Roland Bauerschmidt

I am a Ph.D. student in mathematics in the Probability Theory Group at the University of British Columbia.

University of British Columbia
Department of Mathematics
121-1984 Mathematics Road
Vancouver, BC, V6T 1Z2, Canada

E-mail address: brt at the same domain as this webpage

In Fall 2013, I will be at the Institute for Advanced Study, Princeton.

Curriculum Vitae

Research in mathematics

My mathematical research interest is in probability theory, analysis, and their applications; in particular, I'm interested in multiscale and renormalization group methods in the context of random fields and self-interacting random walks. My Ph.D. supervisors are Gordon Slade and David Brydges. I have obtained my B.Sc. and M.Sc. degrees in physics from ETH Zürich. My master's thesis was supervised by Jürg Fröhlich and Wojciech de Roeck.

Current projects (in progress)

• Logarithmic corrections to the scaling behavior of four dimensional weakly self-avoiding walks.
  The ultimate goal is to establish that the extent of four dimensional weakly self-avoiding walks of length t grows asymptotically like t^1/2 |log t|^1/8. This is in contrast to the simple random walk and the self-avoiding walk in dimensions strictly above four which both grow like t^1/2, and the self-avoiding walk in dimensions strictly below four which is conjectured (but not known rigorously) to grow like t^α with α > 1/2. More immediate goals are to prove such asymptotic behavior in averaged form, e.g. that the susceptibility and the correlation lengths of order p have the corresponding divergences as the critical point is approached.
• Linear polymers with self-attraction in dimension four and higher.
  The self-avoiding walk is a basic model for a long molecule chain in a good solution. The self-avoidance constraint models the volume effect of the polymer. In a poor solution, there are two competing forces, a repelling one that models the volume effect of the polymer, and an attractive force that accounts for the fact that the polymer tries to avoid contact with the solution. We show that the renormalization group method for the weakly self-avoiding walk developed by Brydges and Slade can be extended to show that the two-point function has mean-field behavior in a region of the extended phase of the polymer.

Completed manuscripts (preprints)

	Structural stability of a dynamical system near a non-hyperbolic fixed point R. Bauerschmidt, D.C. Brydges, and G. Slade Revised version will appear in Annales Henri Poincaré.
	A simple method for finite range decomposition of quadratic forms and Gaussian fields R. Bauerschmidt Accepted for publication in Probability Theory and Related Fields.
	Lectures on Self-Avoiding Walks R. Bauerschmidt, H. Duminil-Copin, J. Goodman, and G. Slade Probability and Statistical Physics in Two and More Dimensions, Clay Mathematics Proceedings, vol. 15, Amer. Math. Soc., 2010, pp. 395-476

Related slides

Finite range decomposition of Green's functions McGill University Analysis Seminar

Related material

• Perturbation theory for self-avoiding walks in Python

Teaching

• MATH 102 Labs (fall 2012)
• MATH 100 (fall 2011)
• Exercises for Gordon Slade's Buzios course on Self-Avoiding Walks (2010)

Miscellaneous

My favorite author is Paul Auster.