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Colloquium
Department of Mathematics
Colloquium: Math SIUC
Title: Bursting Synchronization of Map-based Neuron Networks
Speaker: Hongjun Cao, Department of Mathematics, Beijing Jiaotong University
Date: Thursday, April 26, 2012
Place: Neckers 156
Time: 3:00pm
Abstract:Abstract: In this talk, first of all, the map-based neuron network coupled by reciprocal excitatory and/or inhibitory chemical and electrical synapses is introduced. Secondly, some classic analytical methods are applied to take into account the map-based neuron model, such as the fast-slow decomposing technique, and the phase plane analysis. Thirdly, a simple system consisting of two identical Rulkov map-based neuron model is taken as an example. The goal is to predict the bursting and the bursting synchronization of the neuron model. Finally, some numerical simulations are extended to large-scale neuron networks. Flier.
Video of Colloquium
Colloquium: Math SIUC
Title: Automorphic representations of GL(n) and their L-functions
Speaker: Dr. Shuichiro Takeda fromDepartment of Mathematics,University of Missouri.
Date: Thursday, March 29, 2012
Place: Neckers 156
Time: 3:00pm
Abstract:Abstract: The concept of automorphic representations, which can be considered as a huge generalization of classical modular forms, is one of the central themes of modern number theory known as the Langlands program. In this talk, I will introduce automorphic representations of GL(n) and their L-functions in a way accessible to non-experts and briefly discuss some recent developments. Flier.
Video of the Colloquium (If you double-click on the smaller video playing it will become full screen.)
Colloquium: Math SIUC
Title: Integral quadratic forms: from local to global
Speaker: Professor Wai Kiu Chan, Wesleyan University
Date: Thursday, March 22, 2012
Place: Neckers 156
Time: 3:00pm
Abstract:Abstract: An integral quadratic form is called regular if it represents all integers which cannot be ruled out by congruence considerations. Examples are the sum of three squares and universal quadratic forms. The goal of this this talk is to describe some of the recent results in the study of regular quadratic forms and generalizations, with emphasis on various finiteness results. Flier.
Video of Colloquium
Langenhop Lecture | Peter Sarnak
7:30PM, Monday, March 5, 2012 | Morris Library Auditorium | Video of Lecture
Part of the Little Egypt Math Week | Organized by Department of Mathematics at SIUC
Event Flier
Colloquium: Math SIUC
Title:Fifteen Theorem and Kloosterman Problem for Hermitian lattices
Speaker: Professor Kim, Ji Young, (Seoul National University)
Date: Thursday, Februaru 16, 2012
Place: Neckers 156
Time: 3:00pm
Abstract:Colloquium flyer.
Video of Colloquium
Colloquium: Math SIUC
Title:Practical Multivariate Robust Statistics
Speaker:Professor David Olive, SIUC
Date: Thursday, December 1, 2011
Place: Neckers 156
Time: 3:00pm
Video of Colloquium
Abstract: Statistics is the science of extracting useful information from data, and a statistical model is used to provide a useful approximation to some of the important characteristics of the population which generated the data.
Multivariate Robust Statistics tries to find methods that give good results for multiple linear regression or multivariate location and dispersion for a large group of underlying distributions and that are useful for detecting certain types of outliers, which are observations that lie far away from the bulk of the data. Plots for detecting outliers and high leverage cases, and prediction intervals and regions that work for large classes of distributions are also of interest. This talk will survey the practical methods that I have been developing since 2004 and give a preview of the Fall 2012 Math 583 class Robust Multivariate Analysis.
Almost all of the competing literature on multivariate robust statistics follows the Rousseeuw and Yohai paradigm which is based on one of the largest and longest running scientific hoaxes in history: that impractical multivariate robust estimators can be efficiently computed by using some criterion to select a fit from a fixed number of easily computed trial fits. Hence this literature is untrustworthy: the best papers either give large sample theory for brand name estimators that take far too long to compute, or give practical outlier resistant methods that are not backed by large sample theory. Click here for the flier.
Colloquium: Math SIUC
Title:Utility Maximization and (F)BSDE of Quadratic Growth
Speaker:Peter Imkeller, HU Berlin, CV
Date: Thursday, November 17, 2011
Place: Neckers 156
Time: 3:00pm
Video of Colloquium
A financial market model is considered on which agents (e.g. insurers) are subject to an exogenous financial risk, which they trade by issuing a risk bond. They are able to invest in a market asset correlated with the exogenous risk. We investigate their utility maximization problem, and calculate bond prices using utility indifference. In the case of exponential utility, this hedging concept is interpreted by means of martingale optimality, and solved with BSDE with drivers of quadratic growth in the control variable.
For more general utility functions defined on the whole real line we show that if an optimal strategy exists then it is given in terms of the solution (X, Y, Z) of a fully coupled FBSDE. Conversely if the FBSDE admits a solution (X, Y, Z) then an optimal strategy can be obtained. In the complete market case, an assumption on the risk aversion guarantees that the FBSDE admits a solution for any finite time horizon. As a particular example of our approach we recover the BSDE for exponential utility, and are able to treat non-classical utility functions like the sum of exponential ones.
For utility functions defined on the half line we also reduce the maximization problem to the solution of FBSDE connected with the ones obtained by Peng (1993). In complete markets, once again we provide conditions for solvability that are applicable to the power, the logarithmic and some non-classical utilities. In our approach we propose an alternative form of the maximum principle for which the Hamiltonian is reflected in a remarkable martingale. This is joint work with U. Horst, Y. Hu, A. Réveillac, and J. Zhang. Flier for the colloquium.
Colloquium: Math SIUC
Title: Applying diffusion models to insect dispersal in real landscapes - tales from two systems
Speaker:John Reeve, Southern Illinois University, Carbondale
Date: Thursday, October 20, 2011
Place: Neckers 156
Time: 3:00pm
Video of Colloquium
Dispersal is a fundamental population process in ecology. We use diffusion models to examine dispersal in two systems, bark beetles and their predators in pine ecosystems, and a planthopper and its egg parasitoid in a prairie one. These organisms inhabit complex landscapes that are composed of habitat patches embedded within non-habitat (matrix) regions of several different types. We conducted mark-recapture experiments in which insects were released at different locations within habitat patches, the matrix, and at habitat-matrix edges. We then fitted diffusion models to these observations which incorporated different diffusion rates for habitat vs. matrix as well as edge behavior in the form of a biased random walk. Diffusion rates and edge behavior were species specific and strongly dependent on the matrix type in both these systems. For the planthoppers, differences in edge behavior may explain why the surrounding matrix strongly affects their local population dynamics. For more information about John Reeve go to here. For more information about the colloquium go here.
Colloquium: Math SIUC
Title:Dihedral Fourier Analysis of Symmetry Preference Data
Speaker:Marlos Viana, University of Illinois at Chicago Eye Center, Chicago, USA
Date: Thursday, October 6, 2011
Place: Neckers 156
Time: 3:00pm
Video of Colloquium
In this talk I will briefly review the notion of Fourier analysis over finite groups and emphasize the case of dihedral analysis and its applications in optics and molecular biology. The notion of experimental results indexed by symmetries will be discussed and illustrated with a study in symmetry preferences. The notions of symmetry orbits, symmetry invariants, arbitrariness resolution, as well as the determination of the orbit invariants as Fourier transforms will be discussed and statistically evaluated for particular cases. The experimental design and results to be discussed in the illustration are described in detail and available here. Check out the flier here.
Colloquium: Math SIUC
Title:The Best Conditioned Markov Chains
Speaker: Dr. Jianhong Xu, SIUC
Date: Thursday, September 22, 2011
Place: Neckers A 156
Time: 3:00pm
Video of Colloquium
What makes a best conditioned Markov chain? In addition to its merit in computation, such a chain also shows optimality in its maximum mean first passage time between any two states. Here is the story about the settlement of a then three-year-old conjecture due to Steve Kirkland on best conditioned Markov chains. The counter-examples were sort of elusive. I wouldn't have been able to stumble across them without Mathematica. Event Flier