Spring 2024 Schedule
The regular meeting time for our seminar this semester has changed to Friday 4pm to 5pm.

Mar. 8 2024 Claudio Llosa Isenrich, Karlsruhe Institute of Technology
Time: 16:00  17:00
Place: SCMS 102
Title: Dehn functions of central products of nilpotent groups
Abstract: The Dehn function of a finitely presented group provides a quantitative measure for the difficulty of detecting if a word in its generators represents the trivial element of the group. By work of Gersten, Holt and Riley the Dehn function of a nilpotent group of class c is bounded above by n^{c+1}. However, we are still far from determining the precise Dehn functions of all nilpotent groups. In this talk, I will explain recent results that allow us to determine the Dehn functions of large classes of nilpotent groups arising as central products. As a consequence, for every k>2, we obtain many pairs of finitely presented knilpotent groups with bilipschitz asymptotic cones, but with different Dehn functions. This shows that Dehn functions can distinguish between nilpotent groups with the same asymptotic cone, making them interesting in the context of the conjectural quasiisometry classification of nilpotent groups. This talk is based on joint works with GarcíaMejía, Pallier and Tessera.

Mar. 14 2024 (Special Date, joint with SCMS Colloquium) KaiUwe Bux, Bielefeld University
Time: 17:00  18:00
Place: Gu Lecture Hall SCMS
Title: Telling groups apart by measures of complexity
Abstract: It is hopeless to classify infinite groups up to isomorphism. There are several invariants one can use to chart the vast area inhabited by such groups. I shall discuss several numerical group invariants coming from topology, homology, and geometry:
* finiteness properties * (co)homologicial and geometric dimensions * isoperimetric inequalities
I shall illustrate these concepts by means of examples; and the main source of examples for groups in this talk will be arithmetic groups, e.g., the group of invertible integer nbyn matrices.

Mar. 22 2024,

Mar. 29 2024

Apr. 5 2024

Apr. 12 2024 Biao Ma, Tongji University
Time: 16:00  17:00
Place: TBA

Apr. 19 2024

Apr. 26 2024

May 10 2024

May 17 2024

May 24 2024

May 31 2024

Jun. 7 2024
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 padic cohomology theory, in the sense that it specializes to the classical padic cohomology theories such as the de Rham cohomology and the padic etale cohomology. Originally, this universal padic 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 fourmanifolds
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 MidAutumn 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 directfiniteness conjecture
Abstract: The classical Kaplansky’s directfiniteness 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 RGmodules in connection with some category language

Oct. 19 2023 Li Cai, Xi’an JiaotongLiverpool 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 JiaotongLiverpool 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 PaulHenry Leemann, Xi’an JiaotongLiverpool 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.

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 selfintersections. In particular, for any nonnegative integer k, it is possible to find a pair of curves having the same intersection number with every curve with k selfintersections. Such a pair of curves are called kequivalent curves. In this talk, I will discuss the general picture of a pair of kequivalent curves and the relation between kequivalence relations for different k’s. This is a jointwork with Hugo Parlier.
ChiKwong Fok, Xi’an JiaotongLiverpool 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 GoreskyKottwitzMacpherson, is a desirable property of spaces with group actions. Broad classes of spaces of especial interest are wellknown 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 Ktheory. 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: East Main Guahuang Tower 1801
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) highdimensional 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.
Time: 16:00  17: 30
Place: SCMS 102
Title: Mapping class group of manifolds which look like 3dimensional complete intersections
Abstract: In this talk I will introduce our computation of the mapping class group of closed simplyconnected 6manifolds which look like complete intersections. I will also discuss some algebraic properties of this mapping class group, including the abelianization, the center, and that the mapping class group is residually finite and virtually torsionfree.This is a joint work with M.Kreck.

Jan. 8 2024 Lei Chen, University of Maryland
Time: 16:00  17: 00
Place: SCMS 102
Title: Mapping class groups of circle bundles over a surface
Abstract: In this talk, we study the algebraic structure of mapping class group Mod(M) of 3manifolds M that fiber as a circle bundle over a surface S^1 → M → S_g. We prove an exact sequence 1 → H_1(S_g) → Mod(M) → Mod(S_g) → 1, relate this to the Birman exact sequence, and determine when this sequence splits. We will also discuss the Nielsen realization problem for such manifolds and give a partial answer. This is joint work with Bena Tshishiku.
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: Quasiisometric rigidity for a product of lattices
Abstract: Quasiisometric rigidity theorems contribute to Gromov’s program of classifying finitely generated groups up to quasiisometry. In this talk we discuss the quasiisometric 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 nonuniform lattice in a rank one semisimple Lie group. Such a group is, up to finite noise, an extension by a nilpotent lattice of a nonuniform lattice commensurable to L. This is the first step towards proving quasiisometric rigidity for a class of spaces generalizing highdimensional graph manifolds, as defined by FrigerioLafontSisto.

Mar. 7 2023, Mengmeng Xu， Fudan University
Time: 15：0016：00
Place: 1704， East Main Guahuang Tower
Title: Torsion in 1cusped 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.

Mar. 14 NO TALK

Mar. 21 Benjamin Brück, ETH Zürich
Time: 15:00  17:00
Zoom id: 853 0188 1524 Password:Fudan2023
Title: Computing highdimensional group cohomology via duality
Abstract: In recent years, duality approaches have yielded new results about the highdimensional 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 BorelSerre 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 MillerPatztSrokaWilson and builds on results by ChurchFarbPutman.
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).

Mar. 28 Yi Huang, Tsinghua University
Time: 15:00  17:00
Place: SCMS 346
Title: The earthquake metric
Abstract: Earthquakes are natural generalisations of FenchelNielsen 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 WeilPetersson metric. This is work in collaboration with K. Ohshika, H. Pan and A. Papadopoulos.

Apr. 4 Bin Yu, Tongji University
Time: 15:00  17:00
Place: SCMS 346
Title: The existence of arbitrary large number of non Rcovered Anosov flows on hyperbolic 3manifolds
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 3manifold M that carries at least n pairwise different (i.e., not orbitally equivalent) non Rcovered 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 Btelescopes and discuss several applications.
We give examples of 2generated infinite amenable simple groups. We show that every finitely generated residually finite (amenable) group embeds into a finitely generated (amenable) simple LEFgroup. We construct 2generated 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.

Apr. 18 Dawid Kielak, University of Oxford
Time: 16:00  17:30
Zoom id: 853 0188 1524 Password:Fudan2023
Title: Vitually freebycyclic groups
Abstract: (joint with Marco Linton) I will talk about a homological way of recognising virtually freebycyclic groups among hyperbolic virtually compact special groups. This yields to an interesting observation about onerelator groups with torsion.

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 quasicrystals (Meyer and others).
Approximate groups arise naturally via a cutandproject procedure from lattices in locally compact groups. A central point I want to make is that Sarithmetic groups are, by their standard definition, the result of cutandproject 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 Sarithmetic approximate groups in characteristic 0 that are not groups but resemble Sarithmetic groups in positive characteristic. The finiteness properties of Sarithmetic 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 Sarithmetic approximate groups in characteristic 0.

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 sphericaltype 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 GonzálezMeneses, Bert Wiest, Alexandre Martin and Nicolas Vaskou.

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 Amodules including the computation of E2 pages of Adams spectral sequences.

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

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 andpadicinformation. 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 Einifinity algebras over Fpbarcanb be the algebraic models of padic 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 2adicdiscussion of Ranicki’s theory and one application of this powerful theory to understand Galois actions on smooth complex varieties.
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 quasimedian graphs have rational and computable translation lengths in the corresponding crossing graphs. Quasimedian graphs provide a natural generalisation of median graphs, also known as oneskeletons of CAT(0) cube complexes. They appear naturally in the study of graph products of groups. As a concrete application, the theorem applies to rightangled 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: MilnorWitt cycle modules and perverse homotopy heart Abstract: We define MilnorWitt cycle modules over a base scheme and study the relations with the perverse homotopy tstructure. This is a joint work with F. Déglise and N. Feld.

Sep. 22 2022， Andrea Bianchi, University of Copenhagen
Time: 13:30  15:30 Zoom Id: 853 0188 1524 password: Fudan2022 Title:Trivial and nontrivial 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/nontrivial 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(n1) acts nontrivially 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, SunYat 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 Icohomology 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: 14:3015:30 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, nonnilpotent Lie groups, including the threedimensional group SOL. On such a group, any pair of leftinvariant 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 OregonReyes, giving an opposite conclusion when considering nonelementary wordhyperbolic groups: the latter are found to have large spaces of metric structures. Joint work with Enrico Le Donne and Xiangdong Xie.

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 nonspacialists.

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 PattersonSullivan 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.

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 onerelator 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 onerelator groups. In previous work, we showed that a onerelator group not containing any BaumslagSolitar subgroups is hyperbolic, provided it has a Magnus hierarchy in which no onerelator group with a so called `exceptional intersection' appears. I will define onerelator groups with exceptional intersection, discuss the aforementioned result and will then provide a characterisation of the hyperbolic onerelator groups with exceptional intersection. Finally, I will then discuss how this characterisation can be used to establish properties for all onerelator groups.

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.

Nov. 17 2022, Merlin IncertiMedici, 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 quasiisometries. 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 quasiisometric spaces that have nonhomeomorphic 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 quasiisometryinvariant does not coincide with the topology of the visual boundary and the visual topology is not quasiisometryinvariant 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.

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 WeilPetersson geometry of Teichm\"uller space together with results from algebraic geometry.

Dec. 1 2022. Julien Paupert, Arizona State University
Time: 10：0011：00 (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.

Dec. 8 2022, Anythony genevois, University of Montpellier （CANCELLED）
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 longstanding conjectures on group rings attributed to Kaplansky. For example, the zero divisor conjecture states that the group ring of a torsionfree 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 MahowaldHopkins. 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：86186617196 password: 123555 Title: Proper actions of 3manifold groups on finite product of quasitrees Abstract: Let M be a compact, connected, orientable 3manifold. In this talk, I will study when the fundamental group of M acts properly on a finite product of quasitrees. 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 quasiisometric embedding of $\pi_1(M)$. This is called property (QT) by BestvinaBrombergFujiwara, 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 CrokeKleiner admissible groups and of relatively hyperbolic groups under natural assumptions. Accordingly, this yields that graph 3manifold and mixed 3manifold groups have property (QT). This represents joint work with N.T. Nguyen and S.Z. Han.

Mar. 10 2022, Martin Palmer, Mathematical Institute of the Romanian Academy
Time: 15:0017:00 Zoom Id: 646 617 8889 password: 123456wu Title: Mapping class group representations via Heisenberg, Schrödinger and Stonevon 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 BorelMoore homology of configuration spaces, Schrödinger representations of discrete Heisenberg groups and the Stonevon Neumann theorem.

Mar. 17 2022, Xianchang Meng, Shandong University
Time: 15:00  17:00 Tencent room：86186617196 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. GuthKatz (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 GuthKatz. In particular, for any finite index subgroup of the modular group, we extract out the dependence of the implied constant on the index.

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.

Mar. 31 2022，Bruno Martelli, University of Pisa
Time: 15:00  17:00 Zoom Meeting ID: 956 0945 4208 Passcode: hyperbolic Title: Fibrations on higherdimensional hyperbolic manifolds Abstract: One of the most intriguing aspects in lowdimensional topology is the existence, discovered by Jorgensen in the late 70s, of hyperbolic 3manifolds 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 wellknown open question in geometric group theory (joint works with Battista, Italiano, and Migliorini)

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 nonarithmetic lattices.

Apr. 14 2022, Robert Tang, Xi’an JiaotongLiverpool University
Time: 15:00  17:00
Zoom Meeting ID: 956 0945 4208 Passcode: hyperbolic
Title: Largescale 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 noncrossing 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 quasiisometry type: all saddle connection graphs form a single quasiisometry 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.

Apr. 21 2022，Weiyan Chen, Tsinghua University
Time: 15:00  17:00
Tencent room：86186617196 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.

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.

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 pseudoAnosovs 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) QingRafi's sublinearly Mosre boundaries and (2) limit laws for random 3manifolds.

May 19 2022 Hao Liang, Sun Yatsen University
Time: 15:0017:00 Tencent room：86186617196 password: 123555 Title: Homomorphisms to 3manifold groups Abstract: Following Sela's theory of limit groups (of free group), we define and study limit groups of compact 3manifold groups. We show that the family of compact 3manifold 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 3manifold groups. This is joint work with Daniel Groves and Michael Hull.

May 26 2022, NO Talk due to University Anniversary

Jun. 02 2022, Yi Jiang, Tsinghua University
Time: 15:0017:00 Tencent room：86186617196 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.

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.
Fall 2021 Schedule

Dec. 30 2021, Yang Su Chinese Academy of Sciences
Time: 15:0017:00 Place: Tencent Meeting ID: 573308837 Password: 123455 Title: Geometric structure of self covering manifolds Abstract: A topological space is selfcovering if the space is a nontrivial cover of itself. I will talk about a joint work with Lizhen Qin and Botong Wang on the geometric structure of selfcovering manifolds. For example, we show that in dimension >5, a selfcovering manifold with infinite cyclic fundamental group is a fiber bundle over the circle. We also construct examples of selfcovering manifolds which are not fiber bundle over the circle, where the fundamental group contains torsion.

Dec. 16 2021, Shengkui Ye NYU Shanghai
Time: 15:0017:00 Place: Tencent Meeting ID: 533917811 Password: 123455 Title: The group of quasiisometries of the line cannot act effectively on the line Abstract: Let G be the group of orientationpreserving quasiisometries of the real line. We show that G is leftorderable, but not simple. Moreover, the group G cannot act effectively on the real line R.