Fall 2023 Schedule

The regular meeting time for our seminar this semester has changed to Friday 4pm to 5:30pm.

Sep. 15 2023, Jingbang Guo, Fudan University

Time: 16:00 - 17:30

Place: SCMS 106

Title: Topological Hochschild homology and Prismatic Cohomology

Abstract: The theory of prismatic cohomology is a universal p-adic cohomology theory, in the sense that it specializes to the classical p-adic cohomology theories such as the de Rham cohomology and the p-adic etale cohomology. Originally, this universal p-adic cohomology theory was expected by the calculation of topological Hochschild homology for (integral) perfectoid rings. In this seminar, the basic ideas of prismatic cohomology and topological Hochschild homology will be introduced, and between which the delicate interconnection will be emphasized. Especially the general theory of relative topological Hochschild homology and the phenomena of Bokstedt periodicity, which might benefit the calculation of (absolute) topological cyclic homology through the descent technique, are to be discussed.
Sep. 22 2023

Hongyu Wang,Yangzhou University

Time: 15:00 - 16:00

Place: East Main Guahuang Tower 1801

Title: Donaldson question for tamed closed almost complex four-manifolds

Abstract: TBA

Soumen Sarkar, Indian Institute of Technology Madras

Time: 16:00 - 17:00

Place: East Main Guahuang Tower 1801

Title: Cohomology of quasitoric manifolds over a vertex cut of a finite product of simplices

Abstract: In this talk, I’ll classify the characteristic matrices associated to quasitoric manifolds over a vertex cut of a finite product of simplices satisfying a `sign condition’. I’ll discuss the integral cohomology rings of these quasitoric manifolds with possibly minimal generators and show several relations among the products of these generators. Then, I’ll classify integral cohomology rings (up to isomorphism as graded rings) of the quasitoric manifolds over the vertex cut of a finite product of simplices. This is a joint work with Subhankar Sau.
Sep. 29 2023 No talk due to Mid-Autumn Festeival.
Oct. 6 2023, No talk due to National holiday.
Oct. 13 2023 Bingbing Liang, Soochow University

Time: 16:00 - 17:30

Place: SCMS 102

Title: A general version of Kaplansky‘s direct-finiteness conjecture

Abstract: The classical Kaplansky’s direct-finiteness conjecture says that if a, b are two elements of a group ring KG for a filed K and a group G satisfying that ab=1, then ba=1. Kaplansky proves the case that K is a field of characteristic zero and G is any group. Joint with Hanfeng Li, we prove a general case that K is replaced with a left Noetherian unital ring R and G is a sofic group. The tools of the this proof are refined mean length functions defined on the RG-modules in connection with some category language
Oct. 19 2023 Li Cai, Xi’an Jiaotong-Liverpool University

Time: Oct. 19， 15:00 - 16:00

Place: East Main Guahuang Tower 2001

Title: On graph products of spaces, groups and Hopf algebras

Abstract: In this talk we show that, the loop space X of a graph product of spaces is given by (up to weak homotopy equivalence of topological monoids) a graph product of simplicial groups, using Kan’s construction of loop spaces on simplicial sets. As a consequence, we obtain a theorem of Dobrinskaya: when X is connected, its homology (with coefficients from a field) is a graph product H of connected Hopf algebras. Some properties of the commutator of H will also be discussed.

Fangting Zheng, Xi’an Jiaotong-Liverpool University

Time: 16:00 -17:00

Place: East Main Guahuang Tower 2001

Title: Hyperbolic orbifolds of small volume

Abstract: Volume is a natural measure of complexity of a hyperbolic manifold, especially for the one of odd dimension where the Euler characteristic vanishes. In this talk, I will give a sketchy panorama about simple, i.e., small volume, hyperbolic manifolds and orbifolds.
Oct. 27 2023
Nov. 3 2023
Nov. 10 2023 Paul-Henry Leemann, Xi’an Jiaotong-Liverpool University

Time: 16:00 - 17:30

Place: SCMS 102

Title: Cayley graphs with few automorphisms

Abstract: Let G be a group and S a generating set. Then the group G naturally acts on the Cayley graph Cay(G,S) by left multiplications. The group G is said to be rigid if there exists an S such that the only automorphisms of Cay(G,S) are the ones coming from the action of G. Equivalently, a group G is rigid if there exists a graph X with G=Aut(X) acting simply transitively on the vertices of X. While the classification of finite rigid groups was achieved in 1981, few results were known about infinite groups. In a recent work, with M. de la Salle we gave a complete classification of infinite finitely generated rigid groups. As a consequence, we also obtain that every finitely generated group admits a Cayley graph with countable automorphism group.

Poster

Nov. 17 2023 Binbin Xu, Nankai University

Time: 15:30 - 16:30

Place: SCMS 102

Title: Equivalent Curves on Surfaces

Abstract: We consider a closed oriented surface of genus at least 2. To describe curves on it, one natural idea is to choose once for all a collection of curves as a reference system and to hope that any other curve can be determined by its intersection numbers with reference curves. For simple curves, using the work of Dehn and Thurston, it is possible to find such a reference system consisting of finitely many simple curves. The situation becomes more complicated when curves have self-intersections. In particular, for any non-negative integer k, it is possible to find a pair of curves having the same intersection number with every curve with k self-intersections. Such a pair of curves are called k-equivalent curves. In this talk, I will discuss the general picture of a pair of k-equivalent curves and the relation between k-equivalence relations for different k’s. This is a joint-work with Hugo Parlier.

Chi-Kwong Fok, Xi’an Jiaotong-Liverpool University

Time: 16:30 - 17:30

Place: SCMS 102

Title: Equivariant formality of homogeneous spaces

Abstract: Equivariant formality, a notion in equivariant topology introduced by Goresky-Kottwitz-Macpherson, is a desirable property of spaces with group actions. Broad classes of spaces of especial interest are well-known to be equivariantly formal, e.g., compact symplectic manifolds equipped with Hamiltonian compact Lie group actions and projective varieties equipped with linear algebraic torus actions, of which flag varieties are examples. Less is known about compact homogeneous spaces G/K equipped with the isotropy action of K, which is not necessarily of maximal rank. In this talk we will review the notion of equivariant formality and previous attempts of characterizing equivariant formality of G/K, and then present our results on this problem using an analogue of equivariant formality in K-theory. Part of the work presented in this talk is joint with Jeffrey Carlson.
Nov. 24 2023 Biao Ma, the Technion in Haifa. CANCELLED

Time: CANCELLED

Place: CANCELLED

Title:

Abstract:
Dec. 1 2023 Edward Schesler FernUniversität in Hagen, Postponed

Time: Postponed

Place: Postponed

Title:

Abstract:
Dec. 8 2023 Haimiao Chen, Beijing Technology and Business University

Time: 16:00 - 17:30

Place:

Title: Character varieties and skein modules of knot complements

Abstract: Let $K$ be a knot in $S^3$, and let $\pi(K)$ be the knot group. The character of a representation $\rho:\pi(K)\to{\rm SL}(2,\mathbb{C})$ is the function $x\mapsto{\rm tr}(\rho(x))$. The characters of all representations form the character variety $X(K)$, which is known to encode much topological information on $S^3\setminus K$. Fix a commutative ring $R$ with a distinguished invertible element $A$. The Kauffman bracket skein module $S(K)$ is defined as the $R$-module generated by embedded framed links in $S^3\setminus K$ modulo certain local relations. The skein module encodes more information, and is regarded as a quantization of character variety, in the sense that $S(K)$ recovers $X(K)$ when $R=\mathbb{C}$ and $A=-1$. Based on recent works, we will talk about the following interrelated topics: (1) computing $X(K)$ for arborescent knots $K$; (2) high-dimensional components of $X(K)$, i.e. those $C$ with $\dim C>1$; (3) torsion in $S(K)$ when $K$ is a Montesinos knot.
Dec. 15 2023
Dec. 22 2023 Yang Su, Chinese Academy of Sciences.

Spring 2023 Schedule

The regular meeting time for our seminar this semester has changed to Tuesday 3pm to 5pm.

Feb. 28 2023, Josiah Oh， Fudan University

Time: 15:00 - 17:00

Place: SCMS 102

Title: Quasi-isometric rigidity for a product of lattices

Abstract: Quasi-isometric rigidity theorems contribute to Gromov’s program of classifying finitely generated groups up to quasi-isometry. In this talk we discuss the quasi-isometric rigidity for the class of groups N x L, where N is a lattice in a simply connected nilpotent Lie group and L is a non-uniform lattice in a rank one semisimple Lie group. Such a group is, up to finite noise, an extension by a nilpotent lattice of a non-uniform lattice commensurable to L. This is the first step towards proving quasi-isometric rigidity for a class of spaces generalizing high-dimensional graph manifolds, as defined by Frigerio-Lafont-Sisto.

Poster
Mar. 7 2023, Mengmeng Xu， Fudan University

Time: 15：00-16：00

Place: 1704， East Main Guahuang Tower

Title: Torsion in 1-cusped Picard modular groups

Abstract: We discuss a systematic effective method to construct coarse fundamental domains for the action of the Picard modular groups PU(2,1,O_d). We demand that the ring O_d of algebraic integers in Q(i√d) has class number one, i.e. d=1,2,3,7,11,19,43,67,163. The computations can be performed quickly up to the value d=19. As an application of this method, we classify conjugacy classes of torsion elements, deduce short presentations for the groups, and construct neat subgroups of small index. This is joint work with M. Deraux.

Poster

Mar. 14 NO TALK
Mar. 21 Benjamin Brück, ETH Zürich

Time: 15:00 - 17:00

Zoom id: 853 0188 1524 Password:Fudan2023

Title: Computing high-dimensional group cohomology via duality

Abstract: In recent years, duality approaches have yielded new results about the high-dimensional cohomology of several groups and moduli spaces, such as SL_n(Z) and M_g. I will explain the general strategy of these approaches and survey results that have been obtained so far.

To give an example, I will first explain how Borel-Serre duality can be used to show that the rational cohomology of SL_n(Z) vanishes near its virtual cohomological dimension. This is based on joint work with Miller-Patzt-Sroka-Wilson and builds on results by Church-Farb-Putman.

I will then put this into a more general context by giving an overview of analogous results for mapping class groups of surfaces, automorphism groups of free groups and further arithmetic groups such as SL_n(O_K) and Sp_2n(Z).

Poster
Mar. 28 Yi Huang, Tsinghua University

Time: 15:00 - 17:00

Place: SCMS 346

Title: The earthquake metric

Abstract: Earthquakes are natural generalisations of Fenchel-Nielsen twists deformations on Teichmueller space, and Thurston’s remarkable earthquake theorem asserts that any hyperbolic metric on a given closed surface can be deformed to any other by a unique (left) earthquake. This was famously employed by Kerckhoff in his proof of the Nielsen realisation problem, which quickly cemented their importance in Teichmüller theory. Geometrically speaking, however, (long) Earthquake paths are far from being “twist efficient” - indeed, Mirzakhani shows that earthquake flows on Teichmüller space are measure conjugate to the horocyclic flow. Motivated by wishing to understand how one might efficiently “earthquake” between hyperbolic structures, we initiate the first systematic study of the earthquake metric—a Finsler metric first introduced in Thurston’s “Minimal stretch maps between hyperbolic surfaces” preprint, and discover surprising connections to both the Thurston metric and the Weil-Petersson metric. This is work in collaboration with K. Ohshika, H. Pan and A. Papadopoulos.

Poster
Apr. 4 Bin Yu, Tongji University

Time: 15:00 - 17:00

Place: SCMS 346

Title: The existence of arbitrary large number of non R-covered Anosov flows on hyperbolic 3-manifolds

Abstract: We will talk about a result about Anosov flows on hyperbolic three manifolds, which says that for every positive integer n, there exists a closed hyperbolic 3-manifold M that carries at least n pairwise different (i.e., not orbitally equivalent) non R-covered Anosov flows. This is a joint work with Francois Beguin.
Apr. 11 Eduard Schesler, FernUniversität in Hagen

Time: 15:00 - 17:00

Zoom id: 853 0188 1524 Password:Fudan2023

Title: From telescopes to frames and simple groups

Abstract: I will introduce the notion of a telescope of groups. Very roughly a telescope is a directed system of groups that contains various commuting images of some fixed group B. Imitating known constructions of groups acting on rooted trees, we obtain a number of examples of B-telescopes and discuss several applications.

We give examples of 2-generated infinite amenable simple groups. We show that every finitely generated residually finite (amenable) group embeds into a finitely generated (amenable) simple LEF-group. We construct 2-generated frames in products of finite simple groups and show that there are Grothendieck pairs consisting of amenable groups and groups with property (tau). This talk is based on a joint work with Steffen Kionke.

Poster

Apr. 18 Dawid Kielak, University of Oxford

Time: 16:00 - 17:30

Zoom id: 853 0188 1524 Password:Fudan2023

Title: Vitually free-by-cyclic groups

Abstract: (joint with Marco Linton) I will talk about a homological way of recognising virtually free-by-cyclic groups among hyperbolic virtually compact special groups. This yields to an interesting observation about one-relator groups with torsion.

Poster
Apr. 25 Rachel Skipper ENS Paris

Time: 15:00 - 17:00

Zoom id: 853 0188 1524 Password:Fudan2023

Title: Computing Scale in Neretin’s group

Abstract: For an automorphism of a totally disconnected, locally compact group, Willis introduced the notion of scale which provides information on its behavior. In this talk, we will discuss the setting where the tdlc group is Neretin’s group and where the automorphism comes from conjugation in the group. This is an ongoing joint work with Michal Ferov and George Willis at the University of Newcastle.
May 2, No Talk due to Worker’s day.
May 9, Stefan Witzel, Universität Gießen

Time: 15:00 - 17:00

Zoom id: 853 0188 1524 Password:Fudan2023

Title: Arithmetic approximate lattices and their finiteness properties

Abstract: Approximate groups were identified as a natural framework for geometric group theory by Björklund and Hartnick and further developed by Cordes, Hartnick and Tonić, unifying previous research on apparently disparate areas such as finite approximate groups (Breuillard, Green, Tao) and quasi-crystals (Meyer and others).

Approximate groups arise naturally via a cut-and-project procedure from lattices in locally compact groups. A central point I want to make is that S-arithmetic groups are, by their standard definition, the result of cut-and-project procedure. They happen to be groups as long as S contains all infinite places, an assumption usually imposed.

In the context of approximate groups, that assumption can be lifted and gives rise to S-arithmetic approximate groups in characteristic 0 that are not groups but resemble S-arithmetic groups in positive characteristic. The finiteness properties of S-arithmetic subgroups of reductive groups in positive characteristic are determined by the Rank Theorem (joint with Bux and Köhl). I will present joint work with Tobias Hartnick proving a Rank Theorem for S-arithmetic approximate groups in characteristic 0.

Poster

May 16, Maria Cumplido, University of Seville

Time: 15:00 - 17:00

Zoom id: 853 0188 1524 Password:Fudan2023

Title: Intersection of parabolic subgroups in Artin groups

Abstract: Artin groups are a natural generalisation of braid groups from an algebraic point of view: in the same way that braids are obtained from the presentation of the symmetric group, other Coxeter groups give rise to more general Artin groups. There are very few results proven for every Artin group. To study them, specialists have focused on some special kind of subgroup, called “parabolic subgroups”. These groups are used to build important simplicial complexes, as the Deligne complex or the recent complex of irreducible parabolic subgroups. The question “Is the intersection of parabolic subgroups a parabolic subgroup?” is a very basic question whose answer was only known for RAAGs until 2018. In this talk, we will speak about the progress on that matter since then, starting with the breakthrough of the positive answer for spherical-type Artin groups and we will see how we can answer this question in Artin groups of large type, by using the geometric realisation of the poset of parabolic subgroups, that we have named “Artin complex”. In particular, we will show that this complex in the large case has a property called sistolicity (a sort of weak CAT(0) property) that allows us to apply techniques from geometric group theory. These are a joint works with Volker Gebhardt, Juan González-Meneses, Bert Wiest, Alexandre Martin and Nicolas Vaskou.

Poster
May 23, Weinan Lin, Peking University

Time: 15:30 - 17:00

Place: HGX 506

Title: Noncommutative Gröbner basis and Ext groups

Abstract: The Gröbner basis is a powerful tool in commutative algebra. We can use it to do many calculations such as computing the presentations of the kernel and cokernel of a map between finitely presented modules over a commutative algebra. However, many important algebras including the Steenrod algebra in algebraic topology are not commutative. We make a noncommutative generalization of the Gröbner basis which can be applied to the Steenrod algebra A. This leads to highly efficient calculations in the category of A-modules including the computation of E2 pages of Adams spectral sequences.

Poster

May 30, Kasra Rafi (Colloquium)

Time: 16:00 - 17:00

Place: Gu Lecture Hall, SCMS

Abstract: A theorem of Furstenberg from 1967 states that if Gamma is a lattice in a semisimple Lie group G, then there exists a measure on Gamma with finite first moment such that the corresponding harmonic measure on the Furstenberg boundary is absolutely continuous. We will discuss generalizations of this theorem in the setting of the Mapping class group and Gromov hyperbolic groups

Poster
Jun. 6，Runjie Hu, Stony Brook University

Time: 13:30 -14:30

Place: HGX 506

Title: Algebraic Model of Manifolds

Abstract: The surgery theory of dimension at least 5 stayedinthecentral position of classification of manifolds in the last century. In1970s, Ranicki invented the cosheaf theory of derived quadraticforms to give an algebraic discription of the existence of highdimensional manifolds over a fixed homotopy type andthehomotopy manifold classifications. On the other hand, we couldunderstand a homotopy type by passage to rational andp-adicinformation. Quillen and Sullivan individually developedtherational homotopy theories. Sullivan sketched the approachtoalgebraize simply connected rational manifolds, i.e., a free dgaoverQ together with a Poincare duality and several rational Pontryaginclasses, and Zhixu Su completed the proof in her thesis. About twodecades ago, Mandell proved that E-inifinity algebras over Fp-barcanb be the algebraic models of p-adic nilpotent homotopytypes. Five years ago, Rivera and Zeinalian showed that the cobarconstruction of coalgebras could give algebraic models of integral homotopy types. We want to generalize Sullivan’s rational discussionof manifolds to give algebraic models of manifolds. The project isstill in progress but I will talk about our recent work of 2-adicdiscussion of Ranicki’s theory and one application of this powerful theory to understand Galois actions on smooth complex varieties.

Poster

Anthony Genevois, IMAG

Time: 15:00 - 17:00

Zoom id: 853 0188 1524 Password:Fudan2023

Title: Hyperbolic translation lengths in (quasi-)median graphs

Abstract: Motivated by the fact that elements of a mapping class group have rational and computable translation lengths in the corresponding curve graph, I will explain during the talk how we can show that isometries of quasi-median graphs have rational and computable translation lengths in the corresponding crossing graphs. Quasi-median graphs provide a natural generalisation of median graphs, also known as one-skeletons of CAT(0) cube complexes. They appear naturally in the study of graph products of groups. As a concrete application, the theorem applies to right-angled Artin groups and their extension graphs.

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.

Poster

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.

Poster

Oct. 6 2022, NO TALK due to National holiday.

Oct. 13 2022, Gabriel Pallier, Sorbonne Université

  Time: 14:30-15:30
   
  Zoom Id: 853 0188 1524  password: Fudan2022 
    
  Title: Lie groups with a small space of metric structures

  Abstract: In this talk we will consider a family of solvable, non-nilpotent
  Lie groups, including the three-dimensional group SOL. On such a group, any
  pair of left-invariant Riemannian metrics are found to be roughly similar:
  after multiplying one of them by a suitable multiplicative constant, they
  will differ by at most a bounded amount. This allows one to reformulate
  various earlier results about the quasiisometries of these groups in a 
  common framework. I will compare this result with a recent theorem of
  Oregon-Reyes, giving an opposite conclusion when considering non-elementary
  word-hyperbolic groups: the latter are found to have large spaces of metric 
  structures. Joint work with Enrico Le Donne and Xiangdong Xie.

Poster

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

  Time: 15:00 - 17:00
   
  Zoom Id: 853 0188 1524  password: Fudan2022  
    
  Title: Median geometry and Hyperbolicity
    
  Abstract: I will be discussing triangles in metric spaces, and how 
  informations on triangles can give informations on algebraic properties
  of a cocompact group of isometries of the metric space. This talk will
  be accessible to non-spacialists.

Poster

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

  Time: 15:00 - 17:00
   
  Zoom Id: 853 0188 1524  password: Fudan2022 
    
  Title: Martin, Floyd and Bowditch boundaries of relatively hyperbolic groups
    
  Abstract: Consider a transient random walk on a countable group $G$. The 
  Green distance between two points in the group is defined to be minus the
  boundary of the probability that a random path starting at the first point
  ever reaches the second. The Martin compactification of the random walk is 
  a topological space defined to be the horofunction boundary of the Green 
  distance. It is a topological model for the Poisson boundary.
    
 The Martin boundary typically heavily depends on the random walk; it is thus
 exciting when for some large class of random walks, the Martin boundary is 
 equivariantly homeomorphic to some well known geometric boundary of the group.
 Ancona showed in 1988 that this is the case for finitely supported random walks
 on hyperbolic groups: the Martin boundary is identified with the Gromov boundary.
   
 We generalize Ancona's results to relatively hyperbolic groups: the Martin boundary
 equivariantly continuously surjects onto the Gromov boundary of any hyperbolic space
 on which the group acts geometrically finitely (called the Bowditch boundary), and 
 the preimage of any conical limit point is a singleton. When the parabolic subgroups 
 are virtually abelian (e.g. for Kleinian groups) we show that the preimage of a parabolic 
 fixed point is a sphere of appropriate dimension, so the Martin boundary can be identified
 with a Sierpinski carpet. A major technical tool is a generalization of a deviation
 inequality due to Ancona saying the Green distance is nearly additive along word geodesics, 
 which has various other applications, including to comparing harmonic and Patterson-Sullivan 
 measures for negatively curved manifolds and to local limit theorems for random walks.
   
We do all this using an intermediate construction called the Floyd metric obtaining by 
suitably rescaling the Cayley graph and considering the associated completion called 
the Floyd compactification. We show that for any finitely supported random walk on a 
finitely generated group, the Martin boundary surjects to the Floyd boundary, which 
in turn by work of Gerasimov covers the Bowditch boundary of relatively hyperbolic 
groups. This is based on several joint works with subsets of Dussaule, Gerasimov, 
Potyagailo, and Yang.    

Poster

Nov. 3 2022, Marco Linton, University of Warwick

 Time: 16:00 - 18:00 (Very Special Time)
   
 Zoom Id: 853 0188 1524  password: Fudan2022
   
 Time: Hyperbolic one-relator groups
   
 Abstract: Since their introduction by Gromov in the 80s, a wealth of tools have been
 developed to study hyperbolic groups. Thus, when studying a class of groups, a 
 characterisation of those that are hyperbolic can be very useful. In this talk we
 will turn to the class of one-relator groups. In previous work, we showed that a 
 one-relator group not containing any Baumslag--Solitar subgroups is hyperbolic, 
 provided it has a Magnus hierarchy in which no one-relator group with a so called 
 `exceptional intersection' appears. I will define one-relator groups with exceptional 
 intersection, discuss the aforementioned result and will then provide a characterisation
 of the hyperbolic one-relator groups with exceptional intersection. Finally, I will then 
 discuss how this characterisation can be used to establish properties for all one-relator
 groups.

Poster

Nov. 10 2022, Thomas Ng, Technion – Israel Institute of Technology

 Time: 15:00 - 17:00
   
 Zoom Id: 853 0188 1524  password: Fudan2022
   
 Title: Residually finite quotients via relative cubulation
   
 Abstract: Small cancellation theory is a rich source of cocompactly cubulated 
 groups. The classical C’(1/6) condition has a natural generalization to 
 quotients of free products.  While free products exhibit much more exotic
 behavior than free groups, these quotients act on a Gromov hyperbolic polygonal
 complexes and have been used to solve embedding problems in groups.  When the
 factor groups are assumed to act geometrically on a CAT(0) cube complex, Martin 
 and Steenbock show that such C’(1/6) quotients are again geometrically cubulated. 
 I will describe joint work with Eduard Einstein proving that when the free factors
 are residually finite every C’(1/6) quotient is again residually finite. Our proof
 relies on showing that the quotient groups admit relatively cubulations, a kind of 
 improper action on cube complexes.

Poster

Nov. 17 2022, Merlin Incerti-Medici, Karlsruhe Institute for Technology

 Time: 15:00 -17:00
   
 Zoom Id: 853 0188 1524  password: Fudan2022
   
 Title: Hyperbolic projections and topological invariance of Morse boundaries
   
 Abstract:When studying hyperbolic spaces, they admit a boundary at infinity that is
 invariant under quasi-isometries. This allows us to associate this boundary as a
 topological invariant to hyperbolic groups. This procedure fails quickly when moving
 to other spaces; already for CAT(0) spaces there are quasi-isometric spaces that have
 non-homeomorphic boundary at infinity. In recent years, several notions of boundaries
 have been introduced to remedy this. One such boundary is the Morse boundary, which,
 for CAT(0) spaces, can be seen as subsets of the visual boundary. However, it turns out 
 that the topology that makes the Morse boundary quasi-isometry-invariant does not coincide 
 with the topology of the visual boundary and the visual topology is not quasi-isometry-invariant
 even when restricted to Morse boundaries.
 In this talk, we will show that nevertheless, the visual topology on Morse boundaries has 
 some decent invariance properties for a large class of examples (most cubulated groups). 
 We will do so by introducing a new method to define a topology on Morse boundaries, show that
 this topology has good invariance properties and that it is a naturally occurring topology 
 for many examples.

Poster

Nov. 24 2022, Reid Monroe Harris, The Chinese University of Hong Kong,Shenzhen

 Time: 13:30 - 15:30
   
 Zoom Id: 853 0188 1524  password: Fudan2022
   
 Title: Monodromy of Smooth Quartic Plane Curves
   
 Abstract: We consider the parameter space ${\mathcal U}_d$ of smooth plane curves of degree
 $d$. The universal smooth plane curve of degree $d$ is a fiber bundle 
 $\mathcal{E}_d\to\mathcal{U}_d$ with fiber diffeomorphic to a surface $\Sigma_g$. 
 This bundle gives rise to a monodromy homomorphism $\rho_d:\pi_1(\mathcal{U}_d)\to\mathrm{Mod}(\Sigma_g)$, 
 where $\mathrm{Mod}(\Sigma_g):=\pi_0(\mathrm{Diff}^+(\Sigma_g))$ is the mapping class group of
 $\Sigma_g$. The main result of this paper is that the kernel of 
 $\rho_4:\pi_1(\mathcal{U}_4)\to\mathrm{Mod}(\Sigma_3)$ is isomorphic to 
 $F_\infty\times\mathbb{Z}/3\mathbb{Z}$, where $F_\infty$ is a free group of countably infinite
 rank. In the process of proving this theorem, we show that the complement 
 $\mathcal{T}_g\setminus\mathcal{H}_g$ of the hyperelliptic locus $\mathcal{H}_g$ in 
 Teichm\"uller space $\mathcal{T}_g$ has the homotopy type of an infinite wedge of spheres. 
 As a corollary, we obtain that the moduli space of plane quartic curves is aspherical. 
 The proofs use results from the Weil-Petersson geometry of Teichm\"uller space together 
 with results from algebraic geometry.

Poster

Dec. 1 2022. Julien Paupert, Arizona State University

 Time:  10：00-11：00 (Special Time)
   
 Zoom Id: 853 0188 1524  password: Fudan2022
   
 Title: Presentations for cusped arithmetic hyperbolic lattices
   
 Abstract: We present a general method to compute a presentation for any cusped hyperbolic
 lattice $\Gamma$, applying a classical result of Macbeath to a suitable $\Gamma$-invariant 
 horoball cover of the corresponding symmetric space.  As applications we compute presentations
 for the Picard modular groups ${\rm PU}(2,1,\mathcal{O}_d)$ for $d=1,3,7$ and the quaternionic 
 lattice ${\rm PU}(2,1,\mathcal{H})$ with entries in the Hurwitz integer ring $\mathcal{H}$. 
 This is joint work with Alice Mark.

Poster

Dec. 8 2022, Anythony genevois, University of Montpellier （CANCELLED）
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 Time: TBA
   
 Zoom Id: 853 0188 1524  password: Fudan2022
```

Dec. 15 2022 Giles Gardam, University of Münster

  Time: 13:30 - 15:30
   
  Zoom Id: 853 0188 1524  password: Fudan2022  
    
  Title: The Kaplansky conjectures
    
  Abstract: There is a series of four fundamental and long-standing conjectures on group rings 
  attributed to Kaplansky. For example, the zero divisor conjecture states that the group ring
  of a torsion-free group with field coefficients has no zero divisors. I will discuss these conjectures,
  their connections to other open questions in various areas of mathematics, and my recent disproof of the
  unit conjecture.

Dec. 22 2022 Fei Han, National University of Singapore

Time: 13:30 - 15:30
   
Zoom Id: 853 0188 1524  password: Fudan2022  
  
Title: title: Characteristic numbers and index theoretic invariants for 24 dimensional string manifolds
  
Abstract: A manifolds M is called string manifold i its free loop space LM is spin.
There are many studies on the string geometry. Dimension 24 is in particular
interesting for string geometry. In the talk, I will report our work on the study
of characteristic numbers and index theoretic invariants for 24 dimensional
string manifolds and string cobordism following Mahowald-Hopkins. This represents 
our joint work with Ruizhi Huang

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

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

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