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SUMMARY:2. TP 2025 - Research Seminar Series
DTSTART:20250604T130000Z
DTEND:20250611T140000Z
DTSTAMP:20260416T082200Z
UID:indico-event-421@math-events.uni-bonn.de
DESCRIPTION:Speakers: Leandro Chiarini (Durham University)\, Irene Ayuso V
 entura (Durham University)\n\nAs part of the Trimester Program “Probabil
 istic Methods in Quantum Field Theory”\, this seminar series aims to pro
 vide a dynamic space for participants to share their research and foster d
 iscussions. The focus will be on quantum field theory as well as related t
 opics\, encouraging a broad exchange of ideas.\n \nThe seminars will take
  place on Wednesdays\, alternating weeks (except during the summer school 
 and workshop weeks)\, starting on June 4th.\n \nPlease see the precise da
 tes below. Sessions will be held at 3 pm in the lecture hall of the HIM In
 stitute (Poppelsdorfer Allee 45) and will be followed by a coffee break\, 
 allowing ample time for informal discussions.\nNext seminar: \n\nAugust 1
 3: Alexis Prevost  (Universität Bonn) \n\n \nTitle: Hausdorff dimensio
 n of the critical clusters for the metric graph Gaussian free field\n I w
 ill review recent results concerning the phase transition for a strongly c
 orrelated percolation model called the metric graph Gaussian free field. I
 n particular\, I will focus on the Hausdorff dimension of the critical con
 nected components\, as well as on the critical exponents which describe th
 e volume of these components on graphs of intermediate dimension.\nPast se
 minars: \n\nJune 4: Thierry Levy (LPSM\, Université Sorbonne Paris 6) \
 n\n \nTitle: A combinatorial formula for Wilson loop expectations in 2d 
 Yang-Mills theory\nThe 2d Yang—Mills holonomy process is a collection of
  random unitary matrices indexed by loops on a compact surface. Wilson loo
 p expectations are expectations of products of traces of some of these ran
 dom matrices. They play the role of n-point functions\, and are the fundam
 ental observables of this theory. They can be expressed as integrals over 
 products of finitely many copies of the unitary group\, and therefore be a
 nalysed with the tools of non-commutative Fourier analysis. This yields co
 mbinatorial expressions\, which can be regarded as defining a model of ran
 dom partitions over the surface\, and from which one can nicely derive som
 e of the properties of the Wilson loop expectations\, including the Makeen
 ko—Migdal loop equations\, in the regime where the size of the unitary m
 atrices tends to infinity.\n\nJune 18: Loren Coquille (Institut Fourier\, 
 Université Grenoble Alpes)\n\nTitle:  Delocalisation of the long-range G
 aussian chain with long-range interactions\nI will speak about the localis
 ation/delocalisation properties of the discrete Gaussian chain with long-r
 ange interactions (decaying polynomially with the distance between sites).
  This is a model of statistical physics which was the object of several co
 njectures since the 90s\, due to its connection with the Sine-Gordon model
  describing quantum tunnelling within dissipative systems. In a first pape
 r with van Enter\, Le Ny and Ruszel\, we cooked up a very short proof of t
 he absence of shift-invariant Gibbs states at any temperature for any inte
 raction decay power α>2\, which shows delocalisation of the chain in a n
 on-quantitative manner. Recently\, in a second paper with Dario and Le Ny\
 , we obtained a quantitative version of this delocalisation. Combined with
  the results of Kjaer-Hilhorst\, Fröhlich-Zegarlinski and Garban\, our es
 timates provide an (almost) complete picture for the localisation/delocali
 sation of the discrete Gaussian chain. The proofs are based on graph surge
 ry techniques which have been recently developed by van Engelenburg-Lis an
 d Aizenman-Harel-Peled-Shapiro to study the phase transitions of two-dimen
 sional integer-valued height functions (and of their dual spin systems). 
 \n \n\nJuly 9: Vivian Healey (Texas State University)\n\n \nTitle: Larg
 e Deviations of Dyson Brownian motion on the Circle and Multiradial SLE0+\
 n \n\n\n\n\n\n\n\nWe describe the asymptotic behavior as κ → 0+ of mul
 tiradial Schramm-Loewner evolution\, SLEκ. We show that this process with
  the common parameterization satisfies a finite-time large deviation princ
 iple (LDP) in the Hausdorff metric with non-negative rate function\, the m
 ultiradial Loewner energy. We also characterize the large-time behavior of
  curves with finite energy and zero energy (whose driving functions corres
 pond to the Calogero-Moser-Sutherland system). As the drivers of multiradi
 al SLE evolve according to Dyson Brownian motion\, along the way we prove 
 a finite-time LDP for a more general class of diffusion processes of “Dy
 son-type\,” for a fixed number n of particles as the coupling parameter 
 β = 8/κ tends to ∞. (Joint work with Osama Abuzaid and Eveliina Peltol
 a)\n\n\n\n\n\n\n\n \n \n\nJuly 23: Yan Fyodorov (King's College London)
  \n\n \nTitle: Statistics of extremes in eigenvalue-counting staircases\
 nWe consider the counting function (“spectral staircase”) for eigenval
 ues of a random unitary matrix\, drawn from the corresponding beta-ensembl
 e. Our goal is to characterize the statistics of maximum deviation of this
  staircase from its mean slope in a fixed interval\, when size of the matr
 ix N >>1. We will show that one-sided extremes can be addressed by exploit
 ing a mapping onto the statistical mechanics of log-correlated random proc
 esses and using an extended Fisher-Hartwig conjecture. The resulting stati
 stics exhibits combined features of counting statistics of Fermions with S
 utherland-type interaction and extremal statistics of the fractional Brown
 ian motion with Hurst index H = 0. Some of the features are expected to be
  universal. The talk will be based on a joint paper with Pierre Le Doussal
   (Physical Review Letters\, 2020).\nOrganizers:\nIrene Ayuso Ventura\nLe
 andro Chiarini\n \n*In case of questions concerning services and administ
 ration at the HIM institute\, please contact the coordinators of the HIM T
 rimester Programs\, Emma Seggewiss or Kanami Ueda.\n\nhttps://math-events
 .uni-bonn.de/event/421/
LOCATION:Poppelsdorfer Allee 45\, 1. EG\, Lecture room (HIM)
URL:https://math-events.uni-bonn.de/event/421/
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