Created webpage special session

filippomazzoli · Oct 4, 2024 · b4389d7 · b4389d7
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diff --git a/_includes/text-expand.html b/_includes/text-expand.html
@@ -0,0 +1,16 @@
+<script>
+
+    var elements = document.querySelectorAll('p');
+    Array.prototype.forEach.call(elements, function(el, i){
+        if(el.innerHTML=='[expand]') {
+            var parentcontent = el.parentNode.innerHTML.replace('<p>[expand]</p>','<div class="expand" style="display: none; height: 0; overflow: hidden;">').replace('<p>[/expand]</p>','</div>');
+            el.parentNode.innerHTML = parentcontent;
+        }
+    });
+
+    var elements = document.querySelectorAll('div.expand');
+    Array.prototype.forEach.call(elements, function(el, i){
+        el.previousElementSibling.innerHTML = el.previousElementSibling.innerHTML + '<span>..&nbsp; <a href="#" style="cursor: pointer;" onclick="this.parentNode.parentNode.nextElementSibling.style.display = \'block\'; this.parentNode.parentNode.nextElementSibling.style.height = \'auto\'; this.parentNode.style.display = \'none\';">read&nbsp;more&nbsp;&rarr;</a></span>';
+    });
+
+</script>
diff --git a/_layouts/default.html b/_layouts/default.html
@@ -1,7 +1,6 @@
 <!DOCTYPE html>
 <html lang="{{ site.lang }}">
 
-
   <!-- Head -->
   <head>
     {%- if page.redirect -%}
@@ -62,5 +61,7 @@
     {% include scripts/mathjax.html %}
     {% include scripts/analytics.html %}
     {% include scripts/progressBar.html %}
+
+    {% include text-expand.html %}
   </body>
 </html>
diff --git a/_pages/amsucr2024.md b/_pages/amsucr2024.md
@@ -0,0 +1,95 @@
+---
+layout: page
+permalink: /amsucr2024/
+title: AMS@UCR
+description:
+nav: true
+nav_order: 6
+---
+
+This is the unofficial webpage of the AMS Special Session "Geometry, topology, and dynamics of character varieties", which will take place at UC Riverside on October 26-27, 2024. Here is a link to the official webpage of the 2024 [Fall Western AMS Sectional Meeting](https://www.ams.org/meetings/sectional/2304_program_ss24.html#title).
+
+
+### Speakers
+
++ [Fernando Al Assal](https://alassal.github.io/site/index.html)
++ [Parker Evans](https://sites.google.com/view/parker-evans/home)
++ [Stephen Mackes](https://sites.google.com/uic.edu/smacke5/home)
++ [Sara Maloni](https://sites.google.com/view/sara-maloni)
++ [Giuseppe Martone](https://sites.google.com/view/giuseppemartone/home)
++ Andrew Sanders
++ [Zach Virgilio](https://mathdept.ucr.edu/people/zachary-virgilio)
++ [Teddy Weisman](https://websites.umich.edu/~tjwei/)
++ Vicky Wen
++ [Neza Zager Korenjak](https://neznez.github.io/index.html)
+
+
+## Schedule and Abstracts
+
+Click anywhere on the title of a talk to see the abstract.
+
+### Saturday, October 26
+
+{% details 9-10 am, Room TBA: [Sara Maloni](https://sites.google.com/view/sara-maloni), **Dynamics on the $$\mathrm{SU}(2,1)$$-character varieties of the one-holed torus**. %}
+*Abstract:* In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) $$\mathrm{SU}(2,1)$$–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for $$\mathrm{SL}(2,\mathbb{C})$$–character varieties by Bowditch, Minsky and others.
+{% enddetails %}
+
+{% details 10-10:30 am, Room TBA: [Zach Virgilio](https://mathdept.ucr.edu/people/zachary-virgilio), **Hyperbolic Structures arising from $$\mathrm{SU}(2,1)$$-Higgs bundles**. %}
+*Abstract:*  Geometric structures on manifolds have been objects of interest since Thurston’s work and since then the work of Guichard and Wienhard has shown how certain representations of the fundamental groups of surfaces are closely related to geometric structures. Further objects of interest, introduced by Hitchin, are Higgs bundles and these are tied to surface group representations by the Nonabelian Hodge Correspondence. The goal of this talk is to highlight a method by which Higgs bundles can be used to determine geometric structures on related manifolds. $$\mathrm{SU}(2,1)$$-Higgs bundles satisfying a certain condition naturally give rise to developing maps for complex hyperbolic structures. These techniques also extend to a wider class of Higgs bundles, notably a family of $$\mathrm{SO}(2,n)$$-Higgs bundles. This is joint work between Brian Collier and myself.
+{% enddetails %}
+
+{% details 10:30-11 am, Room TBA: [Stephen Mackes](https://sites.google.com/uic.edu/smacke5/home), **Local embeddedness criterion for equivariant pleated planes**. %}
+*Abstract:* Given a surface, $$S$$, of negative Euler characteristic and some maximal lamination, $$\lambda \subset S$$, Bonahon developed shear-bend coordinates, which identify an open subset of the character variety, $$\chi(\pi_1(S),\mathrm{PSL}_2(\mathbb{C}))$$, that contains all quasi-Fuchsian representations with an open subset of a finite dimensional -vector space, $$\mathcal{H}(\lambda,\mathbb{C})$$. We show that at every Fuchsian representation, there is some definite radius depending only the choice of a train track (which yields a norm on ) and on the injectivity radius determined by the Fuchsian representation so that the ball of this radius in the shear-bend coordinates is entirely contained in the quasi-Fuchsian locus in $$\chi(\pi_1(S),\mathrm{PSL}_2(\mathbb{C}))$$. This work is foreshadowed by the work of Epstein, Marden, and Markovich in which they prove a similar result in the special case that the bending cocycle is also a transverse measure.
+This work is paralleled by a work in progress which is hoped to provide a similar result in $$\chi(\pi_1(S),\mathrm{PSL}_d(\mathbb{C}))$$ and yield definite balls that are contained in the Anosov locus.
+{% enddetails %}
+
+11 am-3 pm, Room TBA: **Lunch break**.
+
+{% details 3-3:50 pm, Room TBA: Andrew Sanders, **Axiom A Flows and Projective Anosov Subgroups**. %}
+*Abstract:* Given a torsion-free word hyperbolic group $$\Gamma$$ and a projective Anosov homomorphism $$\rho : \Gamma \to \mathrm{SL}(n,\mathbb{R})$$, we construct a canonical (usually non-compact) locally homogeneous contact manifold $$\mathcal{M}_\rho$$ equipped with an Axiom A flow $$\phi^t : \mathcal{M}_\rho \to \mathcal{M}_\rho$$ whose holonomy is equal to $$\rho$$. We will discuss several geometric and dynamical consequences: exponential mixing, existence of Ruelle-Pollicott resonant states, and a corresponding spectral gap. As an application, we obtain the exponential mixing of the geodesic flow associated to the Hilbert metric on a strictly convex real projective manifold. This is joint work with Daniel Monclair and Benjamin Delarue.
+{% enddetails %}
+
+{% details 3:50-4:40 pm, Room TBA: [](), **Title**. %}
+*Abstract:*
+{% enddetails %}
+
+{% details 4:40-5:20 pm, Room TBA: [Giuseppe Martone](https://sites.google.com/view/giuseppemartone/home), **Correlation theorem and cusped Hitchin representations**. %}
+*Abstract:* We will discuss a correlation theorem for pairs of locally Hölder continuous potentials with strong entropy gaps at infinity on a topologically mixing countable Markov shift with the BIP property. This extends a result of Lalley on shifts of finite type, and we will explain its application to the dynamics of (pairs of) Hitchin representations of a punctured surface. This talk is based on joint work in progress with Lien-Yung Nyima Kao.
+{% enddetails %}
+
+{% details 5:20-6:10 pm: [](), **Title**. %}
+*Abstract:*
+{% enddetails %}
+
+<br>
+
+### Sunday, October 27
+
+{% details 8:30-9 am, Room TBA: [Parker Evans](https://sites.google.com/view/parker-evans/home), **Geometric Structures for the $$G_2'$$-Hitchin Component**. %}
+*Abstract:*  We discuss an explicit geometric structures, i.e., $$(G,X)$$-structures, interpretation of the $$G_2'$$-Hitchin component of a closed, oriented surface $$S$$ of genus $$g \geq 2$$. A definition of  will be given as well as appropriate background and motivation for the problem. Then, using equivariant almost-complex curves in the pseudosphere $$\hat{\mathbb{S}}^{2,4}$$, we describe the construction of the geometric structures for $$G_2'$$-Hitchin representations. Time permitting, we remark on how these structures are different than those of Guichard-Wienhard.
+{% enddetails %}
+
+{% details 9-9:30 am, Room TBA: Vicky Wen, **Sublinear Morseness in Higher Rank Symmetric space**. %}
+*Abstract:* Ever since Gromov showed the quasi isometries betwen hyperbolic spaces induce homeomorphisms on their visual boundaries, it has been common practice to use boundary of a metric space and use it to study the groups that act on the space isometrically. The problem with this method is that, once we leave the hyperbolic space, the visual boundary of a metric space may not be QI invariant any more.
+This motivated people to try to find good characterizations of hyperbolic-like directions in non-hyperbolic spaces. For example, people have studied the Morse boundary and contracting boundary of CAT(0) spaces. However, this task is particularly hard to accomplish in higher rank symmetric spaces. The existence of an isometrically embedded copy of $$\mathbb{R}^n$$ for $$n \geq 2$$ around every geodesic segment precludes any plausible characterizations for hyperbolicity being satisfied.
+Our goal is to develop a useful notion of sublinear Morse-ness of the action of a discrete subgroup $$\Gamma \subset Isom(X)$$ on a higher rank symmetric space $X$ and show that this gives rise to a well defined, QI invariant boundary that has full measure with respect to the Patterson-Sullivan measure defined by $$\Gamma$$.
+{% enddetails %}
+
+{% details 9:30-10 am, Room TBA: [Teddy Weisman](https://websites.umich.edu/~tjwei/), **Dehn filling in semisimple Lie groups**. %}
+*Abstract:* Thurston’s Hyperbolic Dehn Filling Theorem is a seminal result in the theory of $$3$$-manifolds. Given a single noncompact finite-volume hyperbolic $$3$$-manifold $$M$$, the theorem provides a construction for a countably infinite family of closed hyperbolic 3-manifolds converging to $$M$$ in a geometric sense. The theorem is a major source of examples of 3-manifolds admitting hyperbolic structures, and closely connects the topology of a 3-manifold $$M$$ to the analysis of the character variety of its fundamental group in $$\mathrm{PSL}(2,\mathbb{C})$$. In this talk, we discuss some analogs and generalizations of Thurston’s theorem in the context of general semisimple Lie groups. We will explain how our results provide a way to construct new examples of Anosov and relatively Anosov representations into higher-rank Lie groups; we will also discuss joint work with Jeff Danciger, which applies our results to construct exotic new examples of convex cocompact and geometrically finite groups acting on complex hyperbolic $$3$$-space.
+{% enddetails %}
+
+{% details 10-10:30 am, Room TBA: [Fernando Al Assal](https://alassal.github.io/site/index.html), **Asymptotically geodesic surfaces in hyperbolic 3-manifolds**. %}
+*Abstract:* Let $$M$$ be a hyperbolic 3-manifold. We say a sequence of distinct (non-commensurable) essential closed surfaces in $$M$$ is asymptotically geodesic if their principal curvatures go uniformly to zero. When $$M$$ is closed, these sequences exist abundantly by the Kahn-Markovic surface subgroup theorem, and we will discuss the fact that such surfaces are always asymptotically dense, even though they might not equidistribute. We will also talk about the fact that such sequences do not exist when $$M$$ is convex-cocompact acylindrical of infinite volume. This joint work with Ben Lowe.
+{% enddetails %}
+
+{% details 10:30-11 am, Room TBA: [Neza Zager Korenjak](https://neznez.github.io/index.html), **Proper affine deformations of positive representations**. %}
+*Abstract:* We show that every positive Anosov representation of a free group into $$\mathrm{SO}(2n,2n-1)$$ admits cocycles giving proper actions on affine $$(4n-1)$$-space. We also exhibit fundamental domains for these actions. This is joint work with Jean-Philippe Burelle.
+{% enddetails %}
+
+<br>
+
+#### Organizers
+
++ [Brian Collier](https://sites.google.com/view/brian-collier/home)
++ [Filippo Mazzoli](https://filippomazzoli.github.io/)
diff --git a/_pages/notes.md b/_pages/notes.md
@@ -1,7 +1,7 @@
 ---
 layout: page
 permalink: /notes/
-title: some notes
+title: notes
 description: Still under construction
 nav: true
 nav_order: 5

diff --git a/_plugins/details.rb b/_plugins/details.rb
@@ -1,24 +1,29 @@
 # Code from http://movb.de/jekyll-details-support.html
 
 module Jekyll
-    module Tags
-      class DetailsTag < Liquid::Block
-
-        def initialize(tag_name, markup, tokens)
-          super
-          @caption = markup
-        end
-
-        def render(context)
-          site = context.registers[:site]
-          converter = site.find_converter_instance(::Jekyll::Converters::Markdown)
-          caption = converter.convert(@caption).gsub(/<\/?p[^>]*>/, '').chomp
-          body = converter.convert(super(context))
-          "<details><summary>#{caption}</summary>#{body}</details>"
-        end
-
+  module Tags
+    class DetailsTag < Liquid::Block
+
+      def initialize(tag_name, markup, tokens)
+        super
+        @caption = markup
+      end
+
+      def render(context)
+        site = context.registers[:site]
+        converter = site.find_converter_instance(::Jekyll::Converters::Markdown)
+        caption = converter.convert(@caption).gsub(/<\/?p[^>]*>/, '').chomp
+        body = converter.convert(super(context))
+        "<details>
+            <summary>#{caption}</summary>
+
+            <p>#{body}</p>
+            <br>
+        </details>"
       end
+
     end
   end
-
-  Liquid::Template.register_tag('details', Jekyll::Tags::DetailsTag)
+end
+
+Liquid::Template.register_tag('details', Jekyll::Tags::DetailsTag)
diff --git a/_sass/_distill.scss b/_sass/_distill.scss
@@ -35,6 +35,31 @@ d-article {
     display: inline;
   }
 
+
+  // Style taken from code blocks
+  details {  
+    color: var(--global-text-color);
+    background-color: var(--global-code-bg-color);
+    margin-top: 0;
+    padding: 8px 12px;
+    position: relative;
+    border-radius: 6px;
+    display: block;
+    margin-bottom: 20px;
+    grid-column: text;
+    overflow: auto;
+    max-width: 100%;
+    summary {
+      color: var(--global-theme-color);
+    }
+    p {
+        margin-top: 0.5rem;
+        margin-bottom: 0.5rem;
+    }
+  }
+
+
+
   // Style taken from code blocks
   details {
     color: var(--global-text-color);