-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathmpmss.html
70 lines (64 loc) · 4.14 KB
/
mpmss.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
<!DOCTYPE html>
<html lang="en-UK">
<head>
<title> Mathematical Physics Mini Seminar Series</title>
<meta charset="UTF-8">
<style>
table, td, th {
border: 1px solid black;
}
table {
border-collapse: collapse;
width: 100%;
}
th {
text-align: left;
}
</style>
</head>
<body style="background-color:lightgrey;">
<h1 style="text-align:center;">Mathematical Physics Mini Seminar Series</h1>
<hr>
<p>In February 2018 we decided to start a mini series of seminars for PhD students within the mathematical physics group here at Heriot-Watt. The idea was to introduce the other PhD students to topics that we were interested in and that are, possibly, related to our research.</p>
<p>The idea is that starting on Thursday 8/2 we will meet in T.01 at 4:30pm, after tea time though this is flexible.</p>
<p>The schedule below is provisional and is fairly likely to change.</p>
<table style="width:100%">
<tr>
<th>Date</th>
<th>Speaker</th>
<th>Topic/Title</th>
<th>Abstract/ Summary of the talk</th>
</tr>
<tr>
<td>8/2/18</td>
<td>Lukas Müller</td>
<td>Higher Geometry</td>
<td> Lukas gave an introduction to abelian bundle gerbs from the point of view of Deligne hypercohomology.</td>
</tr>
<tr>
<td>15/2/18</td>
<td>Lukas Müller</td>
<td>Non-Associativity in quantum mechanics arising from smooth distributions of magnetic charge</td>
<td>Canonical quantization of a charged particle in the background of a magnetic field with sources on $\mathbb{R}^3$ is possible only if the sources are localised at isolated points in space and Dirac's charge quantization condition is satisfied. In this case wave functions can be realised as sections of a non trivial line bundle.Otherwise the algebra of operators becomes non-associative and there is no way to represent it on a Hilbert space. In this talk we propose to represent it instead on a 2-Hilbert space of sections of a bundle gerbe.To support this proposal we explicitly construct the action of magnetic translation operators on this 2-Hilbert space. In the case of uniform magnetic charge our construction reproduces known results from deformation quantisation. The categorical structures involved naturally encode the 3-cocycle measuring the non-associativity of the representation. This approach to a basic, but yet unsolved physical problem provides an enriched view on quantum mechanics, and we conclude this talk with a short discussion of the questions it poses regarding its physical interpretation. This is joint work in progress with Severin Bunk and Richard J. Szabo. </td>
</tr>
<tr>
<td>8/3/18</td>
<td>Calum Ross</td>
<td>Spectral curves and Monopoles </td>
<td>I will try and sketch the construction of the spectral curve of a monopole for gauge group $SU(2)$, maybe $SU(n)$ if I have time. To do this we will encounter Euclidean monopoles, their twistor space and how to extract algebrogeometric data from this construction. The talk will be roughly based on these <a href= "https://cdross1.github.io/notes/monopoles_and_spectral_curves.pdf"> notes<a> and the references therein. <font color="blue">In the end we did not get to talking about the spectral curve but did see most of the details of the twistor space construction and a sketch of how it relates to the twistor space of instantons in four dimensions.</font></td>
</tr>
<tr>
<td>15/3/18</td>
<td>Philipp Rüter</td>
<td>QFT and the Jones polynomial</td>
<td>Philipp sketched some of the details from Witten's paper "QFT and the Jones polynomial".</td>
</tr>
<tr>
<td>23/3/2018</td>
<td>Iain Findlay</td>
<td>Integrable Defects in the Liouville Model</td>
<td>N.B. This is on a Friday as it is jointly a PhD seminar. The core of this talk will be the Lax construction of the Liouville model, and the idea of integrable defects in this picture. Combining these two ideas, I will example the effects of the presence of an integrable defect on the Liouville model, comparing it to the effect of a Bäcklund transformation frozen at a specific point in space, and how we can use these to find a solution to the Liouville equation. Based off of the work: <a href="https://arxiv.org/abs/1608.04237"> https://arxiv.org/abs/1608.04237</a></td>
</tr>
</table>
</body>
</html>