-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathDGTsem.html
More file actions
313 lines (246 loc) · 13.8 KB
/
Copy pathDGTsem.html
File metadata and controls
313 lines (246 loc) · 13.8 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
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN">
<HTML>
<HEAD>
<TITLE>Differential Geometry, Topology, and special structures seminar</TITLE>
<META NAME="GENERATOR" CONTENT="Mozilla/3.0Gold (X11; I; SunOS 4.1.4 sun4c)
[Netscape]">
<script>
window.MathJax = {
tex: {
inlineMath: [['$', '$'], ['\\(', '\\)']]
},
svg: {
fontCache: 'global'
}
};
</script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
<!--
<script type="text/x-mathjax-config">
MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}});
</script>
<script type="text/javascript"
src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
-->
</HEAD>
<font size="3" face="Garamond">
<body bgcolor="EAE9CD">
<BODY>
<table width="900" border=0 cellpadding=5>
<tr>
<td align=left>
<img align="left" height="250" src="gc.jpg">
<td align=left>
<h1>
Differential Geometry, Topology, <br> and special structures <br>seminar
</h1>
<h2>
<a href="http://math.gc.cuny.edu">Department of Mathematics</a>
<br>
<a href="http://www.gc.cuny.edu">The Graduate Center of CUNY</a>
</h2>
<h3>
Fridays 11:45noon - 1:45pm
<br>
Location: Room 6494
<br>
Organizers:
<a href="mailto:Luis.Fernandez01@bcc.cuny.edu">Luis Fernandez</a>,
<a href="mailto:mehdi.lejmi@bcc.cuny.edu">Mehdi Lejmi</a>,
<a href="Xi.Shen15@citytech.cuny.edu">Sisi Shen</a>,
<a href="mailto:scott.wilson@qc.cuny.edu">Scott Wilson</a>
</h3>
</table>
Scope: This seminar is devoted to geometric structures on manifolds, and
their topological properties. We are particularly interested in (almost)
complex manifolds, symplectic topology and geometry, (almost) Kahler geometry,
and spin^c geometry, as well as the tools of algebraic topology and geometric analysis that have proven useful
in studying such structures. The goal is expose faculty and students to present day research and foundational material in a relaxed format that includes traditional lectures with an
actively engaged audience.
<br>
Here are links to previous semesters:
<br>
<a href="DGTsemFall25.html">DGT Seminar Fall 2025</a>
<a href="DGTsemSpr25.html">DGT Seminar Spring 2025</a>
<a href="DGTsemFall24.html">DGT Seminar Fall 2024</a>
<a href="DGTsemSpr24.html">DGT Seminar Spring 2024</a>
<a href="DGTsemFall23.html">DGT Seminar Fall 2023</a>,
<br>
<a href="DGTsemSpr23.html">DGT Seminar Spring 2023</a>
<a href="DGTsemFall22.html">DGT Seminar Fall 2022</a>,
<a href="DGTsemSpr22.html">DGT Seminar Spring 2022</a>
<a href="ACGsem.html">ACG seminar</a>
<br>
Link to Homepages:
<a href="https://fsw01.bcc.cuny.edu/mehdi.lejmi/">Mehdi Lejmi</a>
<a href="https://xsshen.github.io/">Xi Sisi Shen</a>
<a href="https://www.scottwilsonmath.com">Scott Wilson</a>
<br>
<table width="750" border=0 cellpadding=5>
<hr>
<tr>
<td align=left>
<h3>Spring 2026: (all meetings in person)</h3>
<hr>
<tr>
<td align=left>
<h4>
1/30: Prof. Sisi Shen (City Tech, CUNY)
<br> <i> Title: The continuity equation for Hermitian metrics
</i>
</h4>
<a>Abstract</a>: Initially introduced by La Nave-Tian, the continuity equation is an elliptic analogue to the K\"ahler-Ricci flow which serves as an alternative way of tackling the Analytic Minimal Model program. Sherman-Weinkove generalized this work to the Hermitian setting, providing an elliptic analogue to the Chern-Ricci flow. We will discuss the behavior of solutions to the continuity equation on Hopf and Inoue surfaces as well as Oeljeklaus-Toma manifolds and compare and contrast the advantages and disadvantages of this approach. In addition, we will discuss some new results on coupled continuity equations that can be used to study the cscK problem.
<br><br>
<hr>
<tr>
<td align=left>
<h4>
2/6: Special event, time and place:
<br>
<br>
<i> Congratualtions to Prof. Mehdi Lejmi (Bronx, CUNY) as recipient of the
<a href="https://www.gc.cuny.edu/cuny-academy-humanities-and-sciences/awards/jerome-krase-sandi-cooper-awards">Sandi Cooper Award</a> for his mathematical research.
</i>
</h4>
Mehdi and other awardees will give short talk at the award ceremony at 1pm on the 8th floor.
<br><br>
<hr>
<tr>
<td align=left>
<h4>
2/13: Prof. Kuan-Hui Lee (McGill University)
<br> <i> Title: The stability of steady generalized Ricci solitons
</i>
</h4>
<a>Abstract</a>: Non-Kähler Calabi-Yau theory is a newly developed subject, and it arises naturally in mathematical physics and generalized geometry. The relevant geometries are pluriclosed metrics which are critical points of the generalized Einstein–Hilbert action which is an extension of Perelman’s F-functional. In this talk, we studied the non-Kähler Calabi-Yau through pluriclosed flow which was first introduced by Streets and Tian a few years ago. We study the critical points of the generalized Einstein-Hilbert action and discuss the stability of critical points which are defined as pluriclosed steady solitons. We proved that all compact Bismut–Hermitian–Einstein metrics are linearly stable.
<br><br>
<hr>
<tr>
<td align=left>
<h4>
2/20: no meeting this week
<br><br>
<hr>
<tr>
<td align=left>
<h4>
2/27: Prof. Manuel Rivera (Purdue U.)
<br> <i> Title: String topology via the coHochschild complex
</i>
</h4>
<a>Abstract</a>: I will describe a tractable chain-level model for the free loop space of a simplicial complex. The construction is based on coHochschild homology theory for coalgebras and does not assume any restrictions on the fundamental group or the commutative ring of coefficients.
I will then describe a way of lifting Poincaré duality to the chain level by adapting the formalism of Pre-Calabi Yau structures (developed independently by Tradler/Zeinalian and Kontsevich/Takeda/Vlassopoulos) to our setting.
Combining the two ingredientes above we produce algebraic formulae for string topology of (possibly non-simply connected) homology manifolds. From these formulae one can observe that assuming locality conditions on the chain-level lift of Poincare duality are necessary to recover the loop coproduct, an operation that can distinguish homotopy equivalent non-homeomorphic manifolds. This is joint work with Alex Takeda.
<br><br>
<hr>
<tr>
<td align=left>
<h4>
3/6: Prof. David Pham (CUNY)
<br> <i> Title: Twists, Codazzi Tensors, and the 6-sphere
</i>
</h4>
<a>Abstract</a>: Starting with an almost Hermitian manifold (M,g,J,\omega) and an automorphism \psi of TM, one can "twist" the existing structure to obtain a new almost Hermitian structure in a rather natural way. In this talk, we will examine these \psi-twisted almost Hermitian structures with particular emphasis on questions regarding the integrability of the twisted almost complex structure J^\psi and the Riemannian geometry of the twisted metric g^\psi. By studying the latter, we identity a certain class of automorphisms of the tangent bundle with nice transformation properties. We call these automorphisms g-Codazzi maps because of their close relationship with Codazzi tensors. The aforementioned results are ultimately applied to the standard nearly Kahler structure on the 6-sphere where we prove a nonintegrability result for the class of g-Codazzi maps.
<br><br>
<hr>
<tr>
<td align=left>
<h4>
3/13: Prof. Junsheng Zhang (NYU)
<br> <i> Title: Gromov-Hausdroff limits of immortal Kahler-Ricci flows
</i>
</h4>
<a>Abstract</a>: We show that the normalized Kahler-Ricci flow on a compact Kahler manifold with semiample canonical bundle converges in the Gromov-Hausdorff topology to the metric completion of the twisted Kahler-Einstein metric on the canonical model, as conjectured by Song-Tian. This is based on joint work with Man-Chun Lee and Valentino Tosatti.
<br><br>
<hr>
<tr>
<td align=left>
<h4>
3/20: no classes at CUNY (no meeting)
<br><br>
<hr>
<tr>
<td align=left>
<h4>
3/27: Prof. Bin Guo (Rutgers)
<br> <i> Title: Geometric estimates on Kahler spaces
</i>
</h4>
<a>Abstract</a>: We will discuss the role of complex Monge-Ampere equations as auxiliary equations in deriving sharp analytic and geometric estimates in Kahler geometry. By studying Green's functions, we will explore how to derive estimates for diameters and establish uniform Sobolev inequalities on Kahler manifolds, which depend only on the entropy of the volume form and are independent of the lower bound of the Ricci curvature.
<br><br>
<hr>
<tr>
<td align=left>
<h4>
4/3: no meeting (Spring break)
<br><br>
<hr>
<tr>
<td align=left>
<h4>
4/10: no meeeting
<br><br>
<hr>
<tr>
<td align=left>
<h4>
4/17: Prof. Ralph Gomez (Swarthmore College)
<br> <i> Title: Transformations in Sasaki-Einstein Geometry
</i>
</h4>
<a>Abstract</a>: In this talk we will spend some time reviewing a construction introduced by C.Boyer and K. Galicki in constructing Sasaki-Einstein manifolds. We will then give a new perspective on this construction by implementing the Berglund-H\"ubsch transpose from BHK mirror symmetry. Once we have discussed this, we will see how this sheds light on so-called "twins" in Sasaki-Einstein rational homology 7-spheres.
<br><br>
<hr>
<tr>
<td align=left>
<h4>
4/24: Prof. Christoforos Neofytidis (University of Cyprus)
<br> <i> Title: A topological interpretation of numbers
</i>
</h4>
<a>Abstract</a>: I will explain how an arbitrary finite set of numbers containing zero can be understood with topology, namely, as the set of degrees of maps between two closed manifolds in any dimension greater than two.
<br><br>
<hr>
<tr>
<td align=left>
<h4>
5/1: Prof. Max Hallgren (Rutgers)
<br> <i> Title: Expanding soliton models for Kahler-Ricci flow near conical singularities
</i>
</h4>
<a>Abstract</a>: Hamilton proved that every compact Riemannian manifold admits a unique short-time solution to the Ricci flow. Since then, much work has been devoted to extending this theory to singular initial data and to understanding the geometry of the resulting flow near singular points. In this talk, I will discuss recent joint work with Longteng Chen and Lucas Lavoyer on Ricci flows whose initial data is a Kahler space with isolated conical singularities. I will explain how expanding solitons arise as models for the flow near the singular set, and I will also discuss the relationship between our solutions and the Kahler–Ricci flow through singularities constructed by Song and Tian.
<br><br>
<hr>
<tr>
<td align=left>
<h4>
5/8: Prof. Mingyang Li (Simons Center)
<br> <i> Title: Poincare Einstein metrics with complex geometry and cusp formations.
</i>
</h4>
<a>Abstract</a>: Poincare-Einstein metrics are a natural class of complete Einstein metrics with negative Einstein constant, though their construction is often difficult. In this talk, I will discuss four-dimensional Poincare-Einstein metrics with complex geometry. In this setting, the Einstein equation reduces to a Toda type nonlinear elliptic equation, yielding an infinite-dimensional, nonperturbative construction of Poincare-Einstein metrics. I will then explain how the same framework extends to metrics with various cusp ends and how it can be used to study degenerations of Poincare-Einstein metrics. This provides a unified analytic perspective on several noncompact Einstein geometries through elliptic boundary value problems. Joint work with Hongyi Liu.
<br><br>
<hr>
<tr>
<td align=left>
<h4>
5/15: Prof. Robert Bryant (Duke U.)
<br> <i> Title: The affine Bonnet problem
</i>
</h4>
<a>Abstract</a>:
The Bonnet problem in Euclidean surface theory is well-known: Given a metric \(g\) on an oriented surface \(M^2\) and a function \(H\), when (and in how many ways) can \((M,g)\) be isometrically immersed in \(\mathbb{R}^3\) with mean curvature \(H\)? For generic data \((g,H)\), such an isometric immersion is impossible and, in the case that it does exist, the immersion is unique. Bonnet showed that, aside from the famous case of surfaces of constant mean curvature, there is a finite dimensional moduli space of \((g,H)\) for which the space of such <em>Bonnet immersions</em> has positive dimension.
<p>
The corresponding problem in affine theory is still not solved. After reviewing the Euclidean results on this problem by O. Bonnet, J. Radon, É. Cartan, and A. Bobenko, I will give a report on affine analogs of these results. In particular, I will consider the classification of the data \((g,H)\) for which the space of <em>affine Bonnet immersions</em> has positive dimension, showing a surprising connection with integrable systems in the case of data with the highest possible dimension of solutions.
</p>
<hr>
</h3>
</p>
</table>
<br><br>
<a href="http://www.mathjax.org">
<img title="Powered by MathJax"
src="http://cdn.mathjax.org/mathjax/badge/badge.gif"
border="0" alt="Powered by MathJax" />
</a>