-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathpapers.html
More file actions
134 lines (101 loc) · 6.72 KB
/
Copy pathpapers.html
File metadata and controls
134 lines (101 loc) · 6.72 KB
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
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta name="description" content="">
<meta name="author" content="">
<title>Ran Cui</title>
<!-- Bootstrap Core CSS -->
<link href="css/bootstrap.min.css" rel="stylesheet">
<!-- Custom CSS -->
<link href="css/simple-sidebar.css" rel="stylesheet">
<link href="font-awesome-4.5.0/css/font-awesome.min.css" rel="stylesheet">
<!-- HTML5 Shim and Respond.js IE8 support of HTML5 elements and media queries -->
<!-- WARNING: Respond.js doesn't work if you view the page via file:// -->
<!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/libs/html5shiv/3.7.0/html5shiv.js"></script>
<script src="https://oss.maxcdn.com/libs/respond.js/1.4.2/respond.min.js"></script>
<![endif]-->
</head>
<body>
<div id="wrapper">
<!-- Sidebar -->
<div id="sidebar-wrapper">
<ul class="sidebar-nav nav-pills nav-stacked">
<div id="profilepic-wrapper" align="center">
<img class="img-circle" src="img/profilepic.jpg" style="width:122px;height:135px;">
</div>
<div id="name-wrapper" align="center">
<font color=#999999><h3>Ran Cui</h3></font>
<font color=#999999><h4>University of Maryland</h4></font>
</div>
<li>
<a href="index.html"><span class="fa-stack fa-lg pull-left"><i class="fa fa-home fa-stack-1x "></i></span> Home</a>
</li>
<li>
<a href="research.html"><span class="fa-stack fa-lg pull-left"><i class="fa fa-book fa-stack-1x "></i></span>Research</a>
</li>
<li class="active">
<a href="papers.html"><span class="fa-stack fa-lg pull-left"><i class="fa fa-pencil-square-o fa-stack-1x "></i></span>Papers/Notes</a>
</li>
<li>
<a href="contact.html"><span class="fa-stack fa-lg pull-left"><i class="fa fa-envelope fa-stack-1x "></i></span>Contact</a>
</li>
</ul>
</div>
<!-- /#sidebar-wrapper -->
<!-- Page Content -->
<div id="page-content-wrapper">
<a href="#menu-toggle" class="btn btn-default" id="menu-toggle"><span class="fa-stack fa-lg pull-left"><i class="fa fa-bars fa-stack-2x "></i></span></a>
<div class="container-fluid">
<div class="row">
<div class="col-lg-12">
<h1>Papers/Notes</h1>
<div id="main">
<ul>
<li>
Ran Cui, "<i>The Real-Quaternionic Indicator</i>" (2016) <a href="pdf/indicator_paper.pdf">pdf</a>
</li>
<p class="indented">A shorter version of the first part of my thesis.</p>
<li>
(Thesis) Ran Cui, "<i>The Real-Quaternionic Indicator of Irreducible Self-Conjugate Representations of Real Reductive Algebraic Groups and A Comment on the Local Langlands Correspondence of GL(2,F).</i>" (2016) <a href="pdf/mainthesis.pdf">pdf</a>
</li>
<p class="indented">In this thesis, we establish a relation between the Real-Quaternionic indicator and the Frobenius-Schur indicator for irreducible self-conjugate (g,K)-modules with real infinitesimal characters. The main tool we used to prove this relation is the c-invariant Hermitian form. This relation is given by the strong real form of G. We also provide formulas for the strong real forms for simple group G of some types.</p>
<p class="indented">We also get into the subject of the local Langlands correspondence of GL(2,F). Many books has description of how to construct this correspondence, some using the theta correspondence such as "<i>The Local Langlands Conjecture for GL(2)</i>" by Bushnell and Henniart; and "<i>Automorphic Forms and Representations</i>" by Bump. We give a detailed computation of how the construction is done that is less circuitous. We use the full strength of the theta correspondence to prove the construction is well defined.</p>
<li>
Ran Cui, "<i>Explicit Construction of Local Langlangds Correspondence of GL(2,F) Using Theta Correspondence.</i>" (2014) <a href="http://arxiv.org/abs/1511.03309">arXiv</a>
</li>
<p class="indented">This paper is the second part of the thesis. It is available on arXiv.</p>
<li>
Ran Cui, "<i>Tamagawa Number for SL(2)</i>" (2013) <a href="pdf/tamagawa_number_sl2.pdf">pdf</a>
</li>
<p class="indented">This is my notes on the Tamagawa number of SL(2). It contains the necessary theory for computing the Tamagawa number and detailed computations.</p>
<li>
Ran Cui, "<i>A Survey on the Finite Harmonic Oscillator and its Applications.</i>" (2012) <a href="pdf/finite_harmonic_oscillator.pdf">pdf</a>
</li>
<p class="indented">A finite oscillator system was introduced by Gurevich, Hadani and Sochen. This is a survey of how the system is constructed using Weil representation on the group SL(2,Fp) and its applications on discrete radar and CDMA system. Finally, explicit algorithms for computing the finite split and non-split oscillator systems are described.</p>
</ul>
</div>
</div>
</div>
</div>
</div>
<!-- /#page-content-wrapper -->
</div>
<!-- /#wrapper -->
<!-- jQuery -->
<script src="js/jquery.js"></script>
<script src="js/jquery-1.12.3.min.js"></script>
<!-- Bootstrap Core JavaScript -->
<script src="js/bootstrap.min.js"></script>
<!-- Menu Toggle Script -->
<script>
$("#menu-toggle").click(function(e) {
e.preventDefault();
$("#wrapper").toggleClass("toggled");
});
</script>
</body>
</html>