Note: All of the following seminars are located at CHL 015 and take place from 12:30 pm until 1:50 pm unless otherwise stated.

Thursday, March 31st
Speaker : Isabella Novik,UW Math
Title : Counting dots
Abstract: In high-school geometry we are often-times asked to calculate areas bounded by polygonal curves all of whose corners have integer coordinates. In this talk we will discuss one remarkably simple formula --- the Pick formula --- that allows us to do it almost instantaneously. If time permits we will also see an application of this formula to elementary number theory.

Thursday, April 7th
Speaker : Eric Machorro
Title : A few examples of the mathematics used in detector and instrumentation design?
Abstract: The mathematics of detectors lies at the cross roads of numerical analysis, signal processing and inverse problems. Some introductory material on Fourier and Radon transforms is presented in the context of a few examples drawn from typical experimental setups in laboratories and universities

Thursday, April 14th
Speaker : Nathan Baker, PNNL
Title : Applied mathematics for multiscale computational biology
Abstract:Biological processes span a wide range of length and time scales where small molecular changes can have important effects on organs and organisms. In this talk, I describe some of our current research developing and applying methods which attempt to combine length scales to address biological phenomena. In particular, I will focus on adaptive finite element methods for continuum models of biomolecular solvation, electrostatics and diffusion. These methods will be described in the context of specific applications.

Thursday, April 21th
Speaker : Bernard Deconinck, UW AMATH
Title : Water waves: how hard can it be?
Abstract: Water waves are all around us: they provide entertainment (surfing) and relaxation, while occasionally being devastating (the recent Tsunami in Japan). Historically, water waves have been examined by many of the giants of mathematics, such as Euler, Stokes, Arnol'd, etc. To this day, mathematics contributes a lot to the theory of water waves, and water waves contribute a lot to mathematics. In this talk, I will provide an introduction to some of the exciting aspects of the theory of water waves, both from an application and a mathematics point of view.

Thursday, April 28th
Speaker : Andrea Barreiro,UW AMATH
Title :Correlations in the brain
Abstract:There are about 100 billion neurons in the human brain: why do we have so many? One reason is that our brain uses large populations of neurons to perform specific tasks. The activity of neurons within a population will be interrelated, or correlated; these correlations can have a huge influence on how information is created and transmitted. The presence of correlations also introduces experimental challenges, because we may have to simultaneously measure the activity of many neurons in a population, rather than measuring them one at a time.
In this talk I discuss recent work towards understanding how correlations develop in small networks of neurons. While I have focused on small, analytically tractable problems that can serve as building blocks for studying larger networks, neuroscience in general is full of problems at all physical and temporal scales, making mathematical and computational neuroscience a rich area for further study.

Thursday, May 5th
Speaker : Jason Slemons, Cray Inc.
Abstract: The search for eigenvalues of a matrix is one of the most important problems in computational science. At Cray Inc, the supercomputer company where I work, we support many different codes that solve this problem and are always trying to make them faster. First I will about Cray, how I came to work there, what exactly I do there. Next, I will talk about how the search for eigenvalues of a matrix is done practically and what codes that are available on Cray machines. Some examples of code, and some of the math pertaining to the eigenproblem will be presented.

Thursday, May 12th
Speaker : William Stein,UW MATH
Title : An Introduction to the Sage Open Source Mathematical Software Project
Abstract :I started the Sage mathematics software project (http://www.sagemath.org) in 2005, and since then many students have used Sage and also contributed code and documentation. Come to this talk and find out more about how Sage is useful to you, and how you might contribute back.
Website address discussed in the lecture.
http://wstein.org/talks
http://flask.sagenb.org
http://sage.math.washington.edu/home/

Thursday, March 19th
Speaker : Peter Hoff, UW STAT, CSSS
Title : Latent variable models for network data
Abstract: Network and relational data structures have increasingly played a role in the understanding of complex biological, social and other relational systems. Statistical models of such systems can give descriptions of global relational features, characterize local network structure, and provide predictions for missing or future relational data. Latent variable models are a popular tool for describing network and relational patterns. Many of these models are based on well-known matrix decomposition methods, and thus have a rich mathematical framework upon which to build. Additionally, the parameters in these models are easy to interpret: Roughly speaking, a latent variable model posits that the relationship between two nodes is a function of observed and unobserved (latent) characteristics, potentially in addition to contextual factors. In this talk I give an introduction to latent variable models for relational and network data. I first provide a mathematical justification for a general latent factor model based on probability considerations. I then describe and illustrate several latent variable models in the context of the statistical analysis of several network datasets.
Lecture slides

Thursday, March 26th
Speaker :Nathan Kutz, UW AMATH
Title : Low-dimensionality modeling methods for complex systems
Abstract: Dimensionality reduction is a common method for rendering tractable a host of problems arising in the physical, engineering and biological sciences. In recent years, methods from data analysis have started playing critical roles in more traditional applied mathematics problems typically analyzed with dynamical systems and PDE techniques. In this talk, three disparate examples will be considered from (i) image processing, (ii) PDE solution techniques and (iii) neuroscience. In each case, dimensionality reduction, typically achieved through a principal component analysis (PCA) or orthogonal mode decomposition (POD), i.e. a singular value decomposition, achieves remarkable success in providing a mathematical framework which is much more amenable to analysis, thus allowing for a better characterization of the physical, engineering or biological system of interest.