Current Academic Year Seminars

BLOCK 7, 2013 - April

Friday April 12th
Noon in TSC 122 Tutt Science Lecture Hall 
Colin Weir, University of Calgary

Title: What the L? An Intro and Application to L-functions

Abstract: The main goal of this talk is to introduce Artin L-funtions, a generalization of the Riemann zeta function, by wandering various realms in the world of mathematics. These will include small secluded islands within the lands of number theory, abstract algebra, representation theory, and complex analysis. Our travels will eventually lead us to the promised land hidden in the very depths of math world - the fountain of eternal theorems. It is here where we will unravel the mysteries of L and harness the power to produce an infinitude of number theory results.

Rating: PG

*********************
BLOCK 6, 2013 - February & March

Monday March 11
Noon - TSC 122 Lecture Hall
Emma Norbrothen (candidate for visiting professor position)

Title: Number Systems Base P

Abstract: Rational numbers can construct the real numbers by using the absolute value metric.  Under different metrics, rationals can construct different types of numbers.  In particular, the p-norm evaluates how much a prime, p, is a factor in a given rational.  We will explore some consequences of the p-norm and what kind of numbers it creates rom the rationals. 

Rating: PG

***

Monday March 4
Noon - TSC 122 Lecture Hall
Colin Weir (candidate for visiting professor position)

Title: When Primes Factor

Abstract: We learned in elementary school that prime numbers are numbers that only factor as 1 times themselves. However, this definition assumes that the only allowable factors are positive integers. What does it mean to be prime if we are allowed to write  or   ? How can a prime number factor if we extend our allowable factors beyond positive integers? We will explore these questions and many others, eventually leading us to areas of modern research in number theory and cryptography.

Rating: Light PG-13 (we will eventually review some abstract algebra)

Tuesday March 5
2:30 pm- TSC 229
Colin Weir (candidate for visiting professor position)

Title: Constructing and Tabulating Algebraic Function Fields

Abstract: Research into the construction of certain low degree function fields has surged in recent years, in part due to the cryptographic significance of elliptic and hyperelliptic curves. However there is comparatively little data available for higher degree function fields, leaving open many questions about the number of function fields of fixed degree and given discriminant. We present a Kummer theoretic algorithm for constructing degree ℓ dihedral function fields over a finite field  with prescribed ramification. We then use this in a tabulation algorithm to construct all cubic function fields over  up to a given discriminant bound and compare the data to known asymptotics. We will also survey other applications where these techniques can be made useful, such as constructing curves with many points, or in implementing cover attacks on hyperelliptic curve cryptography. Moreover, we show how our construction techniques can be extended to characteristic zero to construct interesting curves over number fields.

Rating: R (some Galois theory will be assumed)

***

BLOCK 5, 2013 - January & February

Friday February 8
Noon - TSC 122 Lecture Hall
Taylor McNeill (candidate for visiting professor position)

Title: Twisted Sisters - How a knot becomes a braid

Abstract: What do cancer cells, the sun's corona, and your kid sister's hair have in common? Knots!  In this talk I'll give a brief introduction to knot theory, including a glimpse into its history and applications. After that we'll discuss braids and their correspondence with knots. Finally we'll show that every knot is a braid in disguise. So say "bye-bye" to those tangled earbuds and "hello" to low dimensional topology.

PIZZA will be served.

Rated: G

*

Thursday February 7
3:00pm - TSC 229
Taylor McNeill (candidate for visiting professor position)

Title: A new filtration of the Magnus kernel of the Torelli group. 

Abstract: For a surface S, the mapping class group, Mod(S) is the group of orientation preserving homeomorphisms of S mod isotopy.  A key subgroup of the mapping class group, the Torelli group admits a representation onto a linear group via the Magnus representation.  For many years it was unknown whether the Magnus representation of the Torelli group is faithful.  In recent years there have been many developments on this front including the result of Church and Farb that the kernel of the Magnus representation, denoted Mag(S), is infinitely generated.  I show that, not only is Mag(S) highly non-trivial but that it also has a rich structure as a group. 

Specifically, I define an infinite filtration of Mag(S) by subgroups, called the higher order Magnus subgroups, M_n.  I show that for each n the quotient M_n/M_n+1 is infinitely generated.

Rating: PG-13

*
 

Friday January 25
2:30pm,  TSC 229
Kathy Merrill

Title:  "Simple wavelet sets in n dimensions"  Rating PG

Abstract:  A wavelet set in R^n can be defined analytically as a set whose characteristic function is the Fourier transform of a wavelet.  Alternatively, it can be defined geometrically as a set that tiles n-dimensional space under both translation by the integer lattice and dilation by an expansive integer matrix.  In both contexts, it is somewhat surprising that such sets exist.  However, for some dilations, such sets can be found that are geometrically quite simple, consisting of a finite union of convex sets.  This talk will describe the generalization to arbitrary dimensions of a two dimensional construction of simple wavelet sets presented in a Fearless Friday in late 2011.  In keeping with the title, the proof itself has become simple by making use of a little known combinatorial result.    

Rating: PG (some undergraduate mathematics or computer science understanding)

***

BLOCK 4, 2012 - December

Friday, December 7
Noon, TSC 122
Craig Guilbault (University of Wisconsin-Milwaulkee)

Proof or Swindle? The surprising effectiveness of sketchy technique

Rating: PG (some undergraduate mathematics or computer science understanding)

***

BLOCK 3, 2012 - October

Friday, November 16
2:30pm, TSC 122
Marc Chamberland (Grinnell College)

The Computer's Role in Mathematical Discovery and Proof

Rating: PG (some undergraduate mathematics or computer science understanding)

***

Friday, November 9
Noon, TSC 122
Stefan Erickson (CC)

Mathematics of Poker

BLOCK 2, 2012 - October

Friday, October 5
2:30 pm, TSC 229
Jane McDougall (CC)

Title: Harmonic Mappings and Minimal Surfaces (or what I would be doing if I were on sabbatical)

Abstract:  We will examine briefly some of the highlights in the history of minimal surfaces, with a particular goal of setting in context the classical Scherk doubly-periodic surface and its generalization to the notion of a JS surface. We will then discuss harmonic maps (complex functions which are harmonic rather than analytic) and their connection with minimal surfaces. We explore the advantages of using hyperbolic geometry in constructing harmonic maps with specified properties. Time permitting, we will also consider the construction of harmonic maps onto hexagons that admit a JS surface. Technical aspects of this talk will also be communicated by an appeal to geometric intuition (i.e. there will be pictures).

Rating: PG13

***

Friday, October 12
NOON TSC 122
Kathy Merrill (CC)

Title: Sunrise, Sunset

Abstract:  Although we expect the earliest sunset and latest sunrise to occur on the winter solstice, they do not. The mathematics behind this phenomenon is related to a curve called the analemma. This talk will explore the factors that complicate our view of the path of the sun, and develop a model that accounts for the difference between the solstice and and the extrema of sunrise and sunset times.

Rating: G/PG

***

Thursday October 18, 2012
6:30 pm, Packard Hall
Joel E. Cohen (The Rockefeller University and Columbia University, New York)

Sustainability, nations, globalization: can we have them all with 7 billion people and more?

Whatever sustainability means, it includes protecting Earth's physical, chemical, and biological environments locally and globally for time periods of human concern, subject to natural variability. National governments usually view their primary responsibilities as lying within their own boundaries on the time scales of the next election cycle or, at most, the education of the next generation. Global businesses look for resources and markets wherever they offer economic advantage to globally dispersed stockholders and management in time for the next quarterly report or the next annual meeting of stockholders, or (rarely) over the coming decade. Since 1820, aggregate economic activity grew more than 74-fold, and now the material inputs and outputs of economic activity have magnitudes comparable to what Earth can yield and absorb. Some scientists warn of possible abrupt changes in vital Earth systems. Half of today's 7 billion people remain poor. Billions more people and massive urbanization and ageing are in prospect in the coming decades. In this new world, it is time to create the information, incentives and institutions needed to reconcile environmental sustainability, national governance, and economic globalization.

Friday October 19, 2012
Noon
Joel E. Cohen, The Rockefeller University and Columbia University, New York

Title: Taylor's power law of population variation, stochastic models of population dynamics, and abrupt change

Abstract:
Vital Earth systems have changed abruptly in the past. Some scientists, based on models and data, warn of possible abrupt changes in prospect. My research on mathematical models of population dynamics led recently to an unexpected theoretical example of a singularity in the exponent of Taylor's power law of population variability (or fluctuation scaling) in response to smooth changes in the power spectrum of an environmental factor like temperature. Abrupt changes can arise even where least expected. Are we ready?

BLOCK 1, 2012 - September

Friday, September 7
2:30 pm, TSC 229

Fred Tinsley (CC)

Title: Noncompact Manifolds that are inward tame or "what I did on my sabbatical"

Abstract: This project has its roots in the summer geometric topology workshop
at Colorado College in 2000. By 2002 Craig Guilbault (UW-Milwaukee) and I had
formulated a ‘10-year plan’ to completely understand the ends of open, inward-
tame manifolds in high dimensions. This effort has used extensively theories from
manifold homology and cohomology, combinatorial and geometric group theory,
algebraic K-theory, and manifold topology. I will describe the problem and report
on our progress. This talk should be accessible to any student who has completed
MA 375 Introduction to Mathematical Analysis. I even will pose a problem in
computer graphics for which a solution would be quite helpful.

Rated: R


Friday, September 14
1:00 pm, TSC 122 (Lecture Hall)
Matthew Whitehead (CC)

Title: The End of Privacy? 

Abstract: Do you value your personal privacy?  Are you concerned about the degradation of privacy in the Internet Age?  Your answers may depend on your age and cultural background, but one thing is clear: technology and data mining are redefining our notions of privacy.  In this talk we will discuss domestic surveillance using hummingbird-sized drones, how some of your anonymous data might not be quite so anonymous, and how people are tracked online and shown personalized advertisements chosen by machine learning systems.

Rating: G



Friday, September 21
2:30pm, TSC 229
Mike Siddoway (CC)

Title: "A Wind Erosion Equation"

Abstract:  Wind erosion is still a major problem in the Great Plains.  If you see dust rising off an acre of land, this translates to about a dime's width of soil being liberated from the surface, approximately five tons of particulate. Beginning in the late 1950's, scientists in Canada and the US began an effort to study the factors behind wind erosion. The idea being: "The better we understand the mechanisms of soil loss to wind, the more we can do to prevent catastrophic losses, like those suffered during the Dust Bowl years."  The "equation" (really an algorithm) that was devised in the mid-60's, though improved upon in many ways since, is still the most widely used around the world.  The modeling of "wind erosion," the problem that first brought mathematics deeply into the study of soil processes, is still one of the most actively pursued areas in all of soil science.

Rated: G