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<center><H2>Arithmetic and Dynamics Seminar</H2></center>

<center>
<img src="1106arithmeticseminar1.jpg" height=200>
</center>

<p>

An informal seminar meets weekly in term time, bringing
together those with an interest in arithmetic and dynamics.

<h3>2008-9</h3>
<p>
Monday at 4pm in S01.03.
This year the focus is equidistribution.

<h4>Spring Semester</h4>
<p>
The broad aim this semester will be
to understand the results of
the papers
<ul>
<li>
W. Duke, Z. Rudnick and P. Sarnak:
<a href="http://www.math.tau.ac.il/~rudnick/papers/DRS.pdf">Density
of integer points on
affine homogeneous varieties</a>, <i>Duke Math. Journal</i>
<b>71</b> (1993), and</li>
<li>
A. Eskin and C. Mcmullen:
<a href="http://www.math.uchicago.edu/~eskin/mixing.dvi">Mixing,
counting and equidistribution in
Lie groups</a>, <i>Duke Math. Journal</i>
<b>71</b> (1993).</li>
</ul>
<p>
We are aiming for a leisurely exposition and there should be
ample time for interesting diversions. The seminar is informal and
will not assume any technical prerequisites.
A preliminary list of topics we hope to cover includes:
<ol>
<li>SL(2,R), SL(3,R), SL(2,R) vs SL(3,R).</li>
<li>The geometry of affine symmetric
spaces and homogeneous varieties.</li>
<li>The p-adic picture - Hecke points.</li>
<li>The adelic picture - the Ramanujan conjecture.</li>
</ol>
<p>
Other topics depending on audience tastes.
<h4>Autumn Semester</h4>
<ul>
<li>1 December 2008: Completing the proof of
equidistribution for polynomials (Sawian Jaidee)
<li>17 November 2008: Furstenberg's proof of unique ergodicity
for compact group extensions (Tony Flatters)
<li>10 November 2008: Invariant measures for continuous maps (Tom Ward)
<li>3 November 2008: Invariant measures for continuous maps (Tom Ward)
</ul>
<p>
There are several departmental seminars in related areas:
<ul>
<li>17 November 2008, 14:30 in S01.03 (Departmental seminar):
Diophantine geometry and dynamics
(Alexander Gorodnik (Bristol))
<li>12 November 2008, 14:30 in S01.03 (Departmental seminar):
Rigidity of actions on algebraic spaces
(Alexander Gorodnik (Bristol))
<li>3 November 2008, 14:00 in S3.05 (Departmental seminar):
Some applications of homogeneous dynamics to number theory
(Anish Ghosh)
</ul>

<p>
<b>Participants:</b>
Graham Everest (MTH faculty);
Anthony Flatters (MTH postgraduate student);
Anish Ghosh (MTH faculty);
Sawian Jaidee (MTH postgraduate student);
Apisit Pakapongpun (MTH postgraduate student);
Shaun Stevens (MTH faculty);
Thomas Ward (MTH faculty).

<h3>2007-8</h3>
<p>
Thursday at 12 in S1.20 unless indicated otherwise.
This year the seminar will study some papers
of Bugeaud, Mignotte and Siksek
(<a href="http://xxx.soton.ac.uk/abs/math/0403046">"Classical
and modular approaches to exponential Diophantine equations. I.
Fibonacci and Lucas perfect powers"</a> and
<a href="http://xxx.soton.ac.uk/abs/math/0405220">"Classical
and modular approaches to exponential Diophantine equations II.
The Lebesgue-Nagell equation"</a>) and a paper of
Bennett and Skinner
(<a href="http://www.uea.ac.uk/~h720/research/arithmetic/BennettSkinner.pdf">"Ternary Diophantine Equations via Galois
Representations and Modular Forms"</a>). 
<p>
<b>Participants:</b> David Evans (MTH faculty);
Graham Everest (MTH faculty);
Anthony
Flatters (MTH postgraduate student);
Sawian Jaidee (MTH postgraduate student);
Val&#233;ry
Mah&#233; (EPSRC postdoc);
Apisit Pakapongpun (MTH postgraduate student);
Ouamporn
Phuksuwan (MTH postgraduate student);
Jonathan
Reynolds (MTH postgraduate student);
Shaun Stevens (MTH faculty);
Thomas Ward (MTH faculty);
Yuki Yayama (EPSRC postdoc).

<h4>Talks</h4>
<ul>
<li>Linear forms in three logarithms (Tony Flatters TBC)</li>
<li>13 December 2007: Level-lowering (Jonathan Reynolds)</li>
<li>6 December 2007: Introduction to Newforms
continued (Graham Everest)</li>
<li>29 November 2007: Galois representations associated to elliptic curves
(Shaun Stevens)</li>
<li>22 November 2007: Baker's theory (Tony Flatters)</li>
<li>15 November 2007: Introduction to Newforms (Graham Everest)</li>
<li>8 November 2007: Background on elliptic curves and reduction (Tom Ward;
extra material <a href="page1.pdf">page 1</a>,
<a href="page2.pdf">page 2</a>,
<a href="page3.pdf">page 3</a>)</li>
<li>1 November 2007: Introduction to the work of
Bugeaud-Mignotte-Siksek (Val&#233;ry
Mah&#233;)</li>
<li>25 October 2007: Organisational meeting (Val&#233;ry
Mah&#233;)</li>
</ul>

<h3>2006-7</h3>
<p>
Monday 10am in S1.28 or S2.14 unless indicated
otherwise.
<br>

<b>Participants:</b>
David Evans (MTH faculty);
Graham Everest (MTH faculty);
Anthony
Flatters (MTH postgraduate student);
Sawian Jaidee (MTH postgraduate student);
Moshe Kamensky (MODNET postdoc);
Val&#233;ry
Mah&#233; (EPSRC postdoc);
Richard
Miles (EPSRC postdoc);
Ouamporn
Phuksuwan (MTH postgraduate student);
Jonathan
Reynolds (MTH postgraduate student);
Shaun Stevens (MTH faculty);
Russell Turner (MTH postgraduate student);
Thomas Ward (MTH faculty).

<h4>Talks</h4>
<ul>
<li>11 & 18 December 2006: Motivic integration (Moshe Kamensky,
Room EFRY0.06)</li>
<li>4 December 2006: Model theory background (David Evans,
Room EFRY0.06)</li>
<li>20 November 2006: Local Langlands (Shaun Stevens)</li>
<li>13 November 2006: <a href="jonathanreynoldstalk.pdf">A
Generalisation of Siegel's Theorem</a>
(Jonathan Reynolds)</li>
<li>6 November 2006: Computing in the jacobian of a
superelliptic curve (Following Galbraith, Paulus and Smart)
(Val&#233;ry Mah&#233;)</li>
<li>30 October 2006: Amoebas (Russell Turner)</li>
<li>16 & 23 October 2006: Overview of arithmetic dynamics
(Richard Miles)</li>
<li>9 October: Arithmetic of integer sequences (Graham Everest)</li>
</ul>

<br>

<center>
<img src="1106arithmeticseminar2.jpg" height=200>
</center>

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