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−  <!
 
−  == Thursday, September 17, [http://www.math.ucla.edu/~nickcook/ Nicholas A. Cook], [http://www.math.ucla.edu/ UCLA], <span style="color:red"> 2:25pm Van Vleck B325</span> ==
 
− 
 
−  <div style="width:430px;height:25px;border:5px solid black">
 
−  <b><span style="color:red"> Please note the unusual location, Van Vleck Hall B325 </span></b>
 
−  </div>
 
− 
 
−  Title: '''Random regular digraphs: singularity and spectrum'''
 
− 
 
−  We consider two random matrix ensembles associated to large random regular digraphs: (1) the 0/1 adjacency matrix, and (2) the adjacency matrix with iid bounded edge weights. Motivated by universality conjectures, we show that the spectral distribution for the latter ensemble is asymptotically described by the circular law, assuming the graph has degree linear in the number of vertices. Towards establishing the same result for the adjacency matrix without iid weights, we prove that it is invertible with high probability. Along the way we make use of Stein's method of exchangeable pairs to establish some graph discrepancy properties.
 
− 
 
−  == Thursday, September 24, No seminar <![http://www.math.wisc.edu/~ogrosky/ Reed Ogrosky], [http://www.math.wisc.edu/ UWMadison]> ==
 
− 
 
−  == Thursday, October 1 [http://www.math.wisc.edu/~roch Sebastien Roch], [http://www.math.wisc.edu/ UWMadison] ==
 
− 
 
−  Title: '''Mathematics of the Tree of LifeFrom Genomes to Phylogenetic Trees and Beyond'''
 
− 
 
−  Abstract:
 
−  The reconstruction of the Tree of Life is an old problem in evolutionary biology which has benefited from various branches of mathematics, including probability, combinatorics, algebra, and geometry. Modern DNA sequencing technologies are producing a deluge of new data on a vast array of organismstransforming how we view the Tree of Life and how it is reconstructed. I will survey recent progress on some mathematical and computational questions that arise in this context. No biology background will be assumed. (This is a practice run for a plenary talk at an AMS meeting.)
 
− 
 
−  == Thursday, October 8, No Seminar due to the [http://sites.math.northwestern.edu/mwp/ Midwest Probability Colloquium] ==
 
− 
 
−  [http://sites.math.northwestern.edu/mwp/ Midwest Probability Colloquium]
 
− 
 
−  == Thursday, October 15, <!TBA> [http://math.wisc.edu/~louisfan Louis Fan], [http://www.math.wisc.edu/ UWMadison] ==
 
− 
 
−  Title: '''Reflected diffusions with partial annihilations on a membrane (Part two)'''
 
− 
 
−  Abstract:
 
−  Mathematicians and scientists use interacting particle models to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. In this talk, I will introduce an interacting particle system used to model the transport of positive and negative charges in solar cells. To connect the microscopic mechanisms with the macroscopic behaviors at two different scales, we show that the hydrodynamic limit is a pair of deterministic measures whose densities solve a coupled nonlinear heat equations, while the fluctuation limit can be described by a Gaussian Markov process that solves a stochastic partial differential equation. This is the second part of a previous talk given in the Applied and Computation math seminar. Our proofs are based on a correlation function technique (studying the BBGKY hierarchy) and its generalization. This is joint work with ZhenQing Chen.
 
− 
 
−  == Thursday, October 22, [http://www.math.wisc.edu/~kurtz/ Tom Kurtz], [http://www.math.wisc.edu UWMadison] ==
 
− 
 
− 
 
−  Title: '''Strong and weak solutions for general stochastic models'''
 
− 
 
−  Abstract:
 
−  Typically, a stochastic model relates stochastic “inputs” and, perhaps, controls to stochastic “outputs.” A general version of the YamadaWatanabe and Engelbert theorems relating existence and uniqueness of weak and strong solutions of stochastic equations will be given in this context. A notion of “compatibility” between inputs and outputs is critical in relating the general result to its classical forebears. Timechange equations for diffusion processes provide an interesting example. Such equations arise naturally as limits of analogous equations for Markov chains. For onedimensional diffusions they also are essentially given in the nowfamous notebook of Doeblin. Although requiring nothing more than standard Brownian motions and the Riemann integral to define, the question of strong uniqueness remains unresolved. To prove weak uniqueness, the notion of compatible solution is employed and the martingale properties of compatible solutions used to reduce the uniqueness question to the corresponding question for a martingale problem or an Ito equation.
 
− 
 
−  == Thursday, October 29, [http://www.math.cornell.edu/m/People/EcaterinaSavaHuss Ecaterina SavaHuss], [http://www.math.cornell.edu/m/ Cornell] ==
 
− 
 
−  Title: '''Interpolating between rotor walk and random walk'''
 
− 
 
−  Abstract: After a short introduction on deterministic random walks (called also rotorrouter walks)
 
−  and some related cluster growth models, I will introduce a family of stochastic processes on the integers, depending on a parameter p. These processes interpolate between the deterministic rotor walk (for p=0) and the simple random walk (for p=1/2), and they are not Markovian.
 
−  For such processes, I will prove that the scaling limit is a onesided perturbed Brownian motion, which is a linear combination of a Brownian motion and its running maximum. This is based on joint work with Wilfried Huss and Lionel Levine.
 
− 
 
−  == Thursday, November 5, No Seminar this week ==
 
− 
 
−  == Thursday, November 12, SEMINAR CANCELLED ==
 
− 
 
−  Thunderstorms in Chicago an 11/11 cancelled the speaker's flights; we will try to reschedule.
 
− 
 
−  <![http://www.math.illinois.edu/~lierl/ Janna Lierl], [http://www.math.illinois.edu/ UIUC] ==
 
− 
 
−  Title: '''Parabolic Harnack inequality on fractal Dirichlet spaces'''
 
− 
 
−  Abstract: I will present some recent results on extending the parabolic Moser iteration method to the setting of (fractaltype) metric measure Dirichlet spaces. Under appropriate geometric conditions, we obtain that local weak solutions to heat equation are locally bounded, H\"older continuous, and satisfy a strong parabolic Harnack inequality. If time permits, I will also discuss the case of timedependent Dirichlet forms, or nonsymmetric perturbations of the Dirichlet form.
 
−  Applications of the parabolic Harnack inequality include sharp upper and lower bounds for the associated heat kernel.
 
−  >
 
− 
 
−  == Thursday, November 19, [http://orion.math.iastate.edu/dherzog/ David Herzog] [http://www.math.iastate.edu/ Iowa State] ==
 
− 
 
−  Title: '''Stabilization by noise and the existence of optimal Lyapunov functions'''
 
− 
 
−  Abstract: We discuss certain, explosive ODEs in the plane that become stable under the addition of noise. In each equation, the process by which stabilization occurs is intuitively clear: Noise diverts the solution away from any instabilities in the underlying ODE. However, in many cases, proving rigorously this phenomenon occurs has thus far been difficult and the current methods used to do so are rather ad hoc. Here we present a general, novel approach to showing stabilization by noise and apply it to these examples. We will see that the methods used streamline existing arguments as well as produce optimal results, in the sense that they allow us to understand well the asymptotic behavior of the equilibrium measure at infinity.
 
− 
 
−  == Thursday, November 26, No Seminar, Thanksgiving Break ==
 
−  == Thursday, December 3, [http://www.math.illinois.edu/~lierl/ Janna Lierl], [http://www.math.illinois.edu/ UIUC] ==
 
− 
 
−  Title: '''Parabolic Harnack inequality on fractal Dirichlet spaces'''
 
− 
 
−  Abstract: I will present some recent results on extending the parabolic Moser iteration method to the setting of (fractaltype) metric measure Dirichlet spaces. Under appropriate geometric conditions, we obtain that local weak solutions to heat equation are locally bounded, H\"older continuous, and satisfy a strong parabolic Harnack inequality. If time permits, I will also discuss the case of timedependent Dirichlet forms, or nonsymmetric perturbations of the Dirichlet form.
 
−  Applications of the parabolic Harnack inequality include sharp upper and lower bounds for the associated heat kernel.
 
− 
 
−  == Thursday, December 10, [http://www.case.edu/artsci/math/esmeckes/ Elizabeth Meckes], [http://www.case.edu/artsci/math/ Case Western Reserve University] ==
 
− 
 
−  Title: '''Patterns in Eigenvalues: Random matrices from the compact classical groups.'''
 
− 
 
−  Abstract: There are many striking features of the eigenvalues of random orthogonal and unitary matrices. In this talk, I'll describe Haar measure on those groups and the resulting distributions of the eigenvalues. I will give a survey of nowclassical asymptotic results, and then describe a result of E. Rains and a recent result of mine (joint with M. Meckes), which demonstrate some intriguing selfsimilarities of the eigenvalue processes. Prerequisites will be kept to a minimum.
 
− 
 
− 
 
−  <!
 
−  == Wednesday, <span style="color:red">February 11</span>, [http://www.math.wisc.edu/~stechmann/ Sam Stechmann], [http://www.math.wisc.edu/ UWMadison] ==
 
− 
 
−  <span style="color:red">Please note the unusual time and room.
 
−  </span>
 
− 
 
− 
 
−  Title: Stochastic Models for Rainfall: Extreme Events and Critical Phenomena
 
− 
 
− 
 
−  Abstract:
 
−  In recent years, tropical rainfall statistics have been shown to conform to paradigms of critical phenomena and statistical physics. In this talk, stochastic models will be presented as prototypes for understanding the atmospheric dynamics that leads to these statistics and extreme events. Key nonlinear ingredients in the models include either stochastic jump processes or thresholds (Heaviside functions). First, both exact solutions and simple numerics are used to verify that a suite of observed rainfall statistics is reproduced by the models, including powerlaw distributions and longrange correlations. Second, we prove that a stochastic trigger, which is a timeevolving indicator of whether it is raining or not, will converge to a deterministic threshold in an appropriate limit. Finally, we discuss the connections among these rainfall models, stochastic PDEs, and traditional models for critical phenomena.
 
−  >
 
− 
 
−  == ==
 
   
   