www.mathtube.org - Mathematics
http://www.mathtube.org/taxonomy/term/103/0
enQuantum Graph Theory
http://www.mathtube.org/lecture/video/quantum-graph-theory
<div class="field field-type-text field-field-speaker">
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Speaker: </div>
Vern I. Paulsen </div>
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Date: </div>
<span class="date-display-single">Thu, Mar 9, 2017</span> </div>
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<div class="field field-type-text field-field-location">
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Location: </div>
PIMS, University of Manitoba </div>
</div>
</div>
<div class="field field-type-text field-field-conference">
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<div class="field-label-inline-first">
Conference: </div>
PIMS-UManitoba Distinguished Lecture </div>
</div>
</div>
<div class="field field-type-text field-field-abstract">
<div class="field-label">Abstract: </div>
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<div class="field-item odd">
Many numerical invariants of a graph, such as the independence number, clique number and chromatic number, have game theoretic descriptions. In these games a referee poses questions to two collaborating non-communicating players and they return answers. Quantum graph theory is concerned with how these graph parameters change when the players are allowed to use the random outcomes of quantum experiments to determine their answers.
In this talk I will explain these concepts, focusing on the chromatic number, survey some of what little is known about the quantum chromatic numbers of graphs, explain the connection between these ideas and famous open conjectures of A. Connes and B. Tsirelson, and introduce an algebra
affiliated with a graph whose representation theory determines the values of these parameters.
Biography:
Vern Paulsen is a Professor of Pure Mathematics and the Institute for Quantum Computing at the University of Waterloo. He was a Professor of Mathematics and John and Rebecca Moores Chair at the University of Houston before moving to Waterloo in 2015. His primary research focus is on the theory of operator algebras and their applications in quantum information theory. He is the author of five research monographs and over 100 research articles. He received his PhD from the University of Michigan. </div>
</div>
</div>
ScientificMathematicsFri, 07 Jul 2017 17:38:02 +0000root673 at http://www.mathtube.orgLimit Theorems for the Frontier of One-Dimensional Branching Diffusions
http://www.mathtube.org/lecture/video/limit-theorems-frontier-one-dimensional-branching-diffusions
<div class="field field-type-text field-field-speaker">
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<div class="field-label-inline-first">
Speaker: </div>
Thomas Sellke </div>
</div>
</div>
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<div class="field-label-inline-first">
Date: </div>
<span class="date-display-single">Thu, Nov 24, 2016</span> </div>
</div>
</div>
<div class="field field-type-text field-field-location">
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<div class="field-item odd">
<div class="field-label-inline-first">
Location: </div>
PIMS, University of Manitoba </div>
</div>
</div>
<div class="field field-type-text field-field-conference">
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<div class="field-item odd">
<div class="field-label-inline-first">
Conference: </div>
PIMS-UManitoba Distinguished Lecture </div>
</div>
</div>
<div class="field field-type-text field-field-abstract">
<div class="field-label">Abstract: </div>
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<div class="field-item odd">
This talk will discuss results in a joint paper of mine with Steve Lalley from 1992.
Suppose a particle, starting at position 0, moves according to a diffusion process on the real line. Suppose also that this particle emits daughter particles according to a branching process whose instantaneous rate can depend on location, though not on time. The daughter particles move independently according to the same diffusion process, starting at their points of birth, and in turn emit their own daughters according to the same branching process. The simplest special case of this situation is standard branching Brownian motion, with the rate of reproduction not depending on location.
Let R_t be the position of the right-most particle at time t, and let m_t be the median of R_t. In 1937, Kolmogorov, Petrovskii, and Piskunov showed that, for standard branching Brownian motion, (m_t)/ t converges to SQRT(2) and that (R_t - m_t) converges in distribution to a nondegenerate limiting distribution.It turns out that results like those proved by Kolmogorov, et al, hold in great generality for one-dimensional branching diffusions. If the branching diffusion is "recurrent" (in the sense that the initial position is re-visited at arbitrarily large times by _some_ particle), and if space is rescaled so that m_t grows linearly, then (R_t - m_t) converges in distribution to a location-mixture of extreme value distributions. We also have the Andy Warhol Theorem, according to which every particle ever born has a descendant in the lead at some point in the future. </div>
</div>
</div>
ScientificMathematicsFri, 07 Jul 2017 03:01:21 +0000root672 at http://www.mathtube.orgAsynchronous Consensus
http://www.mathtube.org/lecture/video/asynchronous-consensus
<div class="field field-type-text field-field-speaker">
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Speaker: </div>
Faith Ellen </div>
</div>
</div>
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<div class="field-item odd">
<div class="field-label-inline-first">
Date: </div>
<span class="date-display-single">Thu, Oct 20, 2016</span> </div>
</div>
</div>
<div class="field field-type-text field-field-location">
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<div class="field-item odd">
<div class="field-label-inline-first">
Location: </div>
PIMS, University of Manitoba </div>
</div>
</div>
<div class="field field-type-text field-field-conference">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Conference: </div>
PIMS-UManitoba Distinguished Lecture </div>
</div>
</div>
<div class="field field-type-text field-field-abstract">
<div class="field-label">Abstract: </div>
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<div class="field-item odd">
The consensus problem plays a central role in the theory of distributed computing. I will prove that consensus is impossible to solve in some asynchronous shared memory systems and I will present some algorithms for solving it in others, together with matching lower bounds on the amount of time and space needed. Consensus is universal: using consensus and read/write registers, I will show how to implement any shared object. The consensus hierarchy is used to classify the computational power of shared objects. I will conclude by discussing some limitations of this classification that have been recently discovered. </div>
</div>
</div>
ScientificMathematicsFri, 07 Jul 2017 00:21:42 +0000root671 at http://www.mathtube.orgOn De Giorgi Conjecture and Beyond
http://www.mathtube.org/lecture/video/de-giorgi-conjecture-and-beyond
<div class="field field-type-text field-field-speaker">
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<div class="field-label-inline-first">
Speaker: </div>
Jun-Cheng Wei </div>
</div>
</div>
<div class="field field-type-datetime field-field-date">
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<div class="field-label-inline-first">
Date: </div>
<span class="date-display-single">Thu, Sep 29, 2016</span> </div>
</div>
</div>
<div class="field field-type-text field-field-location">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Location: </div>
PIMS, University of Manitoba </div>
</div>
</div>
<div class="field field-type-text field-field-conference">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Conference: </div>
PIMS-UManitoba Distinguished Lecture </div>
</div>
</div>
<div class="field field-type-text field-field-abstract">
<div class="field-label">Abstract: </div>
<div class="field-items">
<div class="field-item odd">
Classifying solutions is one of central themes in nonlinear partial differential equations. This is the content of various Liouville type theorems and more recently De Giorgi type conjectures. I will report recent progress towards De Giorgi's conjecture for Allen-Cahn equation and free boundary problems, and related issues in nonlinear Schroedinger equations. </div>
</div>
</div>
ScientificMathematicsThu, 06 Jul 2017 22:00:29 +0000root670 at http://www.mathtube.orgExtrema of 2D Discrete Gaussian Free Field - Lecture 16
http://www.mathtube.org/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-16
<div class="field field-type-text field-field-speaker">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Speaker: </div>
Marek Biskup </div>
</div>
</div>
<div class="field field-type-datetime field-field-date">
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<div class="field-item odd">
<div class="field-label-inline-first">
Date: </div>
<span class="date-display-single">Sun, Jul 30, 2017</span> </div>
</div>
</div>
<div class="field field-type-text field-field-location">
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<div class="field-item odd">
<div class="field-label-inline-first">
Location: </div>
PIMS, University of British Columbia </div>
</div>
</div>
<div class="field field-type-text field-field-conference">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Conference: </div>
PIMS-CRM Summer School in Probability 2017 </div>
</div>
</div>
<div class="field field-type-text field-field-abstract">
<div class="field-label">Abstract: </div>
<div class="field-items">
<div class="field-item odd">
The Gaussian free field (GFF) is a fundamental model for random fluctuations of a surface. The GFF is closely related to local times of random walks via relations that originated in the study of spin systems. The continuous GFF appears as the limit law of height functions of dimer covers, uniform spanning trees and other models without apparent Gaussian correlation structure. The GFF is also a simple example of a quantum field theory. Intriguing connections to SLE, the Brownian map and other recently studied problems exist. The GFF has recently become subject of focused interest by probabilists. Through Kahane's theory of multiplicative chaos, the GFF naturally enters into models of Liouville quantum gravity. Multiplicative chaos is also central to the description of level sets where the GFF takes values proportional to its maximum, or values order-unity away from the absolute maximum. Random walks in random environments given as exponentials of the GFF show intriguing subdiffusive behavior. Universality of these conclusions for other models such as gradient systems and/or local times of random walks are within reach.
<p> </p>
<ul>
<li><b>Lectures in this course</b>: <a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-1">1</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-2">2</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-3">3</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-4">4</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-5">5</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-6">6</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-7">7</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-8">8</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-9">9</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-10">10</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-11">11</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-12">12</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-13">13</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-14">14</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-15">15</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-16">16</a>
</li><li><a href="https://www.math.ucla.edu/~biskup/PIMS/plan.html">Notes</a></li>
</ul> </div>
</div>
</div>
ScientificMathematicsProbabilitySun, 02 Jul 2017 07:55:54 +0000root669 at http://www.mathtube.orgGraphical approach to lattice spin models - Lecture 16
http://www.mathtube.org/lecture/video/graphical-approach-lattice-spin-models-lecture-16
<div class="field field-type-text field-field-speaker">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Speaker: </div>
Hugo Duminil-Copin </div>
</div>
</div>
<div class="field field-type-datetime field-field-date">
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<div class="field-item odd">
<div class="field-label-inline-first">
Date: </div>
<span class="date-display-single">Fri, Jun 30, 2017</span> </div>
</div>
</div>
<div class="field field-type-text field-field-location">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Location: </div>
PIMS, University of British Columbia </div>
</div>
</div>
<div class="field field-type-text field-field-conference">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Conference: </div>
PIMS-CRM Summer School in Probability 2017 </div>
</div>
</div>
<div class="field field-type-text field-field-abstract">
<div class="field-label">Abstract: </div>
<div class="field-items">
<div class="field-item odd">
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids (lattice gases). It has been understood since the 1980s that random geometric representations, such as the random walk and random current representations, are powerful tools to understand spin models. In addition to techniques intrinsic to spin models, such representations provide access to rich ideas from percolation theory. In recent years, for two-dimensional spin models, these ideas have been further combined with ideas from discrete complex analysis. Spectacular results obtained through these connections include the proof that interfaces of the two-dimensional Ising model have conformally invariant scaling limits given by SLE curves, that the connective constant of the self-avoiding walk on the hexagonal lattice is given by \u221a 2 + \u221a 2 , and that the magnetisation of the three-dimensional Ising model vanishes at the critical point.
<p> </p>
<ul>
<li><b>Lectures in this course</b>: <a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-1">1</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-2">2</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-3">3</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-4">4</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-5">5</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-6">6</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-7">7</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-8">8</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-9">9</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-10">10</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-11">11</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-12">12</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-13">13</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-14">14</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-15">15</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-16">16</a></li>
<li><a href="https://www.math.ucla.edu/~biskup/PIMS/plan.html">Notes</a></li>
</ul> </div>
</div>
</div>
ScientificMathematicsProbabilitySat, 01 Jul 2017 02:58:16 +0000root668 at http://www.mathtube.orgGraphical approach to lattice spin models - Lecture 15
http://www.mathtube.org/lecture/video/graphical-approach-lattice-spin-models-lecture-15
<div class="field field-type-text field-field-speaker">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Speaker: </div>
Hugo Duminil-Copin </div>
</div>
</div>
<div class="field field-type-datetime field-field-date">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Date: </div>
<span class="date-display-single">Thu, Jun 29, 2017</span> </div>
</div>
</div>
<div class="field field-type-text field-field-location">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Location: </div>
PIMS, University of British Columbia </div>
</div>
</div>
<div class="field field-type-text field-field-conference">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Conference: </div>
PIMS-CRM Summer School in Probability 2017 </div>
</div>
</div>
<div class="field field-type-text field-field-abstract">
<div class="field-label">Abstract: </div>
<div class="field-items">
<div class="field-item odd">
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids (lattice gases). It has been understood since the 1980s that random geometric representations, such as the random walk and random current representations, are powerful tools to understand spin models. In addition to techniques intrinsic to spin models, such representations provide access to rich ideas from percolation theory. In recent years, for two-dimensional spin models, these ideas have been further combined with ideas from discrete complex analysis. Spectacular results obtained through these connections include the proof that interfaces of the two-dimensional Ising model have conformally invariant scaling limits given by SLE curves, that the connective constant of the self-avoiding walk on the hexagonal lattice is given by \u221a 2 + \u221a 2 , and that the magnetisation of the three-dimensional Ising model vanishes at the critical point.
<p> </p>
<ul>
<li><b>Lectures in this course</b>: <a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-1">1</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-2">2</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-3">3</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-4">4</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-5">5</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-6">6</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-7">7</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-8">8</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-9">9</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-10">10</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-11">11</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-12">12</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-13">13</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-14">14</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-15">15</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-16">16</a></li>
<li><a href="https://www.math.ucla.edu/~biskup/PIMS/plan.html">Notes</a></li>
</ul> </div>
</div>
</div>
ScientificMathematicsProbabilityFri, 30 Jun 2017 04:17:30 +0000root667 at http://www.mathtube.orgExtrema of 2D Discrete Gaussian Free Field - Lecture 15
http://www.mathtube.org/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-15
<div class="field field-type-text field-field-speaker">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Speaker: </div>
Marek Biskup </div>
</div>
</div>
<div class="field field-type-datetime field-field-date">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Date: </div>
<span class="date-display-single">Thu, Jun 29, 2017</span> </div>
</div>
</div>
<div class="field field-type-text field-field-location">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Location: </div>
PIMS, University of British Columbia </div>
</div>
</div>
<div class="field field-type-text field-field-conference">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Conference: </div>
PIMS-CRM Summer School in Probability 2017 </div>
</div>
</div>
<div class="field field-type-text field-field-abstract">
<div class="field-label">Abstract: </div>
<div class="field-items">
<div class="field-item odd">
The Gaussian free field (GFF) is a fundamental model for random fluctuations of a surface. The GFF is closely related to local times of random walks via relations that originated in the study of spin systems. The continuous GFF appears as the limit law of height functions of dimer covers, uniform spanning trees and other models without apparent Gaussian correlation structure. The GFF is also a simple example of a quantum field theory. Intriguing connections to SLE, the Brownian map and other recently studied problems exist. The GFF has recently become subject of focused interest by probabilists. Through Kahane's theory of multiplicative chaos, the GFF naturally enters into models of Liouville quantum gravity. Multiplicative chaos is also central to the description of level sets where the GFF takes values proportional to its maximum, or values order-unity away from the absolute maximum. Random walks in random environments given as exponentials of the GFF show intriguing subdiffusive behavior. Universality of these conclusions for other models such as gradient systems and/or local times of random walks are within reach.
<p> </p>
<ul>
<li><b>Lectures in this course</b>: <a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-1">1</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-2">2</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-3">3</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-4">4</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-5">5</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-6">6</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-7">7</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-8">8</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-9">9</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-10">10</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-11">11</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-12">12</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-13">13</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-14">14</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-15">15</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-16">16</a>
</li><li><a href="https://www.math.ucla.edu/~biskup/PIMS/plan.html">Notes</a></li>
</ul> </div>
</div>
</div>
ScientificMathematicsProbabilityFri, 30 Jun 2017 01:47:08 +0000root666 at http://www.mathtube.orgGraphical approach to lattice spin models - Lecture 14
http://www.mathtube.org/lecture/video/graphical-approach-lattice-spin-models-lecture-14
<div class="field field-type-text field-field-speaker">
<div class="field-items">
<div class="field-item odd">
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Speaker: </div>
Hugo Duminil-Copin </div>
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Date: </div>
<span class="date-display-single">Tue, Jun 27, 2017</span> </div>
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</div>
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Location: </div>
PIMS, University of British Columbia </div>
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Conference: </div>
PIMS-CRM Summer School in Probability 2017 </div>
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</div>
<div class="field field-type-text field-field-abstract">
<div class="field-label">Abstract: </div>
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<div class="field-item odd">
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids (lattice gases). It has been understood since the 1980s that random geometric representations, such as the random walk and random current representations, are powerful tools to understand spin models. In addition to techniques intrinsic to spin models, such representations provide access to rich ideas from percolation theory. In recent years, for two-dimensional spin models, these ideas have been further combined with ideas from discrete complex analysis. Spectacular results obtained through these connections include the proof that interfaces of the two-dimensional Ising model have conformally invariant scaling limits given by SLE curves, that the connective constant of the self-avoiding walk on the hexagonal lattice is given by √ 2 + √ 2 , and that the magnetisation of the three-dimensional Ising model vanishes at the critical point.
<p> </p>
<ul>
<li><b>Lectures in this course</b>: <a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-1">1</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-2">2</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-3">3</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-4">4</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-5">5</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-6">6</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-7">7</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-8">8</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-9">9</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-10">10</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-11">11</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-12">12</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-13">13</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-14">14</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-15">15</a>,
<a href="/lecture/video/graphical-approach-lattice-spin-models-lecture-16">16</a></li>
<li><a href="https://www.math.ucla.edu/~biskup/PIMS/plan.html">Notes</a></li>
</ul> </div>
</div>
</div>
ScientificMathematicsProbabilityWed, 28 Jun 2017 02:20:35 +0000root665 at http://www.mathtube.orgExtrema of 2D Discrete Gaussian Free Field - Lecture 14
http://www.mathtube.org/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-14
<div class="field field-type-text field-field-speaker">
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Speaker: </div>
Marek Biskup </div>
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</div>
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Date: </div>
<span class="date-display-single">Tue, Jun 27, 2017</span> </div>
</div>
</div>
<div class="field field-type-text field-field-location">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Location: </div>
PIMS, University of British Columbia </div>
</div>
</div>
<div class="field field-type-text field-field-conference">
<div class="field-items">
<div class="field-item odd">
<div class="field-label-inline-first">
Conference: </div>
PIMS-CRM Summer School in Probability 2017 </div>
</div>
</div>
<div class="field field-type-text field-field-abstract">
<div class="field-label">Abstract: </div>
<div class="field-items">
<div class="field-item odd">
The Gaussian free field (GFF) is a fundamental model for random fluctuations of a surface. The GFF is closely related to local times of random walks via relations that originated in the study of spin systems. The continuous GFF appears as the limit law of height functions of dimer covers, uniform spanning trees and other models without apparent Gaussian correlation structure. The GFF is also a simple example of a quantum field theory. Intriguing connections to SLE, the Brownian map and other recently studied problems exist. The GFF has recently become subject of focused interest by probabilists. Through Kahane's theory of multiplicative chaos, the GFF naturally enters into models of Liouville quantum gravity. Multiplicative chaos is also central to the description of level sets where the GFF takes values proportional to its maximum, or values order-unity away from the absolute maximum. Random walks in random environments given as exponentials of the GFF show intriguing subdiffusive behavior. Universality of these conclusions for other models such as gradient systems and/or local times of random walks are within reach.
<p> </p>
<ul>
<li><b>Lectures in this course</b>: <a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-1">1</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-2">2</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-3">3</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-4">4</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-5">5</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-6">6</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-7">7</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-8">8</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-9">9</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-10">10</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-11">11</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-12">12</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-13">13</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-14">14</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-15">15</a>,
<a href="/lecture/video/extrema-2d-discrete-gaussian-free-field-lecture-16">16</a>
</li><li><a href="https://www.math.ucla.edu/~biskup/PIMS/plan.html">Notes</a></li>
</ul> </div>
</div>
</div>
ScientificMathematicsProbabilityTue, 27 Jun 2017 23:43:53 +0000root664 at http://www.mathtube.org