Fall 2022 Schedule

Sep. 15 2022, Fangzhou Jin, Tongji University

 Time: 13:30 - 15:30
   
 Place: Room 2201,  East Main Guahuang Tower
   
 Title: Milnor-Witt cycle modules and perverse homotopy heart

 Abstract: We define Milnor-Witt cycle modules over a base scheme and study the 
 relations with the perverse homotopy t-structure. This is a joint work with
 F. Déglise and N. Feld.   

Poster

Sep. 22 2022， Andrea Bianchi, University of Copenhagen

  Time: 13:30 - 15:30
   
  Zoom Id: 853 0188 1524  password: Fudan2022
    
  Title:Trivial and non-trivial actions of the Johnson filtration on the homology
  of configuration spaces
    
  Abstract:Let S=S_{g,1} be a compact, connected, orientable surface of genus g
  with one boundary curve, and let F_n(S) denote the space of ordered 
  configurations of n distinct points in S. The homology groups H_*(F_n(S)) 
  admit a natural action of the mapping class group Mod(S)=pi_0(Diff_+(S,dS)),
  and we are broadly interested in what kind of representations of Mod(S) arise 
  in this way; in particular, how trivial/non-trivial the action of Mod(S) is.
  We consider the Johnson filtration on Mod(S) by subgroups
  J(0)>J(1)>...>J(i)>..., for i>=0. We will compare the following results:
  1) (joint with J.Miller and J.Wilson) J(i) acts trivially on H_*(F_n(S)) for
   i>=n;
  2) (joint with A.Stavrou) If g>=2, J(n-1) acts non-trivially on H_n(F_n(S)).
  3) I will discuss the main ideas of the proofs, and I will conclude with a 
  conjecture.

Sep. 29 2022, Heng Xie, Sun-Yat sen University

  Time: 13:30 - 15:30
   
  Zoom Id: 853 0188 1524  password: Fudan2022 
    
  Title: The real cycle class map and its applications
    
  Abstract:What is the singular cohomology in algebraic geometry? Classically,
  for smooth varieties X over complex numbers, there are cycle class maps 
  from Chow groups to singular cohomology. For smooth varieties X over real
  numbers, I will construct a real cycle class map from I-cohomology to 
  singular cohomology and show that the real cycle class is compatible with 
  pullbacks, pushforwards, and intersection products. These results are proved 
  in a joint work with J. Hornbostel, M. Wendt, and M. Zibrowius. Together with
  F. Jin, we generalize the real cycle class map construction from smooth
  varieties to singular varieties. I will discuss some applications of the real
  cycle class map.

Oct. 6 2022, NO TALK due to National holiday.
Oct. 13 2022, Gabriel Pallier, Sorbonne Université
```
  Time: TBA
   
  Place: TBA  
```

Oct. 20 2022, Indira Chatterji, Universit´e de Nice

  Time: TBA
   
  Place: TBA  
    
  Title: Median geometry for spaces with measured walls and for groups
    
  Abstract: TBA

Oct. 27 2022, Ilya Gekhtman, Technion – Israel Institute of Technology

  Time: TBA
   
  Place: TBA  
    
  Title: Martin boundary covers Floyd boundary
    
  Abstract:

Nov. 3 2022, Marco Linton, University of Warwick
```
 Time: TBA
   
 Place: TBA
```
Nov. 10 2022, Thomas Ng, Technion – Israel Institute of Technology
```
 Time: TBA
   
 Place: TBA
```
Nov. 17 2022, Merlin Incerti-Medici, Karlsruhe Institute for Technology
```
 Time: TBA
   
 Place: TBA
```
Nov. 24 2022, Richard Webb, The University of Manchester
```
 Time: TBA
   
 Place: TBA
```

Dec. 1 2022. Julien Paupert, Arizona State University

 Time:  10：00-11：00 (Special Time)
   
 Zoom:

Dec. 8 2022, Anythony genevois, University of Montpellier
```
 Time: TBA
   
 Place: Zoom
```
Dec. 15 2022 Giles Gardam, University of Münster
```
  Time: 13:30 - 15:30
   
  Place: TBA  
```
Dec. 22 2022
Dec. 30 2022

Spring 2022 Schedule

Mar. 03 2022, Wenyuan Yang, Peking University

Time: 15:00 - 17:00
  
Tencent room：861-8661-7196 password: 123555

 
Title: Proper actions of 3-manifold groups on finite product of quasi-trees

Abstract: Let M be a compact, connected, orientable 3-manifold. In this talk,
I will study when the fundamental group of M acts properly on a finite product 
of quasi-trees. Our main result is that this is so exactly when M does not 
contain Sol and Nil geometries. In addition, if there is no $\widetilde{SL(2, \mathbb{R})}$
geometry either, then the orbital map is a quasi-isometric embedding of $\pi_1(M)$. 
This is called property (QT) by Bestvina-Bromberg-Fujiwara, who established it for 
residually finite hyperbolic groups and mapping class groups. The main step of our 
proof is to show property (QT) for the classes of Croke-Kleiner admissible groups 
and of  relatively hyperbolic groups under natural assumptions. Accordingly, this 
yields that graph 3-manifold and mixed 3-manifold groups have property (QT). This 
represents joint work with N.T. Nguyen and S.Z. Han.

Poster

Mar. 10 2022, Martin Palmer, Mathematical Institute of the Romanian Academy

Time: 15:00-17:00
  
Zoom Id: 646 617 8889  password: 123456wu

Title: Mapping class group representations via Heisenberg, Schrödinger and 
Stone-von Neumann

Abstract: One of the first interesting representations of the braid groups is 
the Burau representation. It is the first of the family of Lawrence representations, 
defined topologically by viewing the braid group as the mapping class group of a 
punctured disc. Famously, the Burau representation is almost never faithful, but 
the k = 2 Lawrence representation is always faithful: this is a celebrated theorem 
of Bigelow and Krammer and it implies that braid groups are linear (embed into 
general linear groups over a field).

Motivated by this, and by the open question of whether mapping class groups are 
linear, I will describe recent joint work with Christian Blanchet and Awais Shaukat
in which we construct analogues of the Lawrence representations for mapping class 
groups of compact, orientable surfaces. Tools include twisted Borel-Moore homology 
of configuration spaces, Schrödinger representations of discrete Heisenberg groups 
and the Stone-von Neumann theorem.

Poster

Mar. 17 2022, Xianchang Meng, Shandong University

Time: 15:00 - 17:00
  
Tencent room：861-8661-7196 password: 123555
  
Title: Distinct distances on hyperbolic surfaces
  
Abstract:  Erdős (1946) proposed the question of finding the minimal number of 
distinct distances among any N points in the plane. Guth-Katz (2015) gave almost
sharp answer for this question using incidence geometry and polynomial 
partitioning. We consider this problem in hyperbolic surfaces associated with
cofinite Fuchsian groups, i.e. the volume of the surface is finite. We prove
a lower bound of the same strength as Guth-Katz. In particular, for any finite
index subgroup of the modular group, we extract out the dependence of the implied 
constant on the index.

Poster

Mar. 24 2022, Edgar A. Bering IV, Technion – Israel Institute of Technology

 Time: 15:00 - 17:00
   
 Zoom Meeting ID: 956 0945 4208 Passcode: hyperbolic
   
 Title: An exhaustion of the sphere complex by finite rigid sets
   
 Abstract: A subcomplex X < C of a simplicial complex is rigid if every locally 
 injective, simplicial map X \to C arises as the restriction of an automorphism 
 of $C$.  Curve complexes and other surface complexes have been found to exhibit 
 remarkable rigidity properties. Aramayona and Leininger proved that the curve complex 
 of an orientable surface can be written as an increasing union of finite rigid sets. 
 The sphere complex of a connect sum of $n$ copies of S^1 \times S^2 is an analog 
 the curve complex of a surface used in the study of Out(F_n). In this talk I will
 present joint work with C. Leininger where we prove that there is an exhaustion of 
 the sphere complex by finite rigid sets when n >= 3.

Poster

Mar. 31 2022，Bruno Martelli, University of Pisa

 Time: 15:00 - 17:00
   
 Zoom Meeting ID: 956 0945 4208 Passcode: hyperbolic
   
 Title: Fibrations on higher-dimensional hyperbolic manifolds
   
 Abstract: One of the most intriguing aspects in low-dimensional topology is the 
 existence, discovered by Jorgensen in the late 70s, of hyperbolic 3-manifolds that
 fiber over the circle. In this talk we will briefly review some aspects of this 
 beautiful theory, with the notable contributions of Thurston, and more recently 
 of Agol and Wise. 

 Then we will show that this phenomenon is not restricted to dimension 3, by 
 exhibiting some examples in dimension 4 and 5 (in even dimension, some critical 
 points are necessary, and we talk about perfect circle valued Morse functions 
 instead of fibrations). As a consequence, we will deduce that a finite type subgroup
 of a hyperbolic group needs not to be hyperbolic, thus answering a well-known open
 question in geometric group theory (joint works with Battista, Italiano, 
 and Migliorini)

Poster

Apr. 07 2022, John R. Parker, Durham University

Time: 15:00 - 17:00

Zoom Meeting ID: 956 0945 4208 Passcode: hyperbolic

Title: Complex hyperbolic lattices

Abstract: I will give a survey on recent results about complex hyperbolic lattices. A lattice in a Lie group is a discrete subgroup whose quotient has finite Haar measure. In this talk I will concentrate on the Lie group SU(n,1), often restricting to the case where n=2. Elements of this group act as holomorphic isometries of complex hyperbolic space. Roughly speaking, there are four methods of constructing complex hyperbolic lattices. I will discuss how these are related, with particular emphasis on a family of non-arithmetic lattices.

Poster
Apr. 14 2022, Robert Tang, Xi’an Jiaotong-Liverpool University

Time: 15:00 - 17:00

Zoom Meeting ID: 956 0945 4208 Passcode: hyperbolic

Title: Large-scale geometry of the saddle connection graph

Abstract: For a translation surface, the associated saddle connection graph has saddle connections as vertices, and edges connecting pairs of non-crossing saddle connections. This can be viewed as an induced subgraph of the arc graph of the surface. In this talk, I will discuss both the fine and coarse geometry of the saddle connection graph. We show that the isometry type is rigid: any isomorphism between two such graphs is induced by an affine diffeomorphism between the underlying translation surfaces. However, the situation is completely different when one considers the quasi-isometry type: all saddle connection graphs form a single quasi-isometry class. We will also discuss the Gromov boundary in terms of foliations. This is based on joint work with Valentina Disarlo, Huiping Pan, and Anja Randecker.

Poster
Apr. 21 2022，Weiyan Chen, Tsinghua University

Time: 15:00 - 17:00

Tencent room：861-8661-7196 password: 123555

Title: Choosing points on cubic plane curves

Abstract: It is a classical topic to study structures of certain special points on smooth complex cubic plane curves, for example, the 9 flex points and the 27 sextactic points. We consider the following topological question asked by Farb: Is it true that the known algebraic structures give all the possible ways to continuously choose n distinct points on every smooth cubic plane curve, for each given integer n? This work is joint with Ishan Banerjee.

Poster

Apr. 28 2022, Fangzhou Jin, Tongji University (Postponed)

May 05 2022, Brita Nucinkis, Royal Holloway, University of London

  Time: 15:00 - 17:00
   
 Zoom Meeting ID: 956 0945 4208 Passcode: hyperbolic

 Title: Cohomological properties of Mackey functors for totally disconnected locally compact groups
   
 Abstract: Mackey functors for finite groups are well understood. In the early
 2000s this was extended to infinite discrete groups, and their cohomological 
 finiteness conditions have been expressed in terms of relative cohomology and 
 finiteness conditions of          classifying spaces for proper actions. In 
 this talk I will indicate how one can extend the definition to totally 
 disconnected groups, and will indicate some of the obstacles encountered 
 here. This is ongoing work with Ilaria Castellano and Nadia Mazza.           

Poster

May 12 2022 Inheok Choi, KAIST.

 Time: 15:00 - 17:00
   
 Zoom Meeting ID: 956 0945 4208 Passcode: hyperbolic
   
 Title: Typical behavior of random mapping classes and outer automorphisms
   
 Abstract: Random walks on spaces that manifest hyperbolic properties
 have been studied for decades, as a means to investigate the structure of
 the isometry groups of such spaces. Notable results in this topic include
 descriptions of generic random isometries and limit laws for displacements
 and translation lengths. A recent technique called the pivoting technique
 led to further elaborations in these directions. In this talk, I will describe
 properties of generic random isometries of Teichmuller space or Outer
 space. Namely, generic mapping classes are principal pseudo-Anosovs that
 make displacements with many contracting subsegments. This frequently
 contracting property is shared with generic outer automorphisms, which
 are ageometric fully irreducibles and whose expansion factors differ from
 their inverses'. If time permits, I will explain how this description is related
 to (1) Qing-Rafi's sublinearly Mosre boundaries and (2) limit laws for
 random 3-manifolds.

Poster

May 19 2022 Hao Liang, Sun Yat-sen University

 Time: 15:00-17:00
  
 Tencent room：861-8661-7196 password: 123555

 Title: Homomorphisms to 3-manifold groups 

 Abstract: Following Sela's theory of limit groups (of free group), we define
 and study limit groups of compact 3-manifold groups. We show that the family 
 of compact 3-manifold groups are equationally noetherian, which answers a 
 question of Agol and Liu.  The main application of our result is to give a 
 positive answer to a question of Reid, Wang and Zhou about epimorphism 
 sequence of closed orientable aspherical 3-manifold groups. This is joint work
 with Daniel Groves and Michael Hull.
   
[Poster](https://math.fudan.edu.cn/_upload/article/files/70/d4/8c88baff4927b82b75091813d905/82ccdfdb-2d89-4bce-97f8-9c2ace327966.pdf)

May 26 2022, NO Talk due to University Anniversary

Jun. 02 2022, Yi Jiang, Tsinghua University

Time: 15:00-17:00
  
Tencent room：861-8661-7196 password: 123555
  
Title: Involution on pseudoisotopy spaces
  
Abstract: The involution on pseudoisotopy spaces is closely related to the 
homotopy type of the diffeomorphism group of a smooth compact manifold. In
this talk, we will introduce some background, a result on computing the 
involution on pseudoisotopy spaces and its application to space of 
nonnegatively curved metrics on open manifolds. This is joint work with
Mauricio Bustamante and Francis Thomas Farrell.

Poster

Jun. 09 2022, Bin Sun, Oxford University

Time: 15:00 - 17:00

Zoom Meeting ID: 956 0945 4208 Passcode: hyperbolic

Title: Generalized wreath products and rigidity of their von Neumann algebras

Abstract: We construct the first positive examples to the Connes’ Rigidity Conjecture, i.e., we construct groups G with Kazhdan’s property (T) such that if H is a group with the same von Neumann algebra as G, then H is isomorphic to G. In this talk, I will focus on the group theoretic side of this result and talk about how we applied geometric group theory to solve problems from von Neumann algebra.
```
  [Poster](https://scms.fudan.edu.cn/info/3424/4997.htm)   
```

Fall 2021 Schedule

Dec. 30 2021, Yang Su Chinese Academy of Sciences

Time: 15:00-17:00
Place: Tencent Meeting ID: 573-308-837 Password: 123455
 
Title:  Geometric structure of self covering manifolds

Abstract: A topological space is self-covering if the space is a non-trivial
cover of itself. I will talk about a joint work with Lizhen Qin and Botong 
Wang on the geometric structure of self-covering manifolds. For example, 
we show that in dimension >5, a self-covering manifold with infinite cyclic 
fundamental group is a fiber bundle over the circle. We also construct examples
of self-covering manifolds which are not fiber bundle over the circle, where 
the fundamental group contains torsion.

Poster

Dec. 16 2021, Shengkui Ye NYU Shanghai

Time: 15:00-17:00
Place: Tencent Meeting ID: 533-917-811 Password: 123455
 
Title: The group of quasi-isometries of the line cannot act effectively on the 
line

Abstract: Let G be the group of orientation-preserving quasi-isometries of the 
real line. We show that G is left-orderable, but not simple. Moreover, the group
G cannot act effectively on the real line R.

Poster