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BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260702T161500
DTEND;TZID=Europe/Berlin:20260702T161500
DTSTAMP:20260826T002227
CREATED:20260722T095653Z
LAST-MODIFIED:20260722T100231Z
UID:10000159-1783008900-1783008900@www.trr352.de
SUMMARY:A Spectral Transition in the Stability Theory of the 1-D Soler Model
DESCRIPTION:In this talk I will present recent spectral results related to the stability theory of standing waves ψ(t\,x) = e−iωtφ(x) for the one-dimensional Soler model\, a nonlinear Dirac equation\, with power nonlinearity.\n \n\n  f(s) = s|s|p−1\, p > 0.\n \n\n  The analysis is motivated by the so-called gap property arising in the stability theory of nonlinear Schrödinger equations. More precisely\, we study the spectral structure of the Dirac operators obtained by linearization around standing waves\, focusing on the existence of eigenvalues inside the spectral gap and resonances at the thresholds of the essential spectrum.\n \n\n  I will describe a sharp spectral transition in the nonlinearity at the critical exponent p = 1: threshold resonances present in the Gross–Neveu case generate eigenvalues inside the spectral gap for 0 < p < 1\, whereas no threshold resonances occur for p > 1.
URL:http://www.trr352.de/event/a-spectral-transition-in-the-stability-theory-of-the-1-d-soler-model/
LOCATION:Room A 027\, Theresienstr. 37\, Munich\, 80333\, Germany
CATEGORIES:Talks
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BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260707T160000
DTEND;TZID=Europe/Berlin:20260707T160000
DTSTAMP:20260826T002227
CREATED:20260712T223845Z
LAST-MODIFIED:20260712T223845Z
UID:10000155-1783440000-1783440000@www.trr352.de
SUMMARY:Rapid mixing in long-range Lindbladians and static properties of their fixed points
DESCRIPTION:The classification of mixed-state phases requires criteria beyond two-point correlation functions\, such as the decay of the mutual information (MI) and the conditional mutual information(CMI)\, with the latter encapsulated in the notion of Markov length. In this talk\, we show how such static properties of the fixed point of a Lindbladian follow from natural dynamical features of its generator: rapid mixing and frustration-freeness. We focus on systems with long-range interactions\, and prove i)that local Lindbladians satisfying\n(global) rapid mixing and frustration-freeness have fixed-points whose CMI decays with the shielding distance\, and ii) that (local) rapid mixing together with primitivity and regularity implies global decay of MI. For long-range interactions both quantities decay polynomially rather than exponentially\, in contrast to the finite- and short-range regimes where exponential decay (a finite Markov length) is expected within a phase. We further show that Gibbs states of long-range\, non-commuting Hamiltonians satisfy a local Markov property at any temperature.
URL:http://www.trr352.de/event/rapid-mixing-in-long-range-lindbladians-and-static-properties-of-their-fixed-points/
LOCATION:Room 5608.02.020 (Seminarraum (M11))\, Boltzmannstr. 3\, Garching b. München\, 85748\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260707T161500
DTEND;TZID=Europe/Berlin:20260707T174500
DTSTAMP:20260826T002227
CREATED:20260723T124853Z
LAST-MODIFIED:20260728T113530Z
UID:10000160-1783440900-1783446300@www.trr352.de
SUMMARY:Symmetry of optimizers by examples
DESCRIPTION:The course is intended especially for Master’s students\, PhD students\, and postdoctoral researchers\, but everyone interested is warmly welcome to attend. \nIf a variational problem has a symmetry\, it is natural to ask whether an optimizer has the same symmetry. Symmetries offer clear advantages for computing optimizers and determining the optimal value of a variational problem. \nIn general\, however\, optimizers do not necessarily reflect the underlying symmetry: symmetry may be broken. The mathematical analysis must therefore focus on relevant\, non-trivial examples and the techniques used to study them. \nKey examples will include the sharp Sobolev inequality and its generalization\, the Caffarelli–Kohn–Nirenberg inequalities\, as well as sharp Hardy–Littlewood–Sobolev inequalities and Beckner’s inequality. \nParticular emphasis will be placed on techniques such as the use of the isoperimetric inequality and rearrangements\, flows\, and Obata-type identities\, as well as the analysis of the second variation operator for proving symmetry breaking. \nIf time permits\, sharp spinor inequalities will also be discussed. \nThe course is intended especially for Master’s students\, PhD students\, and postdoctoral researchers\, but everyone interested is warmly welcome to attend. \nNo registration is required. \nDates and Rooms \nTuesday\, 7 July\n16:15–17:45 · Room B 047 \nWednesday\, 8 July\n16:15–17:45 · Room A 027 \nFriday\, 10 July\n16:15–17:45 · Room A 027 \nLocation \nLMU Munich · Mathematical Institute\nTheresienstr. 39
URL:http://www.trr352.de/event/symmetry-of-optimizers-by-examples/
LOCATION:Room A 027\, Theresienstr. 37\, Munich\, 80333\, Germany
CATEGORIES:Mini Course
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260710T000000
DTEND;TZID=Europe/Berlin:20260710T235959
DTSTAMP:20260826T002227
CREATED:20260626T074059Z
LAST-MODIFIED:20260626T074117Z
UID:10000154-1783641600-1783727999@www.trr352.de
SUMMARY:Probability Colloquium Augsburg-Munich
DESCRIPTION:Speakers:  \n  \n\n Maria Deijfen\n Remco van der Hofstad\n\n  \nSchedule: \n  \n14:30    Welcome\n15:00    Talk Maria Deijfen\n16:00    Refreshment break\n16:30    Talk Remco van der Hofstad\n18:30    Option for common dinner\n\n  \n\n\nTitles and abstracts:\n  \nMia Deijfen: Into space – and back again! \nAbstract: The configuration model is a standard model for generating a random graph with a prescribed degree distribution. I will describe attempts to analyze a spatial version of the model\, and ongoing work to revert the spatial model to the non-spatial setting. \n  \nRemco van der Hofstad: The number and structure of connected graphs with a fixed degree sequence \nWe study connected graphs with a fixed degree sequence\, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model\, we identify the number of such connected graphs up to a subexponential order. We do this by viewing a connected graph with a given degree distribution as the realization of the giant component in a larger configuration model\, and carefully choosing the degree distribution of the larger graph so that it is likely that its giant component has the required degree distribution. To ensure that the connected graph has exactly the correct degrees\, we use a switching argument. We further identify the local structure of a uniform random graph with prescribed degrees. This is joint work with Sasha Bell and Serte Donderwinkel.
URL:http://www.trr352.de/event/probability-colloquium-augsburg-munich/
LOCATION:University of Augsburg\, Room 2004 (L1)\, Universitätsstraße 14\, Augsburg\, 86159
CATEGORIES:Colloquia
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260715T161500
DTEND;TZID=Europe/Berlin:20260715T161500
DTSTAMP:20260826T002227
CREATED:20260720T205939Z
LAST-MODIFIED:20260720T205939Z
UID:10000157-1784132100-1784132100@www.trr352.de
SUMMARY:Positive Hankel operators
DESCRIPTION:I will discuss some aspects of spectral theory of positive semi-definite Hankel operators\, realised as integral operators on the positive semi-axis with integral kernels of the form h(x+y). I will focus on some remarkable similarities between spectral theory of Hankel operators in this class and spectral theory of one-dimensional Schrodinger operators.
URL:http://www.trr352.de/event/positive-hankel-operators/
LOCATION:Room A 027\, Theresienstr. 37\, Munich\, 80333\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260720T150000
DTEND;TZID=Europe/Berlin:20260720T160000
DTSTAMP:20260826T002227
CREATED:20260715T052533Z
LAST-MODIFIED:20260717T081714Z
UID:10000156-1784559600-1784563200@www.trr352.de
SUMMARY:The Polaron Problem. A Journey through Stochastic and Analytical methods.
DESCRIPTION:A charged particle\, such as an electron\, travelling through a periodic lattice produces a polarization field that induces oscillations in the crystal structure. A polaron is defined as the dressing of the charged particle by the quantized lattice oscillations\, modelled by bosonic fields. The polaron was originally introduced in 1933 by L.  Landau\, and later considered in 1946 by S. Pekar\, to study the selftrapping phenomenon that an electron incurs into by deforming a lattice structure with its polarization field. The energy spectrum and the dynamics of a polaron are described by an Hamiltonian operator in second quantization\, the coupling interaction being linear in creation and annihilation operators. In recent times\, significant advances have been made toward the understanding of the mathematical properties of polaron Hamiltonians and\, in particular\, for the Fröhlich polaron where the dressing is described by a dipolar interaction. The mathematical description of polarons admits both an analytic and a probabilistic approach. In fact\, the spectral properties of a polaron Hamiltonian can be derived through the analysis of the partition function of the model by means of the theory of Brownian motion or by means of methods purely from functional analysis and the spectral calculus. I will discuss the modern mathematical techniques to study polaron problems and discuss the state of the art.
URL:http://www.trr352.de/event/the-polaron-problem-a-journey-through-stochastic-and-analytical-methods/
LOCATION:Room B 349\, Theresienstr. 39\, Munich\, 80333\, Germany
CATEGORIES:Junior Coffee Breaks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260721T161500
DTEND;TZID=Europe/Berlin:20260721T161500
DTSTAMP:20260826T002227
CREATED:20260720T210224Z
LAST-MODIFIED:20260720T210224Z
UID:10000158-1784650500-1784650500@www.trr352.de
SUMMARY:Topology of the Ritz energy landscape
DESCRIPTION:Motivated by questions from quantum chemistry and spectral optimization\, this talk explores the topology of the Ritz energy landscape. Ritz values are the eigenvalues of a larger matrix (or operator) B compressed to a smaller trial subspace S. We can view the k-th Ritz value as a real-valued function (“Ritz energy landscape”) on the manifold of all possible\ns-dimensional trial subspaces\, the Grassmannian Gr(n\,s). \nWe show that the k-th Ritz value (for any k) is a perfect Morse function\, once the definition of “perfection” is suitably adjusted. A Morse function is called perfect if it describes the topology of its domain in the most efficient way possible\, meaning the number of its critical points of each type exactly matches the corresponding Betti number of the space. While the k-th eigenvalue is Lipschitz rather than smooth and while its critical points are not isolated — and not even Morse-Bott — its critical point count is nevertheless well-defined and reflects the topology of the Grassmannian in a minimal\, perfect way. \nThe proof proceeds by introducing a suitable perturbation which ensures that points of non-smoothness are not critical (by a theorem of Zelenko and the presenter) and that the critical points that remain are isolated. We also show that the notion of perfection we introduce (“homological perfection”) is closed under such perturbations. \nBased on joint work with Mark Goresky (IAS).
URL:http://www.trr352.de/event/topology-of-the-ritz-energy-landscape/
LOCATION:Room 5608.02.020 (Seminarraum (M11))\, Boltzmannstr. 3\, Garching b. München\, 85748\, Germany
CATEGORIES:Talks
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