March 7th, 2017
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.
Continue reading Student Talk Series: Joe Lauer 3/9 @ noon in Olin 268 »
February 17th, 2017
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 […]
Continue reading Distinguished Visiting Professor Talk: Il Bong Jung 2/28 @ 4 pm in Olin 372 »
February 17th, 2017
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 […]
Continue reading Distinguished Visiting Professor Talk: Il Bong Jung 2/23 @ 4 pm in Olin 372 »
February 15th, 2017
Title: Beyond Standard Scores: Using Item-level Responses From Clinical Measures to Detect Atypical Developmental Patterns Abstract: Developmental deviance (DDEV) refers to the non-sequential attainment of milestones within a developmental domain. This observation is in contrast to developmental delay (DD), where milestones are reached in the typical sequence, but the timeline of attainments is delayed. There is evidence that DDEV is associated with certain neurobehavioral diagnoses, such as autism spectrum disorder (ASD). Clinically, the attainment of developmental milestones is assessed through standardized measures of developmental domains. Many psychometric tests are arranged hierarchically, and on the surface, two individuals with the same […]
Continue reading Student Talk Series: Abby Hare-Harris 2/16 @ noon in Olin 268 »
January 27th, 2017
Title: Modeling lamprey swimming with mathematics and computation Abstract: Locomotion — swimming, running, flying — is one of the most basic animal behaviors. In order for an animal (like a lamprey) to swim, a lot has to happen, including neural signaling, muscle contractions, interactions between the body and the water, and adjustments from sensory feedback. How do we use mathematics to better understand the underlying mechanisms that drive locomotion? We will explore how we can use mathematical models to describe these individual systems and then coordinate the systems to produce a naturally emerging behavior in computer simulations of swimming lampreys.
Continue reading Student Talk Series: Christy Hamlet 2/2 @ noon in Olin 268 »
January 27th, 2017
Title: The multiplicity one theorem for paramodular forms. Abstract: Classical modular forms are known to have the “strong multiplicity one” property: A cuspidal eigenform is determined by almost all of its Hecke eigenvalues. Siegel modular forms, on the other hand, do not have this nice property. The main theorem presented in this talk states that strong multiplicity one still holds for an important class of Siegel modular forms known as “paramodular forms”. The latter have gained prominence because of their appearance in the “paramodular conjecture”, a degree-2 version of Shimura-Taniyama-Weil.
Continue reading Distinguished Visiting Professor Talk: Ralf Schmidt 2/2 @ 4 pm in Olin 372 »
January 27th, 2017
Title: What is Number Theory? Abstract: In its original meaning, Number Theory is concerned with the properties of the “natural” numbers 1, 2, 3, … In this talk we will attempt to explain how the consequent study of “elementary” properties of numbers leads naturally to the theory of automorphic forms and the vast web of conjectures known as the “Langlands program”.
Continue reading Distinguished Visiting Professor Talk: Ralf Schmidt 1/31 @ 4 pm in Olin 372 »
November 7th, 2016
Title: 1+2+3+4+… = -1/12 Abstract: Infinite series. Every Calculus II student hates them; every mathematician loves them. So, why do mathematicians love infinite series? Well, ask one, and you’ll never hear the end of it… (just sum math humor). We’ll see how two standard examples of series, the geometric series and the zeta function (p-series), lead to beautiful applications, such as in economics and signal processing. We’ll also see how even divergent series are fascinating.
Continue reading Student Talk Series: Sharon Garthwaite 11/10 @ noon in Olin 268 »
October 25th, 2016
Title: Wavelet-based Probit Functional Models Abstract: Recent advances in functional regression include the development of a wide range of function-on-scalar regression models where outcome is a function of time regressed onto a set of scalar covariates. Most of these methodologies require the outcome to be normally distributed. However, very little work has been done on the case where the outcome is categorical. In this talk, we will discuss a flexible Bayesian procedure for function-on-scalar regression for categorical functional outcomes of varying levels. Simulations and data examples will be presented to illustrate the methodology.
Continue reading DVP Talk: Mark Meyer, 11/1 @ 4 pm »
October 21st, 2016
Title: Losing Altitude: A story of airplanes, heart rate, and one “controversial” dataset Abstract: When you ride in an airplane, the lowered pressure in the cabin causes your blood oxygen levels to decrease. If oxygen saturation levels go low enough, you may experience some interesting side effects (like temporary color blindness, for example), that much we know. What we don’t know is if there is also an impact on the functioning of the heart. Partially motivated by a rash of flight related medical case studies, a study was conducted in 2007 to more formally assess the effects of exposure to altitude […]
Continue reading Student Talk Series: Mark Meyer 10/27 @ noon in Olin 268 »