var bibbase_data = {"data":"<img src=\"//bibbase.org/img/ajax-loader.gif\" id=\"spinner\"\n  style=\"display: none;\" alt=\"Loading..\" />\n\n<div id=\"bibbase\">\n\n  <script type=\"text/javascript\">\n    var bibbase = {\n      params: {\"bib\":\"https://bibbase.org/network/files/ZmFaZDQXbe4PQS9kb\",\"noBootstrap\":\"1\",\"jsonp\":\"1\",\"host\":\"bibbase.org\"},\n      data: [{\"bibtype\":\"misc\",\"type\":\"misc\",\"title\":\"Generic stabilizers for simple algebraic groups acting on orthogonal and symplectic Grassmannians\",\"author\":[{\"firstnames\":[\"Aluna\"],\"propositions\":[],\"lastnames\":[\"Rizzoli\"],\"suffixes\":[]}],\"year\":\"2023\",\"eprint\":\"2308.08214\",\"archiveprefix\":\"arXiv\",\"primaryclass\":\"math.GR\",\"bibtex\":\"@misc{rizzoli2023generic,\\n      title={Generic stabilizers for simple algebraic groups acting on orthogonal and symplectic Grassmannians}, \\n      author={Aluna Rizzoli},\\n      year={2023},\\n      eprint={2308.08214},\\n      archivePrefix={arXiv},\\n      primaryClass={math.GR}\\n}\\n\\n\\n\\n\",\"author_short\":[\"Rizzoli, A.\"],\"key\":\"rizzoli2023generic\",\"id\":\"rizzoli2023generic\",\"bibbaseid\":\"rizzoli-genericstabilizersforsimplealgebraicgroupsactingonorthogonalandsymplecticgrassmannians-2023\",\"role\":\"author\",\"urls\":{},\"metadata\":{\"authorlinks\":{\"rizzoli, a\":\"https://rizzoli.me/publications/\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Modules for algebraic groups with finitely many orbits on totally singular 2-spaces\",\"journal\":\"Journal of Algebra\",\"volume\":\"606\",\"pages\":\"104-169\",\"year\":\"2022\",\"issn\":\"0021-8693\",\"doi\":\"https://doi.org/10.1016/j.jalgebra.2022.05.006\",\"url\":\"https://www.sciencedirect.com/science/article/pii/S0021869322002101\",\"author\":[{\"firstnames\":[\"Aluna\"],\"propositions\":[],\"lastnames\":[\"Rizzoli\"],\"suffixes\":[]}],\"keywords\":\"Algebraic groups, Representation theory, Group theory\",\"abstract\":\"This is the author's second paper treating the double coset problem for classical groups. Let G be an algebraic group over an algebraically closed field K. The double coset problem consists of classifying the pairs H,J of closed connected subgroups of G with finitely many (H,J)-double cosets in G. The critical setup occurs when H is reductive and J is a parabolic subgroup. Assume that G is a classical group, H is simple and J is a maximal parabolic Pk, the stabilizer of a totally singular k-space. We show that if there are finitely many (H,Pk)-double cosets in G, then the triple (G,H,k) belongs to a finite list of candidates. Most of these candidates have k=1 or k=2. The case k=1 was solved in [23] and here we deal with k=2. We solve this case by determining all faithful irreducible self-dual H-modules V, such that H has finitely many orbits on totally singular 2-spaces of V.\",\"bibtex\":\"@article{Rizzoli2,\\ntitle = {Modules for algebraic groups with finitely many orbits on totally singular 2-spaces},\\njournal = {Journal of Algebra},\\nvolume = {606},\\npages = {104-169},\\nyear = {2022},\\nissn = {0021-8693},\\ndoi = {https://doi.org/10.1016/j.jalgebra.2022.05.006},\\nurl = {https://www.sciencedirect.com/science/article/pii/S0021869322002101},\\nauthor = {Aluna Rizzoli},\\nkeywords = {Algebraic groups, Representation theory, Group theory},\\nabstract = {This is the author's second paper treating the double coset problem for classical groups. Let G be an algebraic group over an algebraically closed field K. The double coset problem consists of classifying the pairs H,J of closed connected subgroups of G with finitely many (H,J)-double cosets in G. The critical setup occurs when H is reductive and J is a parabolic subgroup. Assume that G is a classical group, H is simple and J is a maximal parabolic Pk, the stabilizer of a totally singular k-space. We show that if there are finitely many (H,Pk)-double cosets in G, then the triple (G,H,k) belongs to a finite list of candidates. Most of these candidates have k=1 or k=2. The case k=1 was solved in [23] and here we deal with k=2. We solve this case by determining all faithful irreducible self-dual H-modules V, such that H has finitely many orbits on totally singular 2-spaces of V.}\\n}\\n\\n\\n\",\"author_short\":[\"Rizzoli, A.\"],\"key\":\"Rizzoli2\",\"id\":\"Rizzoli2\",\"bibbaseid\":\"rizzoli-modulesforalgebraicgroupswithfinitelymanyorbitsontotallysingular2spaces-2022\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://www.sciencedirect.com/science/article/pii/S0021869322002101\"},\"keyword\":[\"Algebraic groups\",\"Representation theory\",\"Group theory\"],\"metadata\":{\"authorlinks\":{\"rizzoli, a\":\"https://rizzoli.me/publications/\"}},\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"title\":\"Finite singular orbit modules for algebraic groups\",\"journal\":\"Journal of Algebra\",\"volume\":\"570\",\"pages\":\"75 - 118\",\"year\":\"2021\",\"issn\":\"0021-8693\",\"doi\":\"https://doi.org/10.1016/j.jalgebra.2020.11.006\",\"url\":\"http://www.sciencedirect.com/science/article/pii/S0021869320305688\",\"author\":[{\"firstnames\":[\"Aluna\"],\"propositions\":[],\"lastnames\":[\"Rizzoli\"],\"suffixes\":[]}],\"keywords\":\"Algebraic groups, Double coset problem, Rational modules\",\"abstract\":\"Building on the classification of modules for algebraic groups with finitely many orbits on subspaces [9], we determine all faithful irreducible modules V for a connected simple algebraic group H, such that H≤SO(V) and H has finitely many orbits on singular 1-spaces of V. We do the same for H connected semisimple, and maximal among connected semisimple subgroups. This question is naturally connected with the problem of finding for which pairs of subgroups H,K of an algebraic group G there are finitely many (H,K)-double cosets. This paper provides a solution to the question when K is a maximal parabolic subgroup P1 of a classical group SOn, where P1 is the stabilizer of a singular 1-space. We find an interesting range of new examples, from a 5-dimensional module for A1 in characteristic p>5, to the spin module for B6 when p=2.\",\"bibtex\":\"@article{rizzoli,\\ntitle = \\\"Finite singular orbit modules for algebraic groups\\\",\\njournal = \\\"Journal of Algebra\\\",\\nvolume = \\\"570\\\",\\npages = \\\"75 - 118\\\",\\nyear = \\\"2021\\\",\\nissn = \\\"0021-8693\\\",\\ndoi = \\\"https://doi.org/10.1016/j.jalgebra.2020.11.006\\\",\\nurl = \\\"http://www.sciencedirect.com/science/article/pii/S0021869320305688\\\",\\nauthor = \\\"Aluna Rizzoli\\\",\\nkeywords = \\\"Algebraic groups, Double coset problem, Rational modules\\\",\\nabstract = \\\"Building on the classification of modules for algebraic groups with finitely many orbits on subspaces [9], we determine all faithful irreducible modules V for a connected simple algebraic group H, such that H≤SO(V) and H has finitely many orbits on singular 1-spaces of V. We do the same for H connected semisimple, and maximal among connected semisimple subgroups. This question is naturally connected with the problem of finding for which pairs of subgroups H,K of an algebraic group G there are finitely many (H,K)-double cosets. This paper provides a solution to the question when K is a maximal parabolic subgroup P1 of a classical group SOn, where P1 is the stabilizer of a singular 1-space. We find an interesting range of new examples, from a 5-dimensional module for A1 in characteristic p>5, to the spin module for B6 when p=2.\\\"\\n}\\n\\n\",\"author_short\":[\"Rizzoli, A.\"],\"key\":\"rizzoli\",\"id\":\"rizzoli\",\"bibbaseid\":\"rizzoli-finitesingularorbitmodulesforalgebraicgroups-2021\",\"role\":\"author\",\"urls\":{\"Paper\":\"http://www.sciencedirect.com/science/article/pii/S0021869320305688\"},\"keyword\":[\"Algebraic groups\",\"Double coset problem\",\"Rational modules\"],\"metadata\":{\"authorlinks\":{\"rizzoli, a\":\"https://rizzoli.me/publications/\"}},\"downloads\":3,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"abstract\":\"Let X be a bounded subset of $}{$\\\\$\\\\$mathbb\\\\R\\\\ ^\\\\d\\\\\\\\$}{$Rdand write $}{$\\\\C_\\\\$\\\\$mathsf\\\\u\\\\\\\\(X)\\\\$}{$Cu(X)for the set of uniformly continuous functions on X equipped with the uniform norm. The lower and upper box dimensions, denoted by $}{$\\\\$\\\\$underline\\\\$\\\\$rm dim\\\\_\\\\$\\\\$mathsf\\\\B\\\\\\\\(\\\\$\\\\$rm graph\\\\(f))\\\\$}{$dim̲B(graph(f))and $}{$\\\\$\\\\$overline\\\\$\\\\$rm dim\\\\_\\\\$\\\\$mathsf\\\\B\\\\\\\\(\\\\$\\\\$rm graph\\\\(f))\\\\$}{$dim¯B(graph(f)), of the graph $}{$\\\\$\\\\$rm graph(f)\\\\$}{$graph(f)of a function $}{$\\\\f$\\\\$in C_\\\\$\\\\$mathsf\\\\u\\\\\\\\(X)\\\\$}{$f∈Cu(X)are defined by$}{$$\\\\$begin\\\\aligned\\\\\\\\$\\\\$underline\\\\$\\\\$rm dim\\\\_\\\\$\\\\$mathsf\\\\B\\\\\\\\(\\\\$\\\\$rm graph\\\\(f))\\\\ = \\\\$\\\\$lim_\\\\$\\\\$delta $\\\\$searrow 0\\\\ \\\\$\\\\$rm inf\\\\\\\\ \\\\$\\\\$frac\\\\\\\\$\\\\$rm log\\\\ N_\\\\$\\\\$delta\\\\(\\\\$\\\\$rm graph\\\\(f))\\\\\\\\-$\\\\$rm log $\\\\$delta\\\\\\\\,$\\\\$$\\\\$\\\\$\\\\$overline\\\\$\\\\$rm dim\\\\_\\\\$\\\\$mathsf\\\\B\\\\\\\\(\\\\$\\\\$rm graph\\\\(f))\\\\ = \\\\$\\\\$lim_\\\\$\\\\$delta $\\\\$searrow 0\\\\ \\\\$\\\\$rm sup\\\\\\\\ \\\\$\\\\$frac\\\\\\\\$\\\\$rm log\\\\ N_\\\\$\\\\$delta\\\\(\\\\$\\\\$rm graph\\\\(f))\\\\\\\\-$\\\\$rm log $\\\\$, $\\\\$delta\\\\\\\\,$\\\\$end\\\\aligned\\\\$}{$dim̲B(graph(f))=limδ↘0inflogNδ(graph(f))-logδ,dim¯B(graph(f))=limδ↘0suplogNδ(graph(f))-logδ,where $}{$\\\\N_\\\\$\\\\$delta\\\\(\\\\$\\\\$rm graph\\\\(f))\\\\$}{$Nδ(graph(f))denotes the number of δ-mesh cubes that intersect $}{$\\\\$\\\\$rm graph(f)\\\\$}{$graph(f).\",\"author\":[{\"propositions\":[],\"lastnames\":[\"Adam-Day\"],\"firstnames\":[\"B.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Ashcroft\"],\"firstnames\":[\"C.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Olsen\"],\"firstnames\":[\"L.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Pinzani\"],\"firstnames\":[\"N.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Rizzoli\"],\"firstnames\":[\"A.\"],\"suffixes\":[]},{\"propositions\":[],\"lastnames\":[\"Rowe\"],\"firstnames\":[\"J.\"],\"suffixes\":[]}],\"da\":\"2018/12/01\",\"date-added\":\"2021-01-09 16:55:29 +0000\",\"date-modified\":\"2021-01-09 16:55:29 +0000\",\"doi\":\"10.1007/s10474-018-0871-2\",\"id\":\"box-dimension\",\"isbn\":\"1588-2632\",\"journal\":\"Acta Mathematica Hungarica\",\"number\":\"2\",\"pages\":\"263–302\",\"title\":\"On the average box dimensions of graphs of typical continuous functions\",\"ty\":\"JOUR\",\"url\":\"https://doi.org/10.1007/s10474-018-0871-2\",\"volume\":\"156\",\"year\":\"2018\",\"bdsk-url-1\":\"https://doi.org/10.1007/s10474-018-0871-2\",\"bdsk-url-2\":\"http://dx.doi.org/10.1007/s10474-018-0871-2\",\"bibtex\":\"@article{box-dimension,\\n\\tAbstract = {Let X be a bounded subset of {\\\\$}{\\\\$}{\\\\{}{$\\\\backslash$}mathbb{\\\\{}R{\\\\}} \\\\^{}{\\\\{}d{\\\\}}{\\\\}}{\\\\$}{\\\\$}Rdand write {\\\\$}{\\\\$}{\\\\{}C{\\\\_}{\\\\{}{$\\\\backslash$}mathsf{\\\\{}u{\\\\}}{\\\\}}(X){\\\\}}{\\\\$}{\\\\$}Cu(X)for the set of uniformly continuous functions on X equipped with the uniform norm. The lower and upper box dimensions, denoted by {\\\\$}{\\\\$}{\\\\{}{$\\\\backslash$}underline{\\\\{}{$\\\\backslash$}rm dim{\\\\}}{\\\\_}{\\\\{}{$\\\\backslash$}mathsf{\\\\{}B{\\\\}}{\\\\}}({\\\\{}{$\\\\backslash$}rm graph{\\\\}}(f)){\\\\}}{\\\\$}{\\\\$}dim̲B(graph(f))and {\\\\$}{\\\\$}{\\\\{}{$\\\\backslash$}overline{\\\\{}{$\\\\backslash$}rm dim{\\\\}}{\\\\_}{\\\\{}{$\\\\backslash$}mathsf{\\\\{}B{\\\\}}{\\\\}}({\\\\{}{$\\\\backslash$}rm graph{\\\\}}(f)){\\\\}}{\\\\$}{\\\\$}dim¯B(graph(f)), of the graph {\\\\$}{\\\\$}{\\\\{}{$\\\\backslash$}rm graph(f){\\\\}}{\\\\$}{\\\\$}graph(f)of a function {\\\\$}{\\\\$}{\\\\{}f{$\\\\backslash$}in C{\\\\_}{\\\\{}{$\\\\backslash$}mathsf{\\\\{}u{\\\\}}{\\\\}}(X){\\\\}}{\\\\$}{\\\\$}f∈Cu(X)are defined by{\\\\$}{\\\\$}{$\\\\backslash$}begin{\\\\{}aligned{\\\\}}{\\\\{}{$\\\\backslash$}underline{\\\\{}{$\\\\backslash$}rm dim{\\\\}}{\\\\_}{\\\\{}{$\\\\backslash$}mathsf{\\\\{}B{\\\\}}{\\\\}}({\\\\{}{$\\\\backslash$}rm graph{\\\\}}(f)){\\\\}} = {\\\\{}{$\\\\backslash$}lim{\\\\_}{\\\\{}{$\\\\backslash$}delta {$\\\\backslash$}searrow 0{\\\\}} {\\\\{}{$\\\\backslash$}rm inf{\\\\}}{\\\\}} {\\\\{}{$\\\\backslash$}frac{\\\\{}{\\\\{}{$\\\\backslash$}rm log{\\\\}} N{\\\\_}{\\\\{}{$\\\\backslash$}delta{\\\\}}({\\\\{}{$\\\\backslash$}rm graph{\\\\}}(f)){\\\\}}{\\\\{}-{$\\\\backslash$}rm log {$\\\\backslash$}delta{\\\\}}{\\\\}},{$\\\\backslash$}{$\\\\backslash$}{\\\\{}{$\\\\backslash$}overline{\\\\{}{$\\\\backslash$}rm dim{\\\\}}{\\\\_}{\\\\{}{$\\\\backslash$}mathsf{\\\\{}B{\\\\}}{\\\\}}({\\\\{}{$\\\\backslash$}rm graph{\\\\}}(f)){\\\\}} = {\\\\{}{$\\\\backslash$}lim{\\\\_}{\\\\{}{$\\\\backslash$}delta {$\\\\backslash$}searrow 0{\\\\}} {\\\\{}{$\\\\backslash$}rm sup{\\\\}}{\\\\}} {\\\\{}{$\\\\backslash$}frac{\\\\{}{\\\\{}{$\\\\backslash$}rm log{\\\\}} N{\\\\_}{\\\\{}{$\\\\backslash$}delta{\\\\}}({\\\\{}{$\\\\backslash$}rm graph{\\\\}}(f)){\\\\}}{\\\\{}-{$\\\\backslash$}rm log {$\\\\backslash$}, {$\\\\backslash$}delta{\\\\}}{\\\\}},{$\\\\backslash$}end{\\\\{}aligned{\\\\}}{\\\\$}{\\\\$}dim̲B(graph(f))=limδ↘0inflogNδ(graph(f))-logδ,dim¯B(graph(f))=limδ↘0suplogNδ(graph(f))-logδ,where {\\\\$}{\\\\$}{\\\\{}N{\\\\_}{\\\\{}{$\\\\backslash$}delta{\\\\}}({\\\\{}{$\\\\backslash$}rm graph{\\\\}}(f)){\\\\}}{\\\\$}{\\\\$}Nδ(graph(f))denotes the number of δ-mesh cubes that intersect {\\\\$}{\\\\$}{\\\\{}{$\\\\backslash$}rm graph(f){\\\\}}{\\\\$}{\\\\$}graph(f).},\\n\\tAuthor = {Adam-Day, B. and Ashcroft, C. and Olsen, L. and Pinzani, N. and Rizzoli, A. and Rowe, J.},\\n\\tDa = {2018/12/01},\\n\\tDate-Added = {2021-01-09 16:55:29 +0000},\\n\\tDate-Modified = {2021-01-09 16:55:29 +0000},\\n\\tDoi = {10.1007/s10474-018-0871-2},\\n\\tId = {Adam-Day2018},\\n\\tIsbn = {1588-2632},\\n\\tJournal = {Acta Mathematica Hungarica},\\n\\tNumber = {2},\\n\\tPages = {263--302},\\n\\tTitle = {On the average box dimensions of graphs of typical continuous functions},\\n\\tTy = {JOUR},\\n\\tUrl = {https://doi.org/10.1007/s10474-018-0871-2},\\n\\tVolume = {156},\\n\\tYear = {2018},\\n\\tBdsk-Url-1 = {https://doi.org/10.1007/s10474-018-0871-2},\\n\\tBdsk-Url-2 = {http://dx.doi.org/10.1007/s10474-018-0871-2}}\\n\\n\\n\",\"author_short\":[\"Adam-Day, B.\",\"Ashcroft, C.\",\"Olsen, L.\",\"Pinzani, N.\",\"Rizzoli, A.\",\"Rowe, J.\"],\"key\":\"box-dimension\",\"bibbaseid\":\"adamday-ashcroft-olsen-pinzani-rizzoli-rowe-ontheaverageboxdimensionsofgraphsoftypicalcontinuousfunctions-2018\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://doi.org/10.1007/s10474-018-0871-2\"},\"metadata\":{\"authorlinks\":{\"rizzoli, a\":\"https://rizzoli.me/publications/\"}},\"downloads\":2,\"html\":\"\"},{\"bibtype\":\"article\",\"type\":\"article\",\"doi\":\"10.1088/1361-6404/aa62c8\",\"url\":\"https://doi.org/10.1088/1361-6404/aa62c8\",\"year\":\"2017\",\"month\":\"mar\",\"publisher\":\"IOP Publishing\",\"volume\":\"38\",\"number\":\"3\",\"pages\":\"035403\",\"author\":[{\"firstnames\":[\"Antje\"],\"propositions\":[],\"lastnames\":[\"Kohnle\"],\"suffixes\":[]},{\"firstnames\":[\"Aluna\"],\"propositions\":[],\"lastnames\":[\"Rizzoli\"],\"suffixes\":[]}],\"title\":\"Interactive simulations for quantum key distribution\",\"journal\":\"European Journal of Physics\",\"abstract\":\"Secure communication protocols are becoming increasingly important, e.g. for internet-based communication. Quantum key distribution (QKD) allows two parties, commonly called Alice and Bob, to generate a secret sequence of 0s and 1s called a key that is only known to themselves. Classically, Alice and Bob could never be certain that their communication was not compromised by a malicious eavesdropper. Quantum mechanics however makes secure communication possible. The fundamental principle of quantum mechanics that taking a measurement perturbs the system (unless the measurement is compatible with the quantum state) also applies to an eavesdropper. Using appropriate protocols to create the key, Alice and Bob can detect the presence of an eavesdropper by errors in their measurements. As part of the QuVis Quantum Mechanics Visualisation Project, we have developed a suite of four interactive simulations that demonstrate the basic principles of three different QKD protocols. The simulations use either polarised photons or spin 1/2 particles as physical realisations. The simulations and accompanying activities are freely available for use online or download, and run on a wide range of devices including tablets and PCs. Evaluation with students over three years was used to refine the simulations and activities. Preliminary studies show that the refined simulations and activities help students learn the basic principles of QKD at both the introductory and advanced undergraduate levels.\",\"bibtex\":\"@article{quantum,\\n\\tdoi = {10.1088/1361-6404/aa62c8},\\n\\turl = {https://doi.org/10.1088/1361-6404/aa62c8},\\n\\tyear = 2017,\\n\\tmonth = {mar},\\n\\tpublisher = {{IOP} Publishing},\\n\\tvolume = {38},\\n\\tnumber = {3},\\n\\tpages = {035403},\\n\\tauthor = {Antje Kohnle and Aluna Rizzoli},\\n\\ttitle = {Interactive simulations for quantum key distribution},\\n\\tjournal = {European Journal of Physics},\\n\\tabstract = {Secure communication protocols are becoming increasingly important, e.g. for internet-based communication. Quantum key distribution (QKD) allows two parties, commonly called Alice and Bob, to generate a secret sequence of 0s and 1s called a key that is only known to themselves. Classically, Alice and Bob could never be certain that their communication was not compromised by a malicious eavesdropper. Quantum mechanics however makes secure communication possible. The fundamental principle of quantum mechanics that taking a measurement perturbs the system (unless the measurement is compatible with the quantum state) also applies to an eavesdropper. Using appropriate protocols to create the key, Alice and Bob can detect the presence of an eavesdropper by errors in their measurements. As part of the QuVis Quantum Mechanics Visualisation Project, we have developed a suite of four interactive simulations that demonstrate the basic principles of three different QKD protocols. The simulations use either polarised photons or spin 1/2 particles as physical realisations. The simulations and accompanying activities are freely available for use online or download, and run on a wide range of devices including tablets and PCs. Evaluation with students over three years was used to refine the simulations and activities. Preliminary studies show that the refined simulations and activities help students learn the basic principles of QKD at both the introductory and advanced undergraduate levels.}\\n}\\n\\n\\n\",\"author_short\":[\"Kohnle, A.\",\"Rizzoli, A.\"],\"key\":\"quantum\",\"id\":\"quantum\",\"bibbaseid\":\"kohnle-rizzoli-interactivesimulationsforquantumkeydistribution-2017\",\"role\":\"author\",\"urls\":{\"Paper\":\"https://doi.org/10.1088/1361-6404/aa62c8\"},\"metadata\":{\"authorlinks\":{\"rizzoli, a\":\"https://rizzoli.me/publications/\"}},\"html\":\"\"}],\n      metadata: {\"owner\":\"rizzoli, a\",\"authorlinks\":{\"rizzoli, a\":\"https://rizzoli.me/publications/\"}},\n      ownerID: \"4bqnrewsCy6bLuNXv\"\n    };\n  </script>\n\n  <script type=\"text/javascript\">\n  var site$;\n  if (typeof $ != 'undefined') {\n    console.log('existing jquery: storing and then restoring');\n    site$ = $;\n    $ = null;\n  }\n  </script>\n\n  <script src=\"https://ajax.googleapis.com/ajax/libs/jquery/2.2.4/jquery.min.js\">\n  </script>\n  <script type=\"text/javascript\">\n  if (site$) {\n    console.log('existing jquery: avoiding conflict and restoring');\n    bb$ = $.noConflict(true);\n    $ = site$;\n  } else {\n    bb$ = $;\n  }\n  </script>\n\n  <script src=\"//bibbase.org/js/bibbase.min.js\"\n          type=\"text/javascript\">\n  </script>\n\n  <script type=\"text/javascript\"\n          src=\"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML\">\n  </script>\n  <script type=\"text/x-mathjax-config\">\n    MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\\\(','\\\\)']]},\n                        skipTags: [\"body\"],\n                        processClass: \"bibbase_paper\"});\n  </script>\n\n  <style>\n  @media print {\n    .dontprint {\n        display: none !important;\n    }\n\n  .bibbase_group {\n    background-color: #E0E0E0;\n    font-style: italic;\n    font-size: larger;\n    text-shadow: 0px 0px 3px #FFFFFF;\n    border-radius: 4px 4px 4px 4px;\n    -moz-border-radius: 4px 4px 4px 4px;\n    -webkit-border-radius: 4px;\n    padding: 5px 40px 5px;\n    margin-top: 10px;\n    margin-bottom: 5px;\n    cursor: pointer;\n  }\n\n  .bibbase_paper {\n    margin-bottom: 5px;\n  }\n\n  }\n  </style>\n\n  \n  <div style=\"float: right; margin-right: 10px; margin-top: 10px; text-align: right; font-size: 12px\">\n    generated by\n    <a href=\"//bibbase.org\"\n       onclick=\"trackOutboundLink('bibbase', 'logo clicked', window.location.href, '//bibbase.org'); return false;\">\n      <img src=\"//bibbase.org/img/logo.svg\"\n           style=\"vertical-align: middle; margin-left: 3px; height: 16px;\"/\n           alt=\"bibbase.org\"\n           title=\"BibBase – The easiest way to maintain your publications page.\"\n        ></a>\n    \n  </div>\n  \n\n  <div id=\"bibbase_header\" class=\"dontprint\" style=\"\">\n\n    <ul class=\"nav nav-pills\" style=\"margin: 0px;\">\n\n      <li class=\"dropdown\" id=\"groupby_dropdown\">\n      <a class=\"dropdown-toggle\"\n         data-toggle=\"dropdown\"\n         href=\"#\">\n          Group by\n          <b class=\"caret\"></b>\n      </a>\n      <ul class=\"dropdown-menu\">\n        <li class=\"groupby year\"><a onclick=\"groupby('year')\">\n            Year</a>\n        </li>\n        <li class=\"groupby author\"><a onclick=\"groupby('author_short')\">\n            Author</a>\n        </li>\n        <li class=\"groupby type\"><a onclick=\"groupby('type')\">\n            Type</a>\n        </li>\n        <li class=\"groupby keyword\"><a onclick=\"groupby('keyword')\">\n            Keyword</a>\n        </li>\n        <li class=\"groupby downloads\"><a onclick=\"groupby('downloads')\">\n            Downloads</a>\n        </li>\n      </ul>\n      </li>\n\n\n      <li class=\"dropdown\" id=\"menu_dropdown\">\n      <a class=\"dropdown-toggle\"\n         data-toggle=\"dropdown\"\n         href=\"#\" alt=\"controls\">\n          <i class=\"fa fa-reorder\" alt=\"controls\"></i>\n          <b class=\"caret\"></b>\n      </a>\n      <ul class=\"dropdown-menu\">\n        <li>\n          <a onclick=\"toggleAll()\">\n            <i class=\"fa fa-chevron-down fa-fw\"></i> Expand/Collapse All\n          </a>\n        </li>\n        <li>\n          <a download=\"ZmFaZDQXbe4PQS9kb\" href=\"data:text/bibtex;base64,@misc{rizzoli2023generic,
      title={Generic stabilizers for simple algebraic groups acting on orthogonal and symplectic Grassmannians}, 
      author={Aluna Rizzoli},
      year={2023},
      eprint={2308.08214},
      archivePrefix={arXiv},
      primaryClass={math.GR}
}





@article{Rizzoli2,
title = {Modules for algebraic groups with finitely many orbits on totally singular 2-spaces},
journal = {Journal of Algebra},
volume = {606},
pages = {104-169},
year = {2022},
issn = {0021-8693},
doi = {https://doi.org/10.1016/j.jalgebra.2022.05.006},
url = {https://www.sciencedirect.com/science/article/pii/S0021869322002101},
author = {Aluna Rizzoli},
keywords = {Algebraic groups, Representation theory, Group theory},
abstract = {This is the author's second paper treating the double coset problem for classical groups. Let G be an algebraic group over an algebraically closed field K. The double coset problem consists of classifying the pairs H,J of closed connected subgroups of G with finitely many (H,J)-double cosets in G. The critical setup occurs when H is reductive and J is a parabolic subgroup. Assume that G is a classical group, H is simple and J is a maximal parabolic Pk, the stabilizer of a totally singular k-space. We show that if there are finitely many (H,Pk)-double cosets in G, then the triple (G,H,k) belongs to a finite list of candidates. Most of these candidates have k=1 or k=2. The case k=1 was solved in [23] and here we deal with k=2. We solve this case by determining all faithful irreducible self-dual H-modules V, such that H has finitely many orbits on totally singular 2-spaces of V.}
}




@article{rizzoli,
title = "Finite singular orbit modules for algebraic groups",
journal = "Journal of Algebra",
volume = "570",
pages = "75 - 118",
year = "2021",
issn = "0021-8693",
doi = "https://doi.org/10.1016/j.jalgebra.2020.11.006",
url = "http://www.sciencedirect.com/science/article/pii/S0021869320305688",
author = "Aluna Rizzoli",
keywords = "Algebraic groups, Double coset problem, Rational modules",
abstract = "Building on the classification of modules for algebraic groups with finitely many orbits on subspaces [9], we determine all faithful irreducible modules V for a connected simple algebraic group H, such that H≤SO(V) and H has finitely many orbits on singular 1-spaces of V. We do the same for H connected semisimple, and maximal among connected semisimple subgroups. This question is naturally connected with the problem of finding for which pairs of subgroups H,K of an algebraic group G there are finitely many (H,K)-double cosets. This paper provides a solution to the question when K is a maximal parabolic subgroup P1 of a classical group SOn, where P1 is the stabilizer of a singular 1-space. We find an interesting range of new examples, from a 5-dimensional module for A1 in characteristic p>5, to the spin module for B6 when p=2."
}



@article{box-dimension,
	Abstract = {Let X be a bounded subset of {\$}{\$}{\{}{$\backslash$}mathbb{\{}R{\}} \^{}{\{}d{\}}{\}}{\$}{\$}Rdand write {\$}{\$}{\{}C{\_}{\{}{$\backslash$}mathsf{\{}u{\}}{\}}(X){\}}{\$}{\$}Cu(X)for the set of uniformly continuous functions on X equipped with the uniform norm. The lower and upper box dimensions, denoted by {\$}{\$}{\{}{$\backslash$}underline{\{}{$\backslash$}rm dim{\}}{\_}{\{}{$\backslash$}mathsf{\{}B{\}}{\}}({\{}{$\backslash$}rm graph{\}}(f)){\}}{\$}{\$}dim̲B(graph(f))and {\$}{\$}{\{}{$\backslash$}overline{\{}{$\backslash$}rm dim{\}}{\_}{\{}{$\backslash$}mathsf{\{}B{\}}{\}}({\{}{$\backslash$}rm graph{\}}(f)){\}}{\$}{\$}dim¯B(graph(f)), of the graph {\$}{\$}{\{}{$\backslash$}rm graph(f){\}}{\$}{\$}graph(f)of a function {\$}{\$}{\{}f{$\backslash$}in C{\_}{\{}{$\backslash$}mathsf{\{}u{\}}{\}}(X){\}}{\$}{\$}f∈Cu(X)are defined by{\$}{\$}{$\backslash$}begin{\{}aligned{\}}{\{}{$\backslash$}underline{\{}{$\backslash$}rm dim{\}}{\_}{\{}{$\backslash$}mathsf{\{}B{\}}{\}}({\{}{$\backslash$}rm graph{\}}(f)){\}} = {\{}{$\backslash$}lim{\_}{\{}{$\backslash$}delta {$\backslash$}searrow 0{\}} {\{}{$\backslash$}rm inf{\}}{\}} {\{}{$\backslash$}frac{\{}{\{}{$\backslash$}rm log{\}} N{\_}{\{}{$\backslash$}delta{\}}({\{}{$\backslash$}rm graph{\}}(f)){\}}{\{}-{$\backslash$}rm log {$\backslash$}delta{\}}{\}},{$\backslash$}{$\backslash$}{\{}{$\backslash$}overline{\{}{$\backslash$}rm dim{\}}{\_}{\{}{$\backslash$}mathsf{\{}B{\}}{\}}({\{}{$\backslash$}rm graph{\}}(f)){\}} = {\{}{$\backslash$}lim{\_}{\{}{$\backslash$}delta {$\backslash$}searrow 0{\}} {\{}{$\backslash$}rm sup{\}}{\}} {\{}{$\backslash$}frac{\{}{\{}{$\backslash$}rm log{\}} N{\_}{\{}{$\backslash$}delta{\}}({\{}{$\backslash$}rm graph{\}}(f)){\}}{\{}-{$\backslash$}rm log {$\backslash$}, {$\backslash$}delta{\}}{\}},{$\backslash$}end{\{}aligned{\}}{\$}{\$}dim̲B(graph(f))=limδ↘0inflogNδ(graph(f))-logδ,dim¯B(graph(f))=limδ↘0suplogNδ(graph(f))-logδ,where {\$}{\$}{\{}N{\_}{\{}{$\backslash$}delta{\}}({\{}{$\backslash$}rm graph{\}}(f)){\}}{\$}{\$}Nδ(graph(f))denotes the number of δ-mesh cubes that intersect {\$}{\$}{\{}{$\backslash$}rm graph(f){\}}{\$}{\$}graph(f).},
	Author = {Adam-Day, B. and Ashcroft, C. and Olsen, L. and Pinzani, N. and Rizzoli, A. and Rowe, J.},
	Da = {2018/12/01},
	Date-Added = {2021-01-09 16:55:29 +0000},
	Date-Modified = {2021-01-09 16:55:29 +0000},
	Doi = {10.1007/s10474-018-0871-2},
	Id = {Adam-Day2018},
	Isbn = {1588-2632},
	Journal = {Acta Mathematica Hungarica},
	Number = {2},
	Pages = {263--302},
	Title = {On the average box dimensions of graphs of typical continuous functions},
	Ty = {JOUR},
	Url = {https://doi.org/10.1007/s10474-018-0871-2},
	Volume = {156},
	Year = {2018},
	Bdsk-Url-1 = {https://doi.org/10.1007/s10474-018-0871-2},
	Bdsk-Url-2 = {http://dx.doi.org/10.1007/s10474-018-0871-2}}




@article{quantum,
	doi = {10.1088/1361-6404/aa62c8},
	url = {https://doi.org/10.1088/1361-6404/aa62c8},
	year = 2017,
	month = {mar},
	publisher = {{IOP} Publishing},
	volume = {38},
	number = {3},
	pages = {035403},
	author = {Antje Kohnle and Aluna Rizzoli},
	title = {Interactive simulations for quantum key distribution},
	journal = {European Journal of Physics},
	abstract = {Secure communication protocols are becoming increasingly important, e.g. for internet-based communication. Quantum key distribution (QKD) allows two parties, commonly called Alice and Bob, to generate a secret sequence of 0s and 1s called a key that is only known to themselves. Classically, Alice and Bob could never be certain that their communication was not compromised by a malicious eavesdropper. Quantum mechanics however makes secure communication possible. The fundamental principle of quantum mechanics that taking a measurement perturbs the system (unless the measurement is compatible with the quantum state) also applies to an eavesdropper. Using appropriate protocols to create the key, Alice and Bob can detect the presence of an eavesdropper by errors in their measurements. As part of the QuVis Quantum Mechanics Visualisation Project, we have developed a suite of four interactive simulations that demonstrate the basic principles of three different QKD protocols. The simulations use either polarised photons or spin 1/2 particles as physical realisations. The simulations and accompanying activities are freely available for use online or download, and run on a wide range of devices including tablets and PCs. Evaluation with students over three years was used to refine the simulations and activities. Preliminary studies show that the refined simulations and activities help students learn the basic principles of QKD at both the introductory and advanced undergraduate levels.}
}


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return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('rizzoli-genericstabilizersforsimplealgebraicgroupsactingonorthogonalandsymplecticgrassmannians-2023')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@misc{rizzoli2023generic,\n      title={Generic stabilizers for simple algebraic groups acting on orthogonal and symplectic Grassmannians}, \n      author={Aluna Rizzoli},\n      year={2023},\n      eprint={2308.08214},\n      archivePrefix={arXiv},\n      primaryClass={math.GR}\n}\n\n\n\n</pre>\n</div>\n\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2022\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2022')\"\n      onkeypress=\"toggleGroup('group_2022')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2022</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"rizzoli-modulesforalgebraicgroupswithfinitelymanyorbitsontotallysingular2spaces-2022\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://www.sciencedirect.com/science/article/pii/S0021869322002101\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'rizzoli-modulesforalgebraicgroupswithfinitelymanyorbitsontotallysingular2spaces-2022', 'https://www.sciencedirect.com/science/article/pii/S0021869322002101', event);\">\n    Modules for algebraic groups with finitely many orbits on totally singular 2-spaces.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://rizzoli.me/publications/\">Rizzoli, A.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Journal of Algebra</i>, 606: 104-169.  2022.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://www.sciencedirect.com/science/article/pii/S0021869322002101\"\n     onclick=\"log_download('rizzoli-modulesforalgebraicgroupswithfinitelymanyorbitsontotallysingular2spaces-2022', 'https://www.sciencedirect.com/science/article/pii/S0021869322002101', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Modules for algebraic groups with finitely many orbits on totally singular 2-spaces [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/https://doi.org/10.1016/j.jalgebra.2022.05.006\"\n     onclick=\"log_download('rizzoli-modulesforalgebraicgroupswithfinitelymanyorbitsontotallysingular2spaces-2022', 'http://doi.org/https://doi.org/10.1016/j.jalgebra.2022.05.006', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/rizzoli-modulesforalgebraicgroupswithfinitelymanyorbitsontotallysingular2spaces-2022\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('rizzoli-modulesforalgebraicgroupswithfinitelymanyorbitsontotallysingular2spaces-2022')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{Rizzoli2,\ntitle = {Modules for algebraic groups with finitely many orbits on totally singular 2-spaces},\njournal = {Journal of Algebra},\nvolume = {606},\npages = {104-169},\nyear = {2022},\nissn = {0021-8693},\ndoi = {https://doi.org/10.1016/j.jalgebra.2022.05.006},\nurl = {https://www.sciencedirect.com/science/article/pii/S0021869322002101},\nauthor = {Aluna Rizzoli},\nkeywords = {Algebraic groups, Representation theory, Group theory},\nabstract = {This is the author&#x27;s second paper treating the double coset problem for classical groups. Let G be an algebraic group over an algebraically closed field K. The double coset problem consists of classifying the pairs H,J of closed connected subgroups of G with finitely many (H,J)-double cosets in G. The critical setup occurs when H is reductive and J is a parabolic subgroup. Assume that G is a classical group, H is simple and J is a maximal parabolic Pk, the stabilizer of a totally singular k-space. We show that if there are finitely many (H,Pk)-double cosets in G, then the triple (G,H,k) belongs to a finite list of candidates. Most of these candidates have k=1 or k=2. The case k=1 was solved in [23] and here we deal with k=2. We solve this case by determining all faithful irreducible self-dual H-modules V, such that H has finitely many orbits on totally singular 2-spaces of V.}\n}\n\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  This is the author's second paper treating the double coset problem for classical groups. Let G be an algebraic group over an algebraically closed field K. The double coset problem consists of classifying the pairs H,J of closed connected subgroups of G with finitely many (H,J)-double cosets in G. The critical setup occurs when H is reductive and J is a parabolic subgroup. Assume that G is a classical group, H is simple and J is a maximal parabolic Pk, the stabilizer of a totally singular k-space. We show that if there are finitely many (H,Pk)-double cosets in G, then the triple (G,H,k) belongs to a finite list of candidates. Most of these candidates have k=1 or k=2. The case k=1 was solved in [23] and here we deal with k=2. We solve this case by determining all faithful irreducible self-dual H-modules V, such that H has finitely many orbits on totally singular 2-spaces of V.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2021\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2021')\"\n      onkeypress=\"toggleGroup('group_2021')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2021</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"rizzoli-finitesingularorbitmodulesforalgebraicgroups-2021\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S0021869320305688\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'rizzoli-finitesingularorbitmodulesforalgebraicgroups-2021', 'http://www.sciencedirect.com/science/article/pii/S0021869320305688', event);\">\n    Finite singular orbit modules for algebraic groups.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  <a class=\"bibbase author link\" href=\"https://rizzoli.me/publications/\">Rizzoli, A.</a>\n</span>\n\n  \n\n</span>\n\n  <i>Journal of Algebra</i>, 570: 75 - 118.  2021.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"http://www.sciencedirect.com/science/article/pii/S0021869320305688\"\n     onclick=\"log_download('rizzoli-finitesingularorbitmodulesforalgebraicgroups-2021', 'http://www.sciencedirect.com/science/article/pii/S0021869320305688', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Finite singular orbit modules for algebraic groups [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/https://doi.org/10.1016/j.jalgebra.2020.11.006\"\n     onclick=\"log_download('rizzoli-finitesingularorbitmodulesforalgebraicgroups-2021', 'http://doi.org/https://doi.org/10.1016/j.jalgebra.2020.11.006', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/rizzoli-finitesingularorbitmodulesforalgebraicgroups-2021\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>3 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('rizzoli-finitesingularorbitmodulesforalgebraicgroups-2021')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n  \n  \n  \n  \n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{rizzoli,\ntitle = &quot;Finite singular orbit modules for algebraic groups&quot;,\njournal = &quot;Journal of Algebra&quot;,\nvolume = &quot;570&quot;,\npages = &quot;75 - 118&quot;,\nyear = &quot;2021&quot;,\nissn = &quot;0021-8693&quot;,\ndoi = &quot;https://doi.org/10.1016/j.jalgebra.2020.11.006&quot;,\nurl = &quot;http://www.sciencedirect.com/science/article/pii/S0021869320305688&quot;,\nauthor = &quot;Aluna Rizzoli&quot;,\nkeywords = &quot;Algebraic groups, Double coset problem, Rational modules&quot;,\nabstract = &quot;Building on the classification of modules for algebraic groups with finitely many orbits on subspaces [9], we determine all faithful irreducible modules V for a connected simple algebraic group H, such that H≤SO(V) and H has finitely many orbits on singular 1-spaces of V. We do the same for H connected semisimple, and maximal among connected semisimple subgroups. This question is naturally connected with the problem of finding for which pairs of subgroups H,K of an algebraic group G there are finitely many (H,K)-double cosets. This paper provides a solution to the question when K is a maximal parabolic subgroup P1 of a classical group SOn, where P1 is the stabilizer of a singular 1-space. We find an interesting range of new examples, from a 5-dimensional module for A1 in characteristic p&gt;5, to the spin module for B6 when p=2.&quot;\n}\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Building on the classification of modules for algebraic groups with finitely many orbits on subspaces [9], we determine all faithful irreducible modules V for a connected simple algebraic group H, such that H≤SO(V) and H has finitely many orbits on singular 1-spaces of V. We do the same for H connected semisimple, and maximal among connected semisimple subgroups. This question is naturally connected with the problem of finding for which pairs of subgroups H,K of an algebraic group G there are finitely many (H,K)-double cosets. This paper provides a solution to the question when K is a maximal parabolic subgroup P1 of a classical group SOn, where P1 is the stabilizer of a singular 1-space. We find an interesting range of new examples, from a 5-dimensional module for A1 in characteristic p>5, to the spin module for B6 when p=2.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2018\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2018')\"\n      onkeypress=\"toggleGroup('group_2018')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2018</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"adamday-ashcroft-olsen-pinzani-rizzoli-rowe-ontheaverageboxdimensionsofgraphsoftypicalcontinuousfunctions-2018\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1007/s10474-018-0871-2\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'adamday-ashcroft-olsen-pinzani-rizzoli-rowe-ontheaverageboxdimensionsofgraphsoftypicalcontinuousfunctions-2018', 'https://doi.org/10.1007/s10474-018-0871-2', event);\">\n    On the average box dimensions of graphs of typical continuous functions.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Adam-Day, B.; Ashcroft, C.; Olsen, L.; Pinzani, N.; <a class=\"bibbase author link\" href=\"https://rizzoli.me/publications/\">Rizzoli, A.</a>;  and Rowe, J.\n</span>\n\n  \n\n</span>\n\n  <i>Acta Mathematica Hungarica</i>, 156(2): 263–302.  2018.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://doi.org/10.1007/s10474-018-0871-2\"\n     onclick=\"log_download('adamday-ashcroft-olsen-pinzani-rizzoli-rowe-ontheaverageboxdimensionsofgraphsoftypicalcontinuousfunctions-2018', 'https://doi.org/10.1007/s10474-018-0871-2', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"On the average box dimensions of graphs of typical continuous functions [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1007/s10474-018-0871-2\"\n     onclick=\"log_download('adamday-ashcroft-olsen-pinzani-rizzoli-rowe-ontheaverageboxdimensionsofgraphsoftypicalcontinuousfunctions-2018', 'http://doi.org/10.1007/s10474-018-0871-2', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/adamday-ashcroft-olsen-pinzani-rizzoli-rowe-ontheaverageboxdimensionsofgraphsoftypicalcontinuousfunctions-2018\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n  &nbsp;\n  <span class=\"bibbase_stats_paper\" style=\"color: #777;\">\n    <span>2 downloads</span>\n  </span>\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('adamday-ashcroft-olsen-pinzani-rizzoli-rowe-ontheaverageboxdimensionsofgraphsoftypicalcontinuousfunctions-2018')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{box-dimension,\n\tAbstract = {Let X be a bounded subset of {\\$}{\\$}{\\{}{$\\backslash$}mathbb{\\{}R{\\}} \\^{}{\\{}d{\\}}{\\}}{\\$}{\\$}Rdand write {\\$}{\\$}{\\{}C{\\_}{\\{}{$\\backslash$}mathsf{\\{}u{\\}}{\\}}(X){\\}}{\\$}{\\$}Cu(X)for the set of uniformly continuous functions on X equipped with the uniform norm. The lower and upper box dimensions, denoted by {\\$}{\\$}{\\{}{$\\backslash$}underline{\\{}{$\\backslash$}rm dim{\\}}{\\_}{\\{}{$\\backslash$}mathsf{\\{}B{\\}}{\\}}({\\{}{$\\backslash$}rm graph{\\}}(f)){\\}}{\\$}{\\$}dim̲B(graph(f))and {\\$}{\\$}{\\{}{$\\backslash$}overline{\\{}{$\\backslash$}rm dim{\\}}{\\_}{\\{}{$\\backslash$}mathsf{\\{}B{\\}}{\\}}({\\{}{$\\backslash$}rm graph{\\}}(f)){\\}}{\\$}{\\$}dim¯B(graph(f)), of the graph {\\$}{\\$}{\\{}{$\\backslash$}rm graph(f){\\}}{\\$}{\\$}graph(f)of a function {\\$}{\\$}{\\{}f{$\\backslash$}in C{\\_}{\\{}{$\\backslash$}mathsf{\\{}u{\\}}{\\}}(X){\\}}{\\$}{\\$}f∈Cu(X)are defined by{\\$}{\\$}{$\\backslash$}begin{\\{}aligned{\\}}{\\{}{$\\backslash$}underline{\\{}{$\\backslash$}rm dim{\\}}{\\_}{\\{}{$\\backslash$}mathsf{\\{}B{\\}}{\\}}({\\{}{$\\backslash$}rm graph{\\}}(f)){\\}} = {\\{}{$\\backslash$}lim{\\_}{\\{}{$\\backslash$}delta {$\\backslash$}searrow 0{\\}} {\\{}{$\\backslash$}rm inf{\\}}{\\}} {\\{}{$\\backslash$}frac{\\{}{\\{}{$\\backslash$}rm log{\\}} N{\\_}{\\{}{$\\backslash$}delta{\\}}({\\{}{$\\backslash$}rm graph{\\}}(f)){\\}}{\\{}-{$\\backslash$}rm log {$\\backslash$}delta{\\}}{\\}},{$\\backslash$}{$\\backslash$}{\\{}{$\\backslash$}overline{\\{}{$\\backslash$}rm dim{\\}}{\\_}{\\{}{$\\backslash$}mathsf{\\{}B{\\}}{\\}}({\\{}{$\\backslash$}rm graph{\\}}(f)){\\}} = {\\{}{$\\backslash$}lim{\\_}{\\{}{$\\backslash$}delta {$\\backslash$}searrow 0{\\}} {\\{}{$\\backslash$}rm sup{\\}}{\\}} {\\{}{$\\backslash$}frac{\\{}{\\{}{$\\backslash$}rm log{\\}} N{\\_}{\\{}{$\\backslash$}delta{\\}}({\\{}{$\\backslash$}rm graph{\\}}(f)){\\}}{\\{}-{$\\backslash$}rm log {$\\backslash$}, {$\\backslash$}delta{\\}}{\\}},{$\\backslash$}end{\\{}aligned{\\}}{\\$}{\\$}dim̲B(graph(f))=limδ↘0inflogNδ(graph(f))-logδ,dim¯B(graph(f))=limδ↘0suplogNδ(graph(f))-logδ,where {\\$}{\\$}{\\{}N{\\_}{\\{}{$\\backslash$}delta{\\}}({\\{}{$\\backslash$}rm graph{\\}}(f)){\\}}{\\$}{\\$}Nδ(graph(f))denotes the number of δ-mesh cubes that intersect {\\$}{\\$}{\\{}{$\\backslash$}rm graph(f){\\}}{\\$}{\\$}graph(f).},\n\tAuthor = {Adam-Day, B. and Ashcroft, C. and Olsen, L. and Pinzani, N. and Rizzoli, A. and Rowe, J.},\n\tDa = {2018/12/01},\n\tDate-Added = {2021-01-09 16:55:29 +0000},\n\tDate-Modified = {2021-01-09 16:55:29 +0000},\n\tDoi = {10.1007/s10474-018-0871-2},\n\tId = {Adam-Day2018},\n\tIsbn = {1588-2632},\n\tJournal = {Acta Mathematica Hungarica},\n\tNumber = {2},\n\tPages = {263--302},\n\tTitle = {On the average box dimensions of graphs of typical continuous functions},\n\tTy = {JOUR},\n\tUrl = {https://doi.org/10.1007/s10474-018-0871-2},\n\tVolume = {156},\n\tYear = {2018},\n\tBdsk-Url-1 = {https://doi.org/10.1007/s10474-018-0871-2},\n\tBdsk-Url-2 = {http://dx.doi.org/10.1007/s10474-018-0871-2}}\n\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Let X be a bounded subset of $}{$\\$\\$mathbb\\R\\ ^\\d\\\\$}{$Rdand write $}{$\\C_\\$\\$mathsf\\u\\\\(X)\\$}{$Cu(X)for the set of uniformly continuous functions on X equipped with the uniform norm. The lower and upper box dimensions, denoted by $}{$\\$\\$underline\\$\\$rm dim\\_\\$\\$mathsf\\B\\\\(\\$\\$rm graph\\(f))\\$}{$dim̲B(graph(f))and $}{$\\$\\$overline\\$\\$rm dim\\_\\$\\$mathsf\\B\\\\(\\$\\$rm graph\\(f))\\$}{$dim¯B(graph(f)), of the graph $}{$\\$\\$rm graph(f)\\$}{$graph(f)of a function $}{$\\f$\\$in C_\\$\\$mathsf\\u\\\\(X)\\$}{$f∈Cu(X)are defined by$}{$$\\$begin\\aligned\\\\$\\$underline\\$\\$rm dim\\_\\$\\$mathsf\\B\\\\(\\$\\$rm graph\\(f))\\ = \\$\\$lim_\\$\\$delta $\\$searrow 0\\ \\$\\$rm inf\\\\ \\$\\$frac\\\\$\\$rm log\\ N_\\$\\$delta\\(\\$\\$rm graph\\(f))\\\\-$\\$rm log $\\$delta\\\\,$\\$$\\$\\$\\$overline\\$\\$rm dim\\_\\$\\$mathsf\\B\\\\(\\$\\$rm graph\\(f))\\ = \\$\\$lim_\\$\\$delta $\\$searrow 0\\ \\$\\$rm sup\\\\ \\$\\$frac\\\\$\\$rm log\\ N_\\$\\$delta\\(\\$\\$rm graph\\(f))\\\\-$\\$rm log $\\$, $\\$delta\\\\,$\\$end\\aligned\\$}{$dim̲B(graph(f))=limδ↘0inflogNδ(graph(f))-logδ,dim¯B(graph(f))=limδ↘0suplogNδ(graph(f))-logδ,where $}{$\\N_\\$\\$delta\\(\\$\\$rm graph\\(f))\\$}{$Nδ(graph(f))denotes the number of δ-mesh cubes that intersect $}{$\\$\\$rm graph(f)\\$}{$graph(f).\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n  <div class=\"bibbase_group_whole\" id=\"group_2017\">\n    <div class=\"bibbase_group\"\n      onclick=\"toggleGroup('group_2017')\"\n      onkeypress=\"toggleGroup('group_2017')\"\n      tabindex=\"0\">\n      <i class=\"fa fa-angle-down bibbase_group_head_icon\"></i>&nbsp;\n      <span>2017</span>\n      <span class=\"bibbase_group_count\">\n        \n        (1)\n        \n      </span>\n    </div>\n    <div class=\"bibbase_group_body\">\n      \n  \n  <div class=\"bibbase_paper\" id=\"kohnle-rizzoli-interactivesimulationsforquantumkeydistribution-2017\">\n  <span class=\"bibbase_paper_titleauthoryear\">\n\n  \n  <span class=\"bibbase_paper_title\">\n  \n  \n  \n  <a href=\"https://doi.org/10.1088/1361-6404/aa62c8\"\n     onclick=\"return trackOutboundLink('publications', 'click', 'kohnle-rizzoli-interactivesimulationsforquantumkeydistribution-2017', 'https://doi.org/10.1088/1361-6404/aa62c8', event);\">\n    Interactive simulations for quantum key distribution.\n  </a>\n  \n  \n  \n</span>\n\n  <span class=\"bibbase_paper_author\">\n  Kohnle, A.;  and <a class=\"bibbase author link\" href=\"https://rizzoli.me/publications/\">Rizzoli, A.</a>\n</span>\n\n  \n\n</span>\n\n  <i>European Journal of Physics</i>, 38(3): 035403. mar 2017.\n  <span class=\"note\"></span>\n\n<span class=\"bibbase_note\"></span>\n\n<br class=\"bibbase_paper_content\"/>\n\n<span class=\"bibbase_paper_content dontprint\">\n\n  \n  <a href=\"https://doi.org/10.1088/1361-6404/aa62c8\"\n     onclick=\"log_download('kohnle-rizzoli-interactivesimulationsforquantumkeydistribution-2017', 'https://doi.org/10.1088/1361-6404/aa62c8', event.ctrlKey, event)\">\n    <img src=\"//bibbase.org/img/filetypes/link.svg\"\n\t     alt=\"Interactive simulations for quantum key distribution [link]\"\n       title=\"Paper\"\n\t     class=\"bibbase_icon\"\n         ><span class=\"bibbase_icon_text\">Paper</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"http://doi.org/10.1088/1361-6404/aa62c8\"\n     onclick=\"log_download('kohnle-rizzoli-interactivesimulationsforquantumkeydistribution-2017', 'http://doi.org/10.1088/1361-6404/aa62c8', event.ctrlKey)\"\n     class=\"bibbase doi link\">\n    <span>doi</span></a>\n  &nbsp;\n  \n\n  \n  <a href=\"//bibbase.org/network/publication/kohnle-rizzoli-interactivesimulationsforquantumkeydistribution-2017\"\n     class=\"bibbase bibbase_page link\">link</a>\n  &nbsp;\n  \n\n  <a href=\"#\"\n     onclick=\"showBib(event); return false;\"\n     class=\"bibbase bibtex link\">bibtex\n    <i class=\"fa fa-caret-down\"></i></a>\n\n  \n  &nbsp;\n  <a class=\"bibbase_abstract_link bibbase link\"\n     href=\"#\"\n     onclick=\"showAbstract(event); return false;\">\n    abstract <i class=\"fa fa-caret-down\"></i></a>\n  \n\n  \n\n  <!-- <a class=\"bibbase read link hidden\" -->\n  <!--    href=\"javascript:toggleRead('kohnle-rizzoli-interactivesimulationsforquantumkeydistribution-2017')\" -->\n  <!--    title=\"Marking this paper as read adds it to your library on BibBase.\" -->\n  <!--    > -->\n  <!--   <i class=\"fa fa-check\"></i>&nbsp; -->\n  <!--   <span>mark as read</span> -->\n  <!-- </a> -->\n\n  &nbsp;\n  \n  \n\n</span>\n\n<div class=\"well well-small bibbase\" data-type=\"bibtex\"\n     style=\"display:none\">\n  <pre style=\"white-space: pre-wrap;\">@article{quantum,\n\tdoi = {10.1088/1361-6404/aa62c8},\n\turl = {https://doi.org/10.1088/1361-6404/aa62c8},\n\tyear = 2017,\n\tmonth = {mar},\n\tpublisher = {{IOP} Publishing},\n\tvolume = {38},\n\tnumber = {3},\n\tpages = {035403},\n\tauthor = {Antje Kohnle and Aluna Rizzoli},\n\ttitle = {Interactive simulations for quantum key distribution},\n\tjournal = {European Journal of Physics},\n\tabstract = {Secure communication protocols are becoming increasingly important, e.g. for internet-based communication. Quantum key distribution (QKD) allows two parties, commonly called Alice and Bob, to generate a secret sequence of 0s and 1s called a key that is only known to themselves. Classically, Alice and Bob could never be certain that their communication was not compromised by a malicious eavesdropper. Quantum mechanics however makes secure communication possible. The fundamental principle of quantum mechanics that taking a measurement perturbs the system (unless the measurement is compatible with the quantum state) also applies to an eavesdropper. Using appropriate protocols to create the key, Alice and Bob can detect the presence of an eavesdropper by errors in their measurements. As part of the QuVis Quantum Mechanics Visualisation Project, we have developed a suite of four interactive simulations that demonstrate the basic principles of three different QKD protocols. The simulations use either polarised photons or spin 1/2 particles as physical realisations. The simulations and accompanying activities are freely available for use online or download, and run on a wide range of devices including tablets and PCs. Evaluation with students over three years was used to refine the simulations and activities. Preliminary studies show that the refined simulations and activities help students learn the basic principles of QKD at both the introductory and advanced undergraduate levels.}\n}\n\n\n</pre>\n</div>\n\n\n<div class=\"well well-small bibbase\" data-type=\"abstract\"\n     style=\"display:none\">\n  Secure communication protocols are becoming increasingly important, e.g. for internet-based communication. Quantum key distribution (QKD) allows two parties, commonly called Alice and Bob, to generate a secret sequence of 0s and 1s called a key that is only known to themselves. Classically, Alice and Bob could never be certain that their communication was not compromised by a malicious eavesdropper. Quantum mechanics however makes secure communication possible. The fundamental principle of quantum mechanics that taking a measurement perturbs the system (unless the measurement is compatible with the quantum state) also applies to an eavesdropper. Using appropriate protocols to create the key, Alice and Bob can detect the presence of an eavesdropper by errors in their measurements. As part of the QuVis Quantum Mechanics Visualisation Project, we have developed a suite of four interactive simulations that demonstrate the basic principles of three different QKD protocols. The simulations use either polarised photons or spin 1/2 particles as physical realisations. The simulations and accompanying activities are freely available for use online or download, and run on a wide range of devices including tablets and PCs. Evaluation with students over three years was used to refine the simulations and activities. Preliminary studies show that the refined simulations and activities help students learn the basic principles of QKD at both the introductory and advanced undergraduate levels.\n</div>\n\n\n</div>\n\n\n\n\n\n    </div>\n  </div>\n\n\n\n\n  </div>\n\n\n  <!-- Modal -->\n\n  <!-- <iframe id=\"bibbase_network_frame\" -->\n  <!--         src=\"//bibbase.org/network/control\" -->\n  <!--         style=\"display: none;\"> -->\n  <!-- </iframe> -->\n\n</div>\n"}; document.write(bibbase_data.data);