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AJ Stewart, Seattle University
"A Section on Sections" Abstract: Functions tell us a lot about geometric spaces (whether they’re connected, whether they have corners, etc). However, in order to get a complete picture of spaces a more robust idea is needed; sections. In this talk we’ll explain exactly what a section is and find out why they tell us that giving directions on a M\”{o}bius strip is a bad idea, that there is always a point on the Earth with no wind, and that being able to factor numbers uniquely is actually a geometric property.
December 04, 2014 @ 3:30pm,
Bannan 402


Paul T. Allen, Lewis and Clark College
"Finite Differences and Solvability of Differential Equations Problems" Abstract: When does a differential equations problem have a solution? In even simple situations, this seemingly innocuous question is actually rather tricky to answer. In this talk we explore the question of existence by considering an approximate problem, obtained by finite differences, which suitable for obtaining numerical solutions. It is possible to understand completely when this approximate problem has a solution! This, in turn, gives us a way to understand when to expect that the original problem has a solution. NOTE: THIS IS A WEDNESDAY TALK!!
November 19, 2014 @ TBA,
TBA


Tracey Marsh, University of Washington
"Geometry of efficient estimation." Abstract: Estimation of additive geneenvironment interactions are of significant interest to both basic science research and public health. Recently, much methodological work has been done to support semiparametric estimation of the relative excess risk due to interaction (RERI). Of particular interest is estimation of RERI from casecontrol samples nested within randomized controlled trials, where known geneenvironment independence can be exploited for efficiency gain. One goal of this talk is to introduce the field of Biostatistics (biowhat?) through this estimation problem. Another goal is to highlight the underlying mathematics (advanced versions of geometry, linear algebra, and calculus) on which the statistical efficiency theory of asymptotically linear estimators relies. Familiarity with linear algebra and calculus will be assumed, but no prior knowledge of statistics will be required. This talk should be accessible to undergraduates.
November 13, 2014 @ 3:30pm,
Bannan 402


Katya Yurasovskaya, Seattle Univesity
"Braid Groups: An Introduction" Abstract: A braid may be regarded as a decoration or part of an ornament that we often see in everyday life. However, a braid can be viewed as a mathematical object as well. Braid groups B_n were first described by Emil Artin in 1926 and have enjoyed a long history since then, with applications to knot theory, cryptography, and physics. Working with braid groups involves a beautiful mix of algebraic and geometric techniques. In this talk, we will explore different ways to define the braid group, describe group structure and properties, and look at connections to a variety of mathematical fields.
November 06, 2014 @ 3:30pm,
Bannan 402


Tom Edgar, Pacific Lutheran University
"Generalized Binomial Coefficients via the Dominance Order on Natural Numbers" Abstract: We introduce the study of Pascal's Triangle modulo a fixed integer. In particular, we will discuss famous, yet relatively unknown, results due to Lucas and Kummer. Along the way, we will connect Pascal's Triangle to arithmetic in different bases and to an interesting family of partial orders on the Natural numbers. We will see how these partial orders can describe Pascal's Triangle modulo a prime and how, in turn, both of these relate to counting the number of ``carries" when doing arithmetic. These intertwined connections will then allow us to discuss, and somewhat fix, a problem that we will encounter in our initial investigation of Pascal's Triangle by introducing a new class of sequences and their corresponding generalized binomial coefficients. No prior knowledge of combinatorics or number theory is necessary but may be helpful.
October 30, 2014 @ 3:30pm,
Bannan 402


Michael Schultheis,
"Art and Mathematics" Abstract: Likening his canvas to a chalkboard, Michael Schultheis creates paintings consisting of layers of mathematical notations and drawings that describe the form and motion of threedimensional geometric shapes. The Department of Visual Arts and Art History together with the Department of Mathematics are proud cosponsors of a presentation by Michael Schultheis on his art as the intersection of artistic, mathematical, and philosophical ideas. Free of charge and open to the public. NOTE: THIS PRESENTATION OCCURS ON A WEDNESDAY!
October 22, 2014 @ 5:00 pm,
Wyckoff Aud.


Nicholas Scoville, Ursinus College
" Graph isomorphisms in discrete Morse theory" Abstract: Discrete Morse theory is a new and exciting area of mathematics. It combines aspects of algebra, combinatorics, and topology. In this talk, we will introduce discrete Morse theory on graphs. We discuss an existing notion of equivalence between discrete Morse functions based on a sequence of homology groups (we'll discuss what this means) of the corresponding subgraphs of G. We then use the homology sequence to study a new notion of equivalence between discrete Morse functions. This equivalence is based on the isomorphism type of the subgraphs of G. We count the number of equivalence classes on star graphs and deduce an upper bound for the number of equivalence classes for a collection of graphs. This talk should be accessible to undergraduates.
October 16, 2014 @ 3:30pm,
Bannan 402


David Kung, St. Mary's College of Maryland
"Harmonious Equations: A Mathematical Exploration of Music" Abstract: Mathematics and music seem to come from different spheres (arts and sciences), yet they share an amazing array of commonalities. We will explore these connections by examining the musical experience from a mathematical perspective. The mathematical study of a single vibrating string unlocks a world of musical overtones and harmonicsand even explains why a clarinet plays so much lower than its similarsized cousin the flute. Calculus, and the related field of differential equations, shows us how our ears hear differences between two instrumentswhat musicians call timbreeven when they play the same note at the same loudness. Finally, abstract algebra gives modern language to the structures beneath the surface of Bach's magnificent canons and fugues. Throughout the talk, mathematical concepts will come to life with musical examples played by the speaker, an amateur violinist.
October 09, 2014 @ 3:30pm,
Bannan 402


Jim Humphreys, Seattle University
"Mathematics and Music Theory 101: Number Theory" Abstract: According to legend, mathematics and music theory have been joined from the start. This talk will briefly recount how elementary number theory shows the impossibility of realizing the initial goal of music theory, various attempts by mathematicians through the years to get around the difficulty, and how number theory points toward a (partial) solution.
April 07, 2014 @ 3:30pm,
Bannan 401


Senior synthesis: Nonlinear waves day, Seattle University
"SENIOR SYNTHESIS 2014.I" Abstract: This colloquium will feature 3 senior synthesis presentations on nonlinear waves.
March 13, 2014 @ 3:30pm,
Bannan 401


Eric Woolgar, University of Alberta
"Black holes: What are they, and what governs their mathematics?" Abstract: Black holes are back in the news. Stephen Hawking has recently offered the provocative suggestion that they don't exist, but that ``apparent horizons'' do. In this talk, I will introduce a little Riemannian and Lorentzian geometry, enough so that we can give mathematical meaning to the terms ``black hole'', ``event horizon'', and ``apparent horizon''. The latter is very closely related to the notion of a minimal surface. I will introduce a simple differential equation of Riccati type which can be used to address many questions about black holes. As an example, I will consider the question of whether a black hole can have any topology other than that of a sphere.
March 11, 2014 @ 2:30,
Bannan 401


Stephanie Hatley, Radiant Zemax
"Advancements in Defect Detection: A Mathematical Approach to Modeling the Human Eye" Abstract: With the increasing cost of labor and the higher demands for consumer electronics, the flat panel display industry is looking for ways to decrease cost, increase quality, and meet customer expectations. Radiant Zemax is one of the leading global providers of test and measurement tools designed to analyze quality of displays on the production line. The challenge is simulating the customer experience from a display performance perspective. In my talk, I will discuss how we use color theory and advanced algorithms to mimic the human eye in a fast and quantitative fashion. Only a basic understanding of algebra is required, but applications of integral calculus and differential equations will be discussed. The goal of the talk is to demonstrate how an understanding of mathematics is a tool that can be used to solve complicated problems in the consumer electronics industry.
March 06, 2014 @ 3:30pm,
Bannan 401


Nicholas Cain, Allen Institute
"Mathematical modeling of the mouse brain: a multiscale approach" Abstract: The mammalian central nervous system is the most complicated physical system in known universe, and subserves the full spectrum of higher cognitive abilities. Integral to the proper function of this biological tissue are processes whose dynamics range across many orders magnitude in spatial scale. In my talk, I will describe how mathematical and computational modeling can aide in predicting the dynamics of neuronal networks, and understand how dynamics can interact across these spatial scales. Only a basic understanding of neurobiology is prerequisite, but applications of ordinary/partial differential equations, linear algebra, and graph theory will be presented. The goal of the talk is to expose the audience to applications of mathematics to neurobiology, and demonstrate the range of mathematical tools that can be brought to bear to understand the complicated processes of neuronal networks.
February 27, 2014 @ 3:30pm,
Bannan 401


Eric Woolgar, University of Alberta
"This talk has been postponed." Abstract: This talk has been postponed to March.
February 20, 2014 @ Postponed.,
Postponed.


Bernard Deconinck, University of Washington
"Riemann surfaces and water waves (or: why do we care about Riemann surfaces?)" Abstract: Water waves in shallow water are accurately described by solutions of the Kadomtsev Petviashvili equation. These solutions are parameterized by Riemann surfaces and as such it is important that we can compute on Riemann surfaces as efficiently as we do on the real line. I will demonstrate what we have accomplished over the last 15 years. Different maple demos will be sprinkled throughout the talk.
February 13, 2014 @ 3:30pm,
Bannan 401


Jeff DiFranco, Liberty Mutual
"Mathematics of Insurance Pricing" Abstract: In this talk I will introduce some of the basic mathematical ideas of insurance pricing indications involving loss development, onleveling of premium, application of trend, catastrophe loading and credibility. In addition we will discuss how these basic concepts lead to a wide range of more sophisticated mathematical and statistical processes to investigate these same insurance concepts.
February 06, 2014 @ 3:30pm,
Bannan 401


Steve Klee, Seattle University
"(Linear) algebra, geometry, and sudoku" Abstract: In linear algebra, we learn all about row reduction, which can be used to find a "nice" representation of the solution to a system of linear equations. In this talk, we will generalize the problem of solving systems of linear equations to solving systems of arbitrary polynomial equations. The resulting algebraic and geometric pictures can both become more complicated in this case, but we will study a strong generalization of row reduction that can be used to solve these more general systems. As an application, we will see how to encode a sudoku puzzle as a polynomial system of equations, and determine whether or not a given sudoku puzzle has a solution.
January 30, 2014 @ 3:30pm,
Bannan 401


Dylan Helliwell, Seattle University
"Large numbers" Abstract: The nonnegative integers begin 0, 1, 2, ... and go on for ever. Some numbers in this list have the capacity to generate a sense of wonder, not just because they are large (we can always find a bigger one!) but also because of their significance. In this talk, I would like to share some of my favorite large numbers. These numbers each have a story of their own, and taken together, shed new perspective on this set of numbers upon which we rely so heavily. Our exploration will take us among many disciplines from biology to physics and more, but we will ultimately find ourselves in a purely mathematical setting as we consider numbers going all the way to infinity, and maybe even beyond…
January 23, 2014 @ 3:30pm,
Bannan 401


No talk,
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January 16, 2014 @ ,
Bannan 401


No talk,
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January 09, 2014 @ ,
Bannan 401


Rafe Mazzeo, Stanford University
"Celestial mechanics and the Nbody problem" Abstract: One of the oldest problems in science is to find mathematical rules to predict the motion of heavenly bodies. The search for these rules has driven a surprising amount of the development of mathematics and physics over many hundreds of years. Despite this long history, this field remains an active field of research and there remain many open problems. I will describe how Newton's ``Nbody problem'' is formulated mathematically, give a tour of some known solutions and phenomena and describe some of the active areas of research.
December 05, 2013 @ 3:30pm,
Bannan 401


No talk,
"Happy Thanksgiving" Abstract:
November 28, 2013 @ 3:30pm,
Bannan 401


Christine Cole, Seattle University
"Mathematical Models for Molecular Motors: The Polymerization Ratchet" Abstract: Molecular motors are proteins inside the cell that generate forces and cause the transport of material. The classic examples of molecular motors are myosin, which is responsible for muscle contraction, and kinesin, which is responsible for the transport of cellular materials such as mitochondria and mRNA. Myosin and kinesin both move along polymer tracks, composed of actin filaments and tubulin microtubules respectively. The dynamics of the onedimensional polymer tracks themselves also play important roles in cell motility. One motivating example is the actinpolymerizationdriven motion of the bacteria Listeria monocytogenes. In this talk, a mathematical model for a polymerization "ratchet" system will be introduced. Simulation techniques and some analytical results for the ratchet model will be discussed.
November 21, 2013 @ 3:30pm,
Bannan 401


Jonah Ostroff, UW Math
"ColoringMaps with Many Palettes" Abstract: In a classical vertexcoloring problem, we have a map of countries which we would like to paint using a small list of colors,with the restriction that no two adjacent countries are painted the same color. We'll discuss a variant of this problem known as list coloring: instead of using a single set of colors, we'll have a different list of colors for every country. Does this make the problem easier or harder? Can we put bounds on how many colors we need in each list? We'll explore these questions and more. No prior knowledge of graph theory will be assumed.
November 14, 2013 @ 3:30pm,
Bannan 401


TBA,
"TBA" Abstract:
November 07, 2013 @ 3:30pm,
Bannan 401


Shusen Ding, Seattle University
"From calculus to the Aharmonic equation" Abstract: In our calculus classes, we learned that the value of integrals are determined by both the domain and the integrand. Hence, in order to study the values or existence of this integral, mathematicians have been investigating various integral domains and different integrands, which has lead two research directions in analysis, Domains and Differential Forms. In this talk, we will start with Laplace’s equation or the harmonic equation that we have seen in our calculus classes (MATH 232). This equation has been extended into many different versions in euclidean space. One kind of these extensions is called the Aharmonic equations. We will discuss various versions of the Aharmonic equations and recent results related to this kind of the Aharmonic equations in this talk.
October 31, 2013 @ 3:30pm,
Bannan 401


Matt Patterson, Boeing
"GEODUCK: A Geometry Engine." Abstract: The Generalized Environment for Optimization and Development Using a Common Kernel, or GEODUCK, was developed by Boeing to address needs of various programs and disciplines. GEODUCK provides ways for users to create and manipulate curves, surfaces and Solids as well as more general approximate mappings. This talk will give a quick overview of the mathematics underpinning the geometry engine, and then progress on to a live demo of functionality.
October 24, 2013 @ 3:30pm,
Bannan 401


Laura Matrajit, Fred Hutchinson Cancer Research Center
"Optimal Vaccine Allocation for the Early Mitigation of Pandemic Influenza" Abstract: With new cases of avian influenza H5N1 (H5N1AV) arising frequently, the threat of a new influenza pandemic remains a challenge for public health. Several vaccines have been developed specifically targeting H5N1AV, but their production is limited and only a few million doses are readily available. Because there is an important time lag between the emergence of new pandemic strain and the development and distribution of a vaccine, shortage of vaccine is very likely at the beginning of a pandemic. We coupled a mathematical model with a genetic algorithm to optimally and dynamically distribute vaccine in a network of cities, connected by the airline transportation network. By minimizing the illness attack rate (i.e., the percentage of people in the population who become infected and ill), we focus on optimizing vaccine allocation in a network of 16 cities in Southeast Asia when only a few million doses are available. Our results suggest that cooperative strategies where the resources are optimally distributed among the cities perform much better than the strategies where the vaccine is equally distributed among the network, yielding an illness attack rate 17% lower. We show that it is possible to significantly mitigate a more global epidemic with limited quantities of vaccine, provided that the vaccination campaign is extremely fast and it occurs within the first weeks of transmission.
October 17, 2013 @ 3:30pm,
Bannan 401


Brian Fischer, Seattle University
"Coding for optimal performance in the owl¹s brain" Abstract: Capturing nature¹s statistical structure in the neural code is essential for optimal adaptation to the environment. In this talk I will discuss how the brain can approach statistical optimality in the sound localization system of barn owls. The owl captures prey using sound localization. Although owls accurately localize sources near the center of gaze, they systematically underestimate peripheral source directions. We found that this behavior is predicted by statistical inference, formulated as a Bayesian model that emphasizes central directions. We propose that there is a bias in the neural coding of auditory space, which, at the expense of inducing errors in the periphery, achieves high behavioral accuracy at the ethologically relevant range. We found that the biased coding of sound source direction in the owl¹s neural map of auditory space allows a Bayesian estimate of the direction to be decoded from the neural population activity. Thus, a probabilistic model describes both how the map of auditory space supports behavior and why this representation is optimal.
October 10, 2013 @ 3:30pm,
Bannan 401
