We have studied the structure of these operators since 2012 and obtained some remarkable results about those operators. In this talk we discuss some of the established properties for such operators, for examples, normality, hyponormality, and subnormality, etc. It is well-known that the subnormality of Hilbert space operators is closely related to Stieltjes moment sequences. We consider directed trees with one branching vertex and establish a connection between the subnormality and Stieltjes moment sequences by using the k-step backward extendability of bounded subnormal weighted shifts. In addition, some exotic examples of weighted shifts on directed trees related to Stieltjes moment sequences are discussed.