Summer 2015


Tuesday, May 26th, 2015, DMSC 102 at 2:30pm
Tynan Kelly
Brandeis University 
Title: Twisted linking numbers and Casson-Gordon invariants
Abstract - Casson-Gordon invariants have been used with great success to answer questions in knot concordancesince their introduction in the late 1970's. In this talk, we will begin by briey discussing some classicalknot theory before moving to the calculation of certain link-ing numbers in branched (and unbranched)covers of knots. Then we present an algorithm for using these linking numbers to calculate how certainCasson-Gordon invariants change under particular surgery operations on a knot.

Thursday, May 28th, 2015
Kanadpriya Basu
University of Texas, El Paso
Title: Nonparametric Regression Methods Applied to Geophysical Data
Abstract: In this work we applied several interpolation techniques, including locally weighted scatterplot smoothing techniques (Lowess/Loess) to geophysical  data. The application of these methods to geophysical data set demonstrate that the overall methods are accurate and efficient. In addition, these methods are highly localized and data dependent so that results are dependent on the data trends. Unlike standard modeling implementations, this modeling technique deals with the spatial analysis of the data. Overall this modeling approach proves to be very reliable and useful for handling spatial data in situations where there is lack of sufficient information for applying a time series approach.

Friday, May 29th, 2015, DMSC 102 at 2:30pm
Brendan Sheehan
Colorado State University 
Title: Coupled Multiphysics Simulations: An overview of methods, with model problem examples
 Abstract:Problems of scientific interest often involve multiple physical processes, which may operate on widely differing spatial and temporal scales, either within the same domain or on either side of a boundary. Obtaining accurate numerical solutions to these problems can be quite difficult. Such situations are often handled with operator splitting of one kind or another, and the consequences on stability and accuracy of solutions are an area of active research. An overview of the topic will be provided along with model problem examples and results.  

Monday, June 8th, 2015, DMSC 105 at 2:30pm
Benjamin Fineman, University of California, Davis
Title: The shape of monotone and skew-monotone pattern avoiding Permutations
Abstract: After a brief introduction to the field of pattern avoiding permutations, we describe shape results for the class of permutations avoiding the monotone and skew monotone patterns respectively. Permutations avoiding the monotone pattern [k+1,... 2,1] can be viewed as the union of k increasing sequences. We show that with high probability, each sequence must lie close to the diagonal (when viewing the permutation matrix). First, we describe an injective map from the set of permutations avoiding the given pattern to pairs of sequences, and then use probabilistic techniques to analyze the more general pairs of sequences. Our results then follow by conditioning that these sequences correspond to permutations avoiding the given pattern. We also obtain similar results for the class of permutations avoiding the skew-monotone pattern, by using a bijection of Backelin, West, and Xin. This is joint work with Erik Slivken.