-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy path2025autumn.html
More file actions
417 lines (387 loc) · 18.3 KB
/
2025autumn.html
File metadata and controls
417 lines (387 loc) · 18.3 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
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
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
<!DOCTYPE html>
<html lang="zh-CN">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Number Theory Seminar</title>
<link rel="stylesheet" type="text/css" href="https://cdn.jsdelivr.net/gh/sugina-dev/latin-modern-web@1.0.1/style/latinmodern-sans.css" />
<link rel="stylesheet" type="text/css" href="table.css">
<script>
MathJax = {
tex: {
inlineMath: [['$', '$'], ['\\(', '\\)']],
displayMath: [['$$', '$$'], ['\\[', '\\]']],
processEscapes: true,
processEnvironments: true
},
options: {
skipHtmlTags: ['script', 'noscript', 'style', 'textarea', 'pre']
}
};
</script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<style>
.content {
margin: auto;
padding-right: 1em;
padding-left: 1em;
max-width: 65em;
line-height: 148%;
font-family: Latin Modern Sans, Helvetica, Arial, Georgia, "Source Han Sans SC", "Noto Sans CJK SC", "WenQuanYi Micro Hei", sans-serif;
}
.intro {
margin-top: 2em;
margin-bottom: 2em;
line-height: 1.6;
}
table {
width: 100%;
border-collapse: collapse;
}
th, td {
vertical-align: top;
word-wrap: break-word;
padding: 4px 6px;
}
/* 列宽分配 */
th:nth-child(1), td:nth-child(1) {
width: 22%;
}
th:nth-child(2), td:nth-child(2) {
width: 18%;
}
th:nth-child(3), td:nth-child(3) {
width: 60%;
}
</style>
</head>
<body>
<div class="content">
<h1>数论讨论班</h1>
<p style="font-size: 1.1em; margin-top: 0.5em; margin-bottom: 0;">A joint seminar of <a href="https://math.fudan.edu.cn/main.htm">SMS</a>, <a href="https://scms.fudan.edu.cn/">SCMS</a> and <a href="https://www.simis.cn/">SIMIS</a></p>
<div class="intro">
<p>组织者: <a href="https://scms.fudan.edu.cn/info/1932/6149.htm">陈苗芬</a>, <a href="https://yichenqin.net/">秦翊宸</a>, <a href="https://rufeir.github.io/Rufei_Ren/">任汝飞</a>, <a href="https://wanghaining11.github.io/">王海宁</a>, <a href="https://wangyupeng-wyp.github.io"/> 王宇鹏</a>, <a href="https://sites.google.com/view/ylf/home">易灵飞</a>, <a href="https://zhangdingxin.gitlab.io/math/">张鼎新</a></p>
</div>
<h2 href=>Upcoming Talks</h2>
Please see the <a href="index.html "> main page</a> for upcoming talks.
<!-- Past Talks -->
<!-- Past Talks -->
<h2>2025-2026 Autumn</h2>
<table border="none" cellspacing="0" cellpadding="6" rules="groups" frame="border">
<thead>
<tr>
<th>时间 / 地点</th>
<th>报告人</th>
<th style="width:70%">题目 / 摘要</th>
</tr>
</thead>
<tbody>
<tr>
<td style="white-space: nowrap;">
<p> 9月26日 (周五) </p>
<p> 16:00–17:00 </p>
<p> <a href="https://j.map.baidu.com/5a/dss">光华楼东主楼</a> 1601 </p>
</td>
<td style="white-space: nowrap;">
<p><a href="https://ims.shanghaitech.edu.cn/2022/0916/c4741a842583/page.htm">丁之元</a></p>
<p> <span style="font-family: 'STFangsong', sans-serif; font-size: 90%;">(上海科技大学)</span> </p> </td>
<td><p><b>Title.</b> Reducedness of twisted loop groups</p>
<p> <b>Abstract.</b> In this talk, we give an elementary
proof of the reducedness of twisted loop groups. We
use standard results about structures of algebraic
groups and group schemes without referring to
mixed characteristic.</p></td>
</tr>
<tr>
<td style="white-space: nowrap;">
<p> 10月17日 (周五) </p>
<p> 16:00–17:00 </p>
<p> <a href="https://j.map.baidu.com/85/Awgi">SIMIS</a> 1210 </p>
</td>
<td style="white-space: nowrap;">
<p> <a href="http://shizhang.li/about%20me.html">李时璋</a></p>
<p><span style="font-family: 'STFangsong', 'FangSong', sans-serif; font-size: 90%;">(中科院晨兴数学中心)</span></p>
</td>
<td>
<p><b>Title.</b> On the cohomology of rational
\(p\)-adic local systems </p>
<p><b>Abstract.</b>
In \(p\)-adic geometry, there are more
mysterious rational \(p\)-adic local systems
than in algebraic/complex geometry, for example,
the analytification of \(\mathbb{P}^1\) is no
longer simply connected due to existence of a
rank 2 rational \(p\)-adic local system. The
cohomology of such local systems were studied
previously by Kedlaya–Liu and more recently by
Anschütz–Le Bras–Mann. In this talk, we shall
see a (relatively) low-tech approach to reprove
some of KL/ALBM results. This is a report of an
ongoing work joint with
Nizioł–Reinecke–Zavyalov.</p></td>
</tr>
<tr>
<td>
<p> <a href="./misc/fresan.jpg">复旦大学数学科学学院杰出学者讲坛</a></p>
<p>10月21日 (周二)</p>
<p> 16:00–17:00 </p>
<p> <a href="https://j.map.baidu.com/5a/dss">光华楼东主楼</a> 2201 </p>
</td>
<td><a href="http://javier.fresan.perso.math.cnrs.fr/">Javier Fresán </a> <p>
<span style="font-size: 85%;">(Sorbonne Université)</span></p>
</td>
<td>
<p><b>Title.</b> Infinitely Many Non-Hypergeometric Local Systems</p>
<p><b>Abstract.</b> The Bombieri-Dwork conjecture
predicts that an irreducible differential operator with a G-function
solution comes from geometry, that is, encodes how periods vary in a
pencil of algebraic varieties. This conjecture is completely open for
operators of order at least 2. At the beginning of the 90s, Dwork
proposed a strategy to establish the conjecture for G-operators of
order 2, which would consist in proving that they are all pullbacks by
a correspondence of some Gauss's hypergeometric differential
operator. Sporadic counterexamples to this expectation were found by
Krammer (1996) and Bouw-Möller (2010). I will present a joint work
with Josh Lam and Yichen Qin where we prove that most G-operators of
order 2 coming from geometry are not pullbacks of hypergeometric
differential operators. A key ingredient to construct infinitely many
counterexamples will be the André-Pink-Zannier conjecture for Shimura
varieties, in the cases recently established by Richard and Yafaev.</p>
</td>
</tr>
<tr>
<td><p>10月28日 (周二)</p>
<!-- 10月底 周二 -->
<p> 16:00–17:00 </p>
<p> <a href="https://j.map.baidu.com/85/Awgi">SIMIS</a> 1110 </p>
</td>
<td><a href="https://ams.cnu.edu.cn/rydw/jyry/f6df253f3c16421c907231b6e63a2a84.htm">蔡 立</a> <br>
<span style="font-family: 'STFangsong', 'FangSong', sans-serif; font-size: 90%;">(首都师范大学)</span>
</td>
<td>
<p><b>Title.</b> Automorphic Green Currents and Applications
<p><b>Abstract.</b> Green
currents gives the arithmetic intersection theory at the archimedean
places. In this talk, we consider Green currents for Shimura varieties
and its applications to special value formulae. This is based on a
joint work with Ye Tian and Hang Yin.</td>
</tr>
<tr>
<td><p>11月4日 (周二)</p>
<!-- 10月或12月 周二 -->
<p> 16:00–17:00 </p>
<p> <a href="https://j.map.baidu.com/85/Awgi">SIMIS</a> 1410 </p>
</td>
<td><a href="https://algnt.lab.westlake.edu.cn/">赵以庚</a>
<br><span style="font-family: 'STFangsong', 'FangSong', sans-serif; font-size: 90%;">(西湖大学)</span>
</td>
<td>
<p><b>Title.</b> On Swan classes for constructible étale sheaves</p>
<p><b>Abstract.</b> For constructible étale sheaves on
varieties over fields of positive characteristic,
the Swan class extends the Swan conductor to a
0-cycle, serving as an invariant that measures
ramification. Using different approaches,
Kato-Saito and Saito have constructed two versions
of the Swan class. In this talk, we introduce a
new cohomological Swan class and investigate
Saito's conjecture on its uniqueness. This is a
joint work with Enlin Yang.</p>
</td>
</tr>
<tr>
<td>
<p>11月14日 (周五)</p>
<!-- 11月第一周以后, 周五 -->
<p> 16:00–17:00 </p>
<p> <a href="https://j.map.baidu.com/85/Awgi">SIMIS</a> 1210 </p>
</td>
<td><a href="https://www.hengdumath.com/">杜 衡</a><br>
<span style="font-family: 'STFangsong', 'FangSong', sans-serif; font-size: 90%;">(清华大学)</span>
</td>
<td>
<p><b>Title.</b> A Prismatic Herr Complex for Bloch–Kato Selmer Groups</p>
<p><b>Abstract.</b> Bloch–Kato Selmer groups
encode subtle arithmetic information of \(p\)-adic
Galois representations. Classically, Herr’s
complex is a concrete complex that computes
Galois cohomology via the theory of
\((\varphi,\Gamma)\)-modules. In this talk, I will
introduce a prismatic Herr complex, an explicit
complex built from the prismatic
\((\varphi,\hat{G})\)-module attached to a
(log-)crystalline representation. I will
describe how this complex computes the
Bloch–Kato Selmer group. If time permits, I will
also discuss work in progress toward showing
that this complex computes the cohomology of a
corresponding F-gauge of the crystalline
representation up to inverting \(p\). The talk is
based on joint work with Luming Zhao.
</p>
</td>
</tr>
<tr>
<td>
<p>11月21日 (周五)</p>
<p> 16:00–17:00 </p>
<p> <a href="https://j.map.baidu.com/40/2GNk">SCMS</a> 102 </p>
</td>
<td><a href="https://ningguomath.com/">郭 宁</a>
<br>
<span style="font-family: 'STFangsong', 'FangSong', sans-serif; font-size: 90%;">(哈尔滨工业大学)</span>
</td>
<td>
<p><b>Title.</b> Geometric presentations and torsors over affine lines </p>
<p><b>Abstract.</b> Geometric presentations are an
effective method for simplifying cohomological
problems by reducing their relative
dimension. This talk will trace the history of
this technique, from Artin's “bon voisinage” to
its modern applications. We will particularly
focus on its relevance to the Grothendieck–Serre
conjecture for reductive torsors over regular
local rings. In this context, the talk will also
review recent advances in the analysis of torsors
over affine and projective lines. </p>
</td>
</tr>
<tr>
<td>
<p>12月12日 (周五)</p>
<p>16:00–17:00</p>
<p>SCMS 102</p>
</td>
<td><a href="https://aronheleodoro.com/">Aron Heleodoro</a><br>
<span style="font-family: 'STFangsong', 'FangSong', sans-serif; font-size: 90%;">(SIMIS)</span></td>
<td><p><b>Title.</b> Newton Decomposition of Loop Group and Affine Character Sheaves</p>
<p> <b>Abstract.</b> In this talk I will explain how one can decompose the loop group associated to a connected reductive group G into parts known as Newton strata. These remarkable strata are invariant under the conjugation of LG and by passing to Levi subgroups one can reduce questions on an arbitrary stratum to questions on basic strata, which are more manageable. I will then explain how one can use these strata to define and study a very sought-after category of character sheaves for loop groups (e.g. p-adic groups or Kac—Moody groups). This is based in joint ongoing work with Xuhua He and Xinwen Zhu.</p></td>
</tr>
<tr>
<td>
<p>12月16日 (周二)</p>
<p>16:00–17:00</p>
<p> <a href="https://j.map.baidu.com/85/Awgi">SIMIS</a> 1010 </p>
</td>
<td><p><a href="https://math.bit.edu.cn/szdw/jgml/sxx/fyy/index.htm">范洋宇</a><br>
<span style="font-family: 'STFangsong', 'FangSong', sans-serif; font-size: 90%;">(北京理工大学)</span></p>
</td>
<td>
<p><b>Title.</b> p-adic Gross-Zagier formulae for supersingular elliptic curves</p>
<p><b>Abstract.</b>The p-adic Gross-Zagier formula — the p-adic analogue of the celebrated Gross-Zagier formula — relates the p-adic height of Heegner points to the derivative of p-adic Rankin series. It plays an essential role in the Iwasawa Main Conjecture for elliptic curves and the Birch-Swinnerton-Dyer Formula. In this talk, we report some recent progress regarding the p-adic Gross-Zagier formulae for supersingular elliptic curves. This work is partly based on joint work with Prof. Y. Tian and Dr. J. Pan.</p>
</td>
</tr>
<tr>
<td>
<p>12月24日 (周三)</p>
<p> 14:00–15:00 </p>
<p> <a href="https://scms.fudan.edu.cn/">SCMS</a> 106 </p>
</td>
<td><a href="https://www.math.unipd.it/~baldassa/index.html">Francesco Baldassarri</a>
<br>
<span style="font-family: 'STFangsong', 'FangSong', sans-serif; font-size: 90%;">(University of Padova)</span>
</td>
<td>
<p><b>Title.</b> Entire Fourier expansions on $\mathbb{Q}_p$</p>
<p><b>Abstract.</b> We extend the Iwasawa theory of $p$-adic measures and the Amice--Fourier expansion to bounded uniformly continuous functions on $\mathbb{Q}_p$.</p>
<p>We interpret the $(p,T)$-adic completion $\mathscr{D}$ of the ring $\mathbb{Z}_p\!\left[T^{1/p^\infty}\right]$ as an algebra of $\mathbb{Z}_p$-valued measures on $\mathbb{Q}_p$, via $T=\Delta_1-\Delta_0$ (Dirac masses). It contains the canonical measure
$$
\mu_{\mathrm{can}} := \lim_{n\to +\infty}
E(\Delta_{p^{-n}}-\Delta_0)^{p^n} \in \mathscr{D},
$$
where $E(x)\in\mathbb{Z}_{(p)}[[x]]$ denotes the Artin--Hasse logarithm. The strong $p$-adic dual of $\mathscr{D}$ is the algebra $\mathscr{C}^{\mathrm{unif}}$ of uniformly continuous functions $\mathbb{Q}_p \to \mathbb{Z}_p$. </p>
<p>We extend the Mahler--Amice formula
$$
f(x)=\sum_{n=0}^{\infty} f^{[n]}(0)\binom{x}{n}
=\sum_{n=0}^{\infty}\left(\int_{\mathbb{Z}_p} f\, T^n\right)\binom{x}{n}
$$
to $\mathbb{Q}_p$ as
$$
f(x)=\sum_{q\in S}
\left(\int_{\mathbb{Q}_p} f\, \mu_{\mathrm{can}}^q\right) G_q(x),
$$
where $S=\mathbb{Z}[1/p]\cap\mathbb{R}_{\ge 0}$ and $\{G_q\}_{q\in S}$ is a family of $p$-adically entire functions whose restriction to $\mathbb{Q}_p$ belongs to $\mathscr{C}^{\mathrm{unif}}$ and satisfies
$$
G_q(x+y)=\sum_{q_1+q_2=q} G_{q_1}(x)G_{q_2}(y),
\qquad \forall q\in S.
$$
</p>
</td>
</tr>
<tr>
<td>
<p>12月24日 (周三)</p>
<p> 15:15-16:15 </p>
<p> <a href="https://scms.fudan.edu.cn/">SCMS</a> 106 </p>
</td>
<td><a href="https://www.universiteitleiden.nl/en/staffmembers/peter-stevenhagen">Peter Stevenhagen</a>
<br>
<span style="font-family: 'STFangsong', 'FangSong', sans-serif; font-size: 90%;">(Leiden University)</span>
</td>
<td>
<p><b>Title.</b> Non-primitive points on elliptic curves </p>
<p><b>Abstract.</b> A famous $1927$ conjecture of Emil Artin says that every nonsquare integer different from $-1$ is a primitive root modulo infinitely many primes, and that the set of these primes has some positive density. It was proved after $40$ years by Christopher Hooley, under assumption of the Generalised Riemann Hypothesis.</p>
<p>I will discuss the analogous question for points on elliptic curves over number fields, which goes by the name of Lang-Trotter, and focus on the phenomena that can cause the vanishing of the associated density. This is joint work with Nathan Jones (Chicago) and Francesco Pappalardi (Rome). </p>
</td>
</tr>
<tr>
<td>
<p>12月24日 (周三)</p>
<p> 16:30-17:30</p>
<p> <a href="https://scms.fudan.edu.cn/">SCMS</a> 106 </p>
</td>
<td><a href="https://faculty.ustc.edu.cn/yqliang/index.jsp"> 梁永祺</a>
<br>
<span style="font-family: 'STFangsong', 'FangSong', sans-serif; font-size: 90%;">(中国科学技术大学)</span>
</td>
<td>
<p><b>Title.</b> Hasse principle and Weil restriction </p>
<p><b>Abstract.</b> We consider the Hasse principle for existence of rational points on algebraic varieties defined over number fields. There are many possible cohomological obstructions to the Hasse principle. We compare the etale-Baruer-Manin obstruction on Weil restrictions of a variety with respect to extensions of number fields, and prove that they can be naturally identified to each other. This is a joint work with Yang Cao. </p>
</td>
</tr>
<tr>
<td>
<p>12月30日 (周二)</p>
<p>16:00–17:00</p>
<p>SCMS 446</p>
</td>
<td><a href="https://www.ias.edu/scholars/mingjia-zhang">张明嘉</a><br>
<span style="font-family: 'STFangsong', 'FangSong', sans-serif; font-size: 90%;">(Princeton University)</span></td>
<td><p><b>Title.</b> Abelian type Igusa stacks and applications</p>
<p> <b>Abstract.</b> Given a Shimura data, Scholze conjectures there to exist certain geometric objects (Igusa stacks), whose geometry is closely related to the Shimura varieties. I will present joint work in progress with Daniels, van Hoften and Kim on this conjecture for abelian type Shimura data. This has several applications, in particular, to showing that the construction of the local Langlands correspondence by Fargues-Scholze is compatible with more classical constructions, by Arthur, Mok and others.</p></td>
</tr>
<!-- <tr> -->
<!-- <td>TBA (周五)</td> -->
<!-- <td>TBA</td> -->
<!-- <td><a href="https://ymsc.tsinghua.edu.cn/en/info/1033/2461.htm">Koji Shimizu</a> -->
<!-- <span style="font-family: 'STFangsong', 'FangSong', sans-serif; font-size: 90%;">(清华大学)</span> -->
<!-- </td> -->
<!-- <td></td> -->
<!-- <\!-- </tr> -\-> -->
<!-- <tr> -->
<!-- <td> -->
<!-- <p style="color:red;">12月24日 (周三)</p> -->
<!-- <p> 16:00–17:00 </p> -->
<!-- </td> -->
<!-- <td><a href="https://pub.math.leidenuniv.nl/~stevenhagenp/">Peter Stevenhagen</a> -->
<!-- <br> -->
<!-- <span style="font-family: 'STFangsong', 'FangSong', sans-serif; font-size: 90%;">(Universiteit Leiden)</span> -->
<!-- </td> -->
<!-- <td>TBA</td> -->
<!-- </tr> -->
<!-- <tr> -->
<!-- <td> -->
<!-- <p style="color:red;">12月24日 (周三)</p> -->
<!-- <p> 16:00–17:00 </p> -->
<!-- </td> -->
<!-- <td><a href="https://www.math.unipd.it/~baldassa/">Francesco Baldassarri</a> -->
<!-- <br> -->
<!-- <span style="font-family: 'STFangsong', 'FangSong', sans-serif; font-size: 90%;">(Università di Padova)</span> -->
<!-- </td> -->
<!-- <td>TBA</td> -->
<!-- </tr> -->
</tbody>
</table>
</div>
</body>
</html>