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Abstract:
In these lectures I will give an introduction to the methods of fermionic Renormalization Group and multiscale analysis for some 2-dimensional, non-exactly solvable statistical mechanics models, focusing on the case of close-packed interacting dimer models. I will first define the weakly interacting dimer model and review recent results (in collaboration with V. Mastropietro and F. Toninelli) on the GFF behavior of the height function. Next I will explain how to compute ther-modynamic functions via convergent fermionic perturbation theory, focusing on the free energy. After having explained why naive perturbation theory fails, I will describe renormalized multi-scale expansion and prove its convergence, under the assumption that the effective, scale-dependent, interaction strength remains small, uniformly in the scale index. Finally, I will explain the origin of the cancellations leading to the proof of boundedness of the effective interaction strength, which can be traced back to the exact solvability of a reference model (similar to the Luttinger model) whose asymptotic large-distance behavior is the same as the interacting dimer model.

Schedule:
12.12.2022 – 14:00 - 16:00
13.12.2022 – 14:00 - 16:00
15.12.2022 – 10:00 - 12:00
16.12.2022 – 10:00 - 12:00

Venue: TU Wien, Freihaus Building, Seminarraum DB Gelb 04
Wiedner Hauptstrasse 10, A-1040 Wien, Austria

Contact: fabio.toninelli @ tuwien.ac.at

There is a position Prae-Doc or Post-Doc, on offer at the Faculty of Mathematics at University of Vienna, funded by the Austrian Science Fund (FWF).

Primary collaboration partner is Daniel Bartl and research mostly focuses on statistical aspects within topics related to optimal transport, optimization, and mathematical finance.

Collaboration with other members of the group, in particular Julio Backhoff, Mathias Beiglböck and Walter Schachermayer and their students is possible and welcome.

The Prae-Doc position is for three years, the Post-Doc is for one year with a possible extension for up to three years.

In case of interest, please send a CV and a brief statement regarding research interests to daniel.bartl@univie.ac.at.

• Quantifying the Impact of Model Misspecification , FWF Stand-Alone, PI Daniel Bartl, TBA

• Order-disorder phase transition in 2D lattice models, FWF Stand-Alone, PI Alexander Glazman, 2021 - 2025

• Random Surfaces: growth, fluctuations and universality, FWF Stand-Alone, PI Fabio Toninelli, 2022-2026

• Scaling Limits in random conformal geometry, FWF Stand-Alone, PI Nathanael Berestycki, 2019 - 2023

• Theory and Application of Adapted Wasserstein Distances, FWF Esprit, PI Daniel Bartl, 2022 - 2025

• Transport approach to mimicking processes, FWF Stand-Alone, PIs Mathias Beiglböck and Walter Schachermayer, 2021 - 2025

Our most recent hires are (alphabetically): Damiano De Gaspari, Ivailo Hartarsky, Joona Oikarinen and Joonas Turunen. Welcome!

A PhD position in Probability and (classical) Statistical Mechanics is open at the Technical University of Vienna. Deadline March 4, 2022. Details