Lecture Notes

Technical Talks

• "Macroscopic Dimension" (Ithaca; June 2015; Adventures in Self-Similarity)
• "Dissipation and High Disorder" (Princeton; March 2015; Columbia-Princeton Probab. Day)
• "Nonlinear Noise Excitation" (Evanston; October 2014; Midwest Probab. Colloq., Lecture I)
• "Intermittency and Multifractality" (Evanston; October 2014; Midwest Probab. Colloq., Lecture II)
• "On the Chaotic Character of Some Parabolic SPDEs" (Banff; September 2011; BIRS)
• "An Asymptotic Theory for Randomly-Forced Heat Equations" (Guanajuato; March 2009; CIMAT)
• "Brownian motion and Thermal capacity" (Greifswald September 2008)
• "SPDEs without PDEs" (Madison May 2008)
• "Lévy processes and stochastic partial differential equations" (Copenhagen Aug 2007)
• "Dynamical processes" (Colorado May 2007)
• "On some applications of stable processes" (Houston May 2007)
• "Slices of the Brownian sheet" (Seattle August 2006); David Levin's movie (avi) (67.3 MB)
• "Two tutorials on additive Lévy processes" (Seattle August 2006)
• "Two lectures on additive Lévy processes" (WPA May 06; Taipei)
• "Exceptional Times and Invariance for Dynamical Random Walks"
• "Estimates for the laws of functionals of a Brownian sheet: recent progress and open problem," Swiss Probability Seminar

Expository Talks

• "Roots and Chaos" University of Utah, Summer Research Program for Highschool Students.
• "Good Statistics," University of Utah, Teachers' Math Circle.
• "Random Bits and Pieces: An Introduction to Symbolic Dynamics," University of Utah, Undergraduate Colloquium, November 2006.
• "Remarks on Randomness," University of Utah, Summer Program.
• "What does a typical normal number look like?, and other enchanting tales," University of Utah, Undergraduate Colloquium.
• "Stirling's Formula and Laplace's Method OR How to put your calculus to good use," University of Utah, Department of Mathematics, Undergraduate Colloquium.

Course Materials

• "An Introduction to Parabolic SPDEs"; (Lectures in Probability & Stochastic Processes XI; ISI-Delhi Center; Nov 2016)
• "Gaussian Analysis" (Math. 7880; Spring 2015)
• "Linear Models" (Math 6010; Fall 2011)
• "Lévy Processes (Math 7880, Spring 2011)
• "Introductory Lectures on Stochastic Calculus" (Math 7880, Spring 2008)
• "Summer School on Lévy Processes and Their Applications" (5 lectures at the Sandeberg Manor, Aug '07):
  • Lecture 1: Measure and Dimension
  • Lecture 2: The Range of a Lévy Process
  • Lecture 3: Harmonic Analysis
  • Lecture 4: More on the Range
  • Lecture 5 [Terminus]: Capacity
  • Handout on Riesz kernels
• "Tutorial on SPDEs" (Utah VIGRE Minicourse May '06)
• Slightly idiosyncratic, but hopefully fun, notes on Discrete Math (Summer 2015)
• "Lecture notes on mathematical statistics" (Math 6070):
  • Introduction to Probability.
  • Introduction to Statistics.
  • Chi-Squared Tests.
  • Empirical Processes, and the Kolmogorov-Smirnov Statistic.
  • Density Estimation.
• "Lecture notes on the ergodic theorem" (Math 7880)
• "Lecture notes on Donsker's invariance principle" (Math 7880)
• "Lecture notes on linear statistical models" (Math 6010):
  • Assessing Normality,
  • Least Squares and Projections,
  • Simple Linear Regression.
• "Mathematical Probability," (Math 6040), The University of Utah.
• REU Notes on "Random Walks," The University of Utah.
• "Lectures on Multiparameter Processes," EPF-Lausanne.
• "Lectures on the Brownian sheet," U. Wisconsin-Madison.

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