-
Notifications
You must be signed in to change notification settings - Fork 2
/
2017-schedule.html
239 lines (187 loc) · 9.79 KB
/
2017-schedule.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
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
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
---
layout: 2017-layout
permalink: /2017/schedule.html
---
<h2>Schedule</h2>
<ul>
<li> <a href="/schedule.pdf">pdf version</a>
<li>the coffee breaks are in the <em><a href="https://campusinfo.umich.edu/campusmap/53">East Hall</a>, Common Room</em> (on the 2nd floor)
<li>the talks are in the <em><a href="https://campusinfo.umich.edu/campusmap/53">East Hall</a>, Room 1360</em>
<li>the group work is in the basement of the <em><a href="https://campusinfo.umich.edu/campusmap/111">Modern Languages Building</a></em>,
<dl class="schedule" id="rooms">
<dt>Bhargav Bhatt
<dd>MLBB111
<dt>Brian Conrad
<dd>MLBB115A
<dt>Johan de Jong
<dd>MLBB122
<dt>Matthew Emerton
<dd>MLBB124
<dt>Max Lieblich
<dd>MLBB134
<dt>Davesh Maulik
<dd>MLBB135
</dl>
<li>the (optional) evening sessions are in <em><a href="https://campusinfo.umich.edu/campusmap/53">East Hall</a>, 1360 and Common Room</em>
</ul>
<h3>Monday, July 31</h3>
<dl class="schedule">
<dt>09:00–09:30
<dd>registration
<dt>09:30–10:30
<dd>welcome
<dd>history and future of the Stacks project (<a href="/slides.pdf">slides</a>)
<dt>10:30–11:00
<dd>coffee break
<dt>11:00–12:30
<dd>group work
<dt>14:00–15:30
<dd>group work
<dt>15:30–16:00
<dd>coffee break
<dt>16:00–17:00
<dd class="title"><a href="#mathew">Nonconnective simplicial commutative rings</a>
<dd class="speaker"><span class="name">Akhil Mathew</span>
</dl>
<h3>Tuesday, August 1</h3>
<dl class="schedule">
<dt>09:00–09:30
<dd>coffee break
<dt>09:30–10:30
<dd class="title"><a href="#taelman">Shimura stacks</a>
<dd class="speaker"><span class="name">Lenny Taelman</span>
<dt>10:30–11:00
<dd>coffee break
<dt>11:00–12:30
<dd>group work
<dt>14:00–15:30
<dd>group work
<dt>15:30–16:00
<dd>coffee break
<dt>16:00–17:00
<dd class="title"><a href="#talpo">Geometric realizations of logarithmic schemes</a>
<dd class="speaker"><span class="name">Mattia Talpo</span>
<dt>17:15–18:00
<dd>editing the Stacks project, and an introduction to Git (in EH 1360) (<a href="/git.pdf">slides</a>)
<dt>18:00–...
<dd>cross-referencing, typos and pizza
</dl>
<h3>Wednesday, August 2</h3>
<dl class="schedule">
<dt>09:00–09:30
<dd>coffee break
<dt>09:30–10:30
<dd class="title"><a href="#fedorchuk">Associated forms and applications</a>
<dd class="speaker"><span class="name">Maksym Fedorchuk</span>
<dt>10:30–11:00
<dd>coffee break
<dt>11:00–12:30
<dd>group work
<dt>14:00–15:30
<dd>group work
<dt>15:30–16:00
<dd>coffee break
<dt>16:00–17:00
<dd class="title"><a href="#krashen">Extremely indecomposable division algebras and algebraic cycles</a>
<dd class="speaker"><span class="name">Daniel Krashen</span>
<dt>17:15–18:00
<dd>infrastructure of the Stacks project (<a href="framework.pdf">slides</a>)
<dt>18:00–...
<dd>cross-referencing, typos, hackathon and pizza
</dl>
<h3>Thursday, August 3</h3>
<dl class="schedule">
<dt>09:00–09:30
<dd>coffee break
<dt>09:30–10:30
<dd class="title"><a href="#javanpeykar">Finiteness results for hypersurfaces over number fields</a>
<dd class="speaker"><span class="name">Ariyan Javanpeykar</span>
<dt>10:30–11:00
<dd>coffee break
<dt>11:00–12:30
<dd>group work
<dt>14:00–15:30
<dd>group work
<dt>15:30–16:00
<dd>coffee break
<dt>16:00–17:00
<dd>brainstorming session
</dl>
<h3>Friday, August 4</h3>
<dl class="schedule">
<dt>09:00–09:30
<dd>coffee break
<dt>09:30–10:30
<dd class="title"><a href="#lurie">A gentle approach to crystalline cohomology</a>
<dd class="speaker"><span class="name">Jacob Lurie</span>
<dt>10:30–11:00
<dd>coffee break
<dt>11:00–12:30
<dd>group work
<dt>14:00–15:30
<dd>group work
<dt>15:30–16:00
<dd>coffee break
<dt>16:00–17:00
<dd>group presentations
</dl>
<h2>Abstracts</h2>
<section id="fedorchuk">
<h3 class="title">Associated forms and applications</h3>
<p class="speaker"><span class="name">Maksym Fedorchuk</span> (<span class="affiliation">Boston College</span>)
<blockquote>
I will describe the theory of associated forms (these are Macaulay inverse systems of certain balanced complete intersections) and two of its applications. The first is a proof of their GIT polystability and a resulting invariant-theoretic version of the Mather-Yau theorem for homogeneous hypersurface singularities, obtained in joint work with Alexander Isaev. The second is an if-and-only-if criterion for direct sum decomposability of a smooth homogeneous polynomial in terms of the factorization properties of its associated form. This criterion leads to an algorithm for computing direct sum decompositions over any field either of characteristic zero, or sufficiently large positive characteristic, for which polynomial factorization algorithms exist.
</blockquote>
</section>
<section id="javanpeykar">
<h3 class="title">Finiteness results for hypersurfaces over number fields</h3>
<p class="speaker"><span class="name">Ariyan Javanpeykar</span> (<span class="affiliation">University of Mainz</span>)
<blockquote>
I will explain why the stack of smooth hypersurfaces is uniformisable by a scheme, and use this "uniformisation" to deduce arithmetic consequences of the Lang-Vojta conjecture for smooth hypersurfaces over number fields. This is joint work with Daniel Loughran.
</blockquote>
</section>
<section id="krashen">
<h3 class="title">Extremely indecomposable division algebras and algebraic cycles</h3>
<p class="speaker"><span class="name">Daniel Krashen</span> (<span class="affiliation">University of Georgia</span>)
<blockquote>
In this talk, I will explore some of the connections between the arithmetic of division algebras and the geometry of Brauer-Severi varieties. A division algebra is called decomposable if it may be written as a nontrivial tensor product of two other division algebras. One can strengthen this notion and consider whether or not a division algebra is similar to a tensor product of some number of division algebras of a fixed smaller index. This question is closely tied to the notion of symbol length in Galois cohomology. I will describe how to approach this problem by giving some extensions of results of Karpenko which connect indecomposability of division algebras with the Chow groups and K-theory of the corresponding Brauer-Severi varieties.
</blockquote>
</section>
<section id="lurie">
<h3 class="title">A gentle approach to crystalline cohomology</h3>
<p class="speaker"><span class="name">Jacob Lurie</span> (<span class="affiliation">Harvard University</span>)
<blockquote>
Let \(X\) be a smooth algebraic variety over a field \(k\). The <em>algebraic de Rham cohomology</em> of \(X\) is defined as the (hyper)cohomology of the de Rham complex
$$ \Omega^0_X \rightarrow \Omega^1_{X} \rightarrow \Omega^2_X \rightarrow \cdots$$
When \(k\) is a perfect field of characteristic \(p\), Deligne and Illusie introduced an analogue of the de Rham complex, called the <em>de Rham-Witt complex</em>, which instead computes the crystalline cohomology of \(X\). In this talk, I'll describe an alternative construction of the de Rham-Witt complex, from which one can deduce some of the central properties of crystalline cohomology in an essentially calculation-free way. (Joint work with Bhargav Bhatt and Akhil Mathew.)
</blockquote>
</section>
<section id="mathew">
<h3 class="title">Nonconnective simplicial commutative rings</h3>
<p class="speaker"><span class="name">Akhil Mathew</span> (<span class="affiliation">Harvard University</span>)
<blockquote>
Simplicial commutative rings are one of the first steps into
the world of "derived" rings that one can take (e.g., which allows
derived tensor products of ordinary rings). However, simplicial
commutative rings are always connective, while many objects one wishes
to consider (e.g., arising from cohomology theories) need not be. I
will explain ongoing work with Bhargav Bhatt on an extended theory of
"generalized rings" which extends this category to allow nonconnective
objects. Many "equational" constructions which cannot work with
\(\mathrm{E}_\infty\)-rings extend well to generalized rings.
</blockquote>
</section>
<section id="taelman">
<h3 class="title">Shimura stacks</h3>
<p class="speaker"><span class="name">Lenny Taelman</span> (<span class="affiliation">University of Amsterdam</span>)
<blockquote>
Motivated by questions about complex multiplication, we describe how moduli stacks of abelian varieties and of K3 surfaces are 'stacky' Shimura varieties. This talk will be a mixture of exposition of well-known (folklore) mathematics, new results, and open questions.
</blockquote>
</section>
<section id="talpo">
<h3 class="title">Geometric realizations of logarithmic schemes</h3>
<p class="speaker"><span class="name">Mattia Talpo</span> (<span class="affiliation">Simon Fraser University</span>)
<blockquote>
Logarithmic schemes are schemes equipped with a sheaf of monoids that records some additional information of interest - typically either a boundary divisor or some infinitesimal data about a degeneration, of which our scheme is a fiber. Initially introduced for arithmetic purposes, these objects have later found applications to different areas of algebraic geometry, in particular in moduli theory. I will talk about two different (but related) geometric realizations of logarithmic schemes, the "Kato-Nakayama space" and the "infinite root stack", and about past and upcoming applications of these constructions.
</blockquote>
</section>