Colloquium

Fishing for Invasive Crayfish: Using Mathematical Modeling to Tip the Scales for Endangered California Species

05/02/2018 - 4:15pm
05/02/2018 - 5:15pm
Speaker: 
Courtney Davis (Pepperdine)
Abstract: 

Santa Monica Mountain (SMM) streams are home to endangered steelhead and rainbow trout (Onchorynchus mykiss) as well as the California newt (Taricha torosa), a species of special concern in California.  California’s historically severe drought as well as stream invasion by nonnative crayfish (Procambarus clarkii) that prey upon eggs and aquatic young have decimated reproduction of native species.  This has led to localized trout and newt extinctions in multiple SMM streams.  Restorative measures are currently underway in some SMM streams to remove crayfish through trapping or manual removal in order to prevent or slow the decline of native species.

 

In collaboration with undergraduate students and field biologists, we have created discrete stage-structured models of newt and of trout life history dynamics in SMM streams. With each, we incorporate a model of invasive crayfish trapping and use numerical simulations and sensitivity analysis to investigate which crayfish removal regimes most benefit persistence of these native species in SMM streams.  Model results inform invasive crayfish removal efforts and aid conservation planning for these imperiled native species.

Where: 
Freeberg Forum, LC 62, Kravis Center, CMC

Intrinsic Complexity and its Scaling Law: From Approximation of Random Vectors and Random Fields to High Frequency Waves

04/18/2018 - 4:15pm
04/18/2018 - 5:15pm
Speaker: 
Hongkai Zhao (UC Irvine)
Abstract: 

 We characterize the intrinsic complexity of a set in a metric space by the least dimension of a linear space that can approximate the set to a given tolerance.  This is dual to the characterization using Kolmogorov n-width, the distance from the set to the best n-dimensional linear space.  We start with approximate embedding of a set of random vectors (principal component analysis a.k.a. singular value decomposition), then study the approximation of random fields and high frequency waves.  We provide lower bounds and upper bounds for the intrinsic complexity and its explicit asymptotic scaling laws in terms of the total number of random vectors, the correlation length for random fields, and the wave length for high frequency waves respectively. 

Where: 
Freeberg Forum, LC 62, Kravis Center CMC

Certain Modern Ideas and Methods: A look at the history and philosophy of Charlotte Angas Scott

02/28/2018 - 4:15pm
02/28/2018 - 5:15pm
Speaker: 
Jemma Lorenat (Pitzer College)
Abstract: 

Charlotte Angas Scott was an internationally renowned algebraic geometer, the first British woman to earn a PhD in mathematics, and the chair of the Bryn Mawr mathematics department for forty years.  Through the 1890s, she often motivated her research as building geometric understanding.  Scott revisited the algebraic techniques of her contemporaries to provide graphical analyses, manipulate tangible objects, and show geometrical reality.  This talk will begin with an overview of the main contributions of Scott's career and then focus on her ideas around ontology and aesthetics as illustrated in her publications.  

Where: 
Freeberg Forum, LC 62, Kravis Center, CMC

A Tribute to Euler

02/14/2018 - 4:15pm
02/14/2018 - 5:15pm
Speaker: 
Bill Dunham (Bryn Mawr College)
Abstract: 

Without question, Leonhard Euler (1707-1783) ranks among the greatest mathematicians of all time. The remarkable quality of his achievement is matched only by the equally remarkable quantity of his achievement – indeed, Euler’s collected works contain over 25,000 pages of pure and applied mathematics. In this talk, we sketch his life and mention a handful of his contributions to the mathematical sciences – from number theory to analysis to geometry. Then we examine in detail his derivation, using integral calculus, of what is now known as “Euler’s identity” – i.e., e^{ix} = cos(x) + i*sin(x). This ingenious argument should make clear why Euler is regarded as such a towering figure from the history of mathematics.

NOTE: This talk should be accessible to anyone who has completed the calculus sequence.

 

Where: 
Freeberg Forum, LC 62, Kravis Center, CMC

When MATLAB Gives Wrong Answers

03/28/2018 - 4:15pm
03/28/2018 - 5:15pm
Speaker: 
Steven Leon (Emeritus from UMass Dartmouth)
Abstract: 

MATLAB is generally considered to be the leading software package for scientific computing. In this talk we consider a number of computational examples where MATLAB gives or appears to give wrong answers. These examples are useful to help better understand the inner workings, evolution, limits and tradeoffs of a software package such as MATLAB. The talk should be accessible to both graduate and undergraduate students that have some background in either linear algebra or numerical analysis. The examples should help students gain greater insight into the fundamentals of matrix computations and also into the basics of finite precision arithmetic and related concepts such as round off error, machine precision, numerical stability, and conditioning.

Where: 
Freeberg Forum, LC 62, Kravis Center, CMC

Special Values of L-Series in Positive Characteristic

04/04/2018 - 4:15pm
04/04/2018 - 5:15pm
Speaker: 
Matthew Papanikolas (Texas A&M University)
Abstract: 

There are many parallels between the theories of the integers and the polynomial ring in one variable over a finite field.  In the 1930's Carlitz constructed function field valued analogues of the Riemann zeta function, and in 1980's Goss greatly generalized Carlitz's zeta function to L-functions associated to Drinfeld modules.  It is a natural question to ask how special values of Goss L-series capture arithmetic invariants of their underlying objects.  In spite of tantalizing examples, this remained a mystery for many years, until Taelman proved a class number formula for special values in 2012.  In this talk we will survey the history of Goss L-series and discuss the advances of Taelman, as well as further directions defined by Pellarin on deformations of Goss L-series.  We will also present results on log-algebraic identities for L-series attached to Drinfeld modules (joint with C.-Y. Chang and A. El-Guindy).

Where: 
Freeberg Forum, LC 62, Kravis Center, CMC

Cylinders vs. Moebius Bands: How Can We See the Difference?

03/21/2018 - 4:15pm
03/21/2018 - 5:15pm
Speaker: 
Thomas Banchoff (Brown University)
Abstract: 

When we look at a strip of paper with its ends attached, how can we see whether it is a cylinder with two boundary curves or a Moebius Band with a single boundary curve?  We will develop seven different criteria that arise in  undergraduate calculus and the elementary geometry and topology of surfaces.  Physical models and computer graphics images will illustrate the talk.

Where: 
Freeberg Forum, LC 62, Kravis Center, CMC

Unexpected Particle Motions in Viscous Fluids Undergoing Oscillatory Rotation

01/24/2018 - 4:15pm
01/24/2018 - 5:15pm
Speaker: 
Ali Nadim (CGU)
Abstract: 

In this joint work with former doctoral student Shujing "Flora" Xu, we investigate theoretically the effect of the Coriolis force on the motion of a suspended particle in a viscous fluid undergoing rotation. In normal centrifugation, a particle which is denser than the surrounding fluid is "thrown" away from the rotation axis. However, we find that when the rotation is oscillatory, through a combination of viscous drag and the Coriolis force, dense particles may actually migrate toward the rotation axis for certain parameter regimes. We analyze the nonlinear dynamical system describing the particle trajectories using the method of averaging and derive the criterion for such "counter-centrifugation." We also use numerical simulations to verify our predictions. For details, see Xu and Nadim, Physics of Fluids, 28, 021302 (2016).

 

Where: 
Freeberg Forum, LC 62, Kravis Center, CMC

An Exploration of Triangular-Square Numbers

04/11/2018 - 4:15pm
04/11/2018 - 5:15pm
Speaker: 
Berit N. Givens (Cal State Polytechnic University, Pomona)
Abstract: 

A triangular-square number is both a perfect square of the form m2 and the sum of all integers from 1 to some value n.  In my first year teaching, I assigned a homework problem about triangular-square numbers that turned out to be much harder than I had realized.  The known solutions required material from later in the curriculum.  Years later, a colleague and I became convinced that "morally" there should be a way for students to solve the problem using only the techniques they had been taught so far. That started us on a path of mathematical discovery, learning about Pell's Equation and continued fractions, while also drawing lots and lots of pictures of triangles and squares as we searched for a visual solution to the original problem.  In this talk, I will give an overview of the Pell’s Equation and continued fractions material involved, then show our visual solutions.  The talk will be accessible to students at any level.

Where: 
Freeberg Forum, LC 62, Kravis Center, CMC

Rehumanizing Mathematics: Should That Be Our Goal?

03/07/2018 - 4:15pm
03/07/2018 - 5:15pm
Speaker: 
Rochelle Gutierrez (College of Education at U Illinois at Urbana-Champaign)
Abstract: 

For far too long, we have embraced an "equity" standpoint that has been poorly defined (Gutiérrez, 2002) or constantly shifting (NCTM, 2008). It has been difficult to assess progress beyond closing the achievement gap or recruiting more diverse students into the mathematical sciences. Instead, we should rehumanize mathematics, which considers not just access and achievement, but the politics in teaching and mathematics. This approach begins with 1) acknowledging some of the dehumanizing experiences in mathematics for students and teachers and 2) how students could be provided with windows and mirrors onto the world and ways of relating to each other with dignity. As such, we can begin to think differently about student misconceptions, teachers as identity workers, and why it is not just that diverse people need mathematics but mathematics needs diverse people (Gutiérrez, 2002; 2012). In this talk, I focus on two areas for rehumanization: 1) teaching/learning and 2) scholars and everyday citizens.

With respect to teaching and learning, I present eight dimensions of a rehumanized mathematics classroom: participation/positioning; cultures/histories; windows/mirrors; living practice; broadening maths; creation; body/emotions; and ownership. Then, I offer ways for mathematicians and mathematics educators to take risks in ensuring those dimensions happens in small and large ways. In addition, with the recent national attacks on mathematics education scholars who address social justice and whiteness, I explain a bit about my case and then offer ways to rehumanize our field to affect scholars and everyday citizens. In particular, I highlight how understanding our history (e.g., how scientists in the 1970s stood for political and social action) as well as creating greater alliances between mathematicians and mathematics education scholars might allow us to take greater risks in our everyday work.

Where: 
Freeberg Forum, LC 62, Kravis Center, CMC
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