Organizing Committee
Abstract

This workshop focuses on the interplay between dynamics, rigidity, and arithmetic in hyperbolic geometry and related areas. There have been many striking developments in recent years, particularly related to totally geodesic submanifolds in both finite and infinite volume hyperbolic and even complex hyperbolic manifolds.

One aim of this workshop is to expose young researchers to these breakthroughs providing them with the necessary background from dynamics, and geometry to allow them to appreciate some of these recent advances, and prepare them to make new original contributions. For this purpose, we will have minicourses on "Arithmeticity, Superrigidity and totally geodesic manifolds", and "Rigidity and geodesic planes in infinite volume hyperbolic manifolds". These courses will be preceded by an introductory minicourse on Hyperbolic geometry. We will also have a minicourse on "Understanding of geodesic planes in hyperbolic 3-manifolds via computations and visualization". In addition, we wish to bring together experts in these fields to discuss the recent developments and open problems that lie at the crossroads of these different fields and to encourage more interaction among people working in these diverse areas.

This workshop is partially funded by NSF CAREER award DMS-1651563

Image for "Dynamics, Rigidity and Arithmetic in Hyperbolic Geometry"
Image credit: C. McMullen

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee
  • Fernando Al Assal
    Yale University
  • Alina Al Beaini
    Brown University
  • Konstantin Andritsch
    ETH Zurich
  • Anna Antal
    Yale University
  • Juan Arosemena Serrato
    Rice University
  • Juhun Baik
    KAIST
  • Gregorio Baldi
    Institut des Hautes Études Scientifiques
  • Erin Bevilacqua
    University of Texas at Austin
  • Ian Biringer
    Boston College
  • Christine Breiner
    Brown University
  • Nic Brody
    UC Santa Cruz
  • Tamunonye Cheetham-West
    Rice University
  • Hyein Choi
    Rice university
  • Inhyeok Choi
    Korea Institute for Advanced Study
  • Mikey Chow
    Yale University
  • Ethan Cohen
    Yale University
  • David Constantine
    Wesleyan University
  • Emilio Corso
    University of British Columbia
  • Gregory Cosac
    Universidade de São Paulo (USP)
  • Ozkan Demir
    University of Illinois Chicago
  • Subhadip Dey
    Yale University
  • Ethan Dlugie
    University of California, Berkeley
  • Sami Douba
    Institut des Hautes Études Scientifiques
  • Elias Dubno
    University of Zurich
  • Sara Edelman-Munoz
    Rice University
  • Leonardo Ferrari
    Université de Neuchâtel
  • David Fisher
    Rice University
  • Mikolaj Fraczyk
    University of Chicago
  • Sam Freedman
    Brown University
  • Alex Furman
    University of Illinois at Chicago - UIC
  • Milana Golich
    Purdue University
  • Yanlong Hao
    University of Illinois at Chicago
  • Paige Hillen
    University of California, Santa Barbara
  • Junzhi Huang
    Yale University
  • Sebastian Hurtado
    Yale University
  • Seung uk Jang
    The University of Chicago
  • Yushan Jiang
    City University of New York, the Graduate Center
  • Junehyuk Jung
    Brown University
  • Dubi Kelmer
    Boston College
  • Wooyeon Kim
    ETH Zurich
  • Dongryul Kim
    Yale University
  • Dmitry Kleinbock
    Brandeis University
  • Or Landsberg
    Yale University
  • Minju Lee
    University of chicago
  • Ricky Lee
    University of California, Santa Barbara
  • Homin Lee
    Northwestern University
  • Joaquin Lema
    Boston College
  • Zuo Lin
    University of California San Diego
  • Beibei Liu
    University of California, Davis
  • Trent Lucas
    Brown University
  • Simon Machado
    Institute for Advanced Study
  • Alexandre Maldague
    Rice University
  • Ari Markowitz
    The University of Auckland
  • Curtis McMullen
    Harvard University
  • Jonah Mendel
    Brown University
  • Katherine Merkl
    UC Santa Barbara
  • Nicholas Miller
    University of Oklahoma
  • Shahriar Mirzadeh
    UNIVERSITY OF CINCINNATI
  • Sayantika Mondal
    Graduate school and university center, CUNY
  • Casandra Monroe
    University of Texas - Austin
  • Hamid Naderiyan
    University of North Texas
  • Hee Oh
    Yale university
  • Tariq Osman
    Brandeis University
  • Michael Pandazis
    CUNY Graduate Center
  • Sungjin Park
    Yale University
  • Insung Park
    ICERM
  • Julien Paupert
    Arizona State University
  • Mark Pengitore
    University of Virginia
  • Carsten Peterson
    University of Michigan
  • Lam Pham
    Brandeis University
  • Plinio Pino Murillo
    Fluminense Federal University
  • Amelia Pompilio
    University of Illinois at Chicago
  • Alan Reid
    Rice University
  • Megan Roda
    University of chicago
  • Rafael Saavedra
    Harvard University
  • Anthony Sanchez
    University of California San Diego
  • Geoffrey Sangston
    University of Maryland
  • Pratyush Sarkar
    UC San Diego
  • Connor Sell
    Rice University
  • Juno Seong
    University of California-San Diego
  • Ekaterina Shchetka
    University of Michigan
  • Aleksander Skenderi
    University of Wisconsin-Madison
  • Raz Slutsky
    Weizmann Institute of Science
  • Miri Son
    Rice University
  • Matthew Stover
    Temple University
  • Nattalie Tamam
    University of Michigan
  • Jacob Tolman
    Wesleyan University
  • Tina Torkaman
    Harvard University
  • Bena Tshishiku
    Brown University
  • Hunter Vallejos
    University of Texas at Austin
  • Franco Vargas Pallete
    Yale University
  • Itamar Vigdorovich
    Weizmann Institute of Science
  • Thi Hanh Vo
    Arizona State University
  • Mujie Wang
    Boston College
  • Amy Wang
    Yale University
  • Jane Wang
    University of Maine
  • Zhiren Wang
    Penn State University
  • Vicky Wen
    University of Wisconsin, Madison
  • Anna Wienhard
    Heidelberg University
  • Amanda Wilkens
    University of Texas at Austin
  • Becca Winarski
    MSRI/College of the Holy Cross
  • Karl Winsor
    Fields Institute
  • Christian Wolf
    The City College of New York
  • Leyla Yardimci
    Wesleyan University
  • Matthew Zevenbergen
    Boston College
  • Yongquan Zhang
    Stony Brook University
  • Michael Zshornack
    UC Santa Barbara
  • Jonathan Zung
    Princeton University

Workshop Schedule

Monday, May 15, 2023
  • 9:30 - 9:50 am EDT
    Check In / AM Coffee Break
    Check In - 11th Floor Collaborative Space
  • 9:50 - 10:00 am EDT
    Welcome
    11th Floor Lecture Hall
  • 10:00 - 10:45 am EDT
    Hyperbolic geometry - An Introduction
    11th Floor Lecture Hall
    • Speaker
    • Ian Biringer, Boston College
    • Session Chair
    • David Fisher, Rice University
    Abstract
    The aim of this minicourse is to introduce fundamental concepts in hyperbolic geometry, such as limit sets, geometric finiteness, and critical exponent, and Mostow rigidity. We will discuss examples of arithmetic hyperbolic manifolds, and illustrate flexible geometric constructions like Dehn filling, quasi-conformal deformation, and the gluing constructions of non-arithmetic lattices by Gromov and Piatetski-Shapiro.
  • 11:00 - 11:45 am EDT
    Totally geodesic subvarieties via Hodge theory
    11th Floor Lecture Hall
    • Speaker
    • Gregorio Baldi, Institut des Hautes Études Scientifiques
    • Session Chair
    • David Fisher, Rice University
    Abstract
    In this Mini Course, following a joint work with E.Ullmo, I will explain how (integral) Hodge theory naturally comes up in the study of totally geodesic subvarieties of a complex hyperbolic ball quotient S. From such a point of view, the finiteness of the maximal totally geodesics of S becomes a consequence of a very general conjecture about 'unlikely intersections'. The two lectures will give some motivations and an introduction to such techniques (no prior knowledge in Hodge theory will be assumed).
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:15 pm EDT
    Geometric, dynamical and arithmetic properties of Anosov representations
    11th Floor Lecture Hall
    • Speaker
    • Anna Wienhard, Heidelberg University
    • Session Chair
    • Nattalie Tamam, University of Michigan
    Abstract
    Anosov representations provides a rich class of discrete embeddings of hyperbolic groups into semisimple Lie groups, which generalizes the classes of convex cocompact subgroups to the setting of higher rank Lie groups. In this talk I will discuss some results (old and new) regarding geometric, dynamical and arithmetic properties.
  • 2:30 - 3:15 pm EDT
    Hyperbolic geometry - An Introduction
    11th Floor Lecture Hall
    • Speaker
    • Ian Biringer, Boston College
    • Session Chair
    • Nattalie Tamam, University of Michigan
    Abstract
    The aim of this minicourse is to introduce fundamental concepts in hyperbolic geometry, such as limit sets, geometric finiteness, and critical exponent, and Mostow rigidity. We will discuss examples of arithmetic hyperbolic manifolds, and illustrate flexible geometric constructions like Dehn filling, quasi-conformal deformation, and the gluing constructions of non-arithmetic lattices by Gromov and Piatetski-Shapiro.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    Rigidity and geodesic planes in infinite volume hyperbolic manifolds
    11th Floor Lecture Hall
    • Speaker
    • Hee Oh, Yale university
    • Session Chair
    • Nattalie Tamam, University of Michigan
    Abstract
    The aim of this mini course is to discuss some basic theory of homogeneous dynamics on the quotient of SO(n,1) by a discrete subgroup and to explain the topological rigidity of geodesic planes in hyperbolic n-manifolds of Fuchsian ends which was proved by McMullen-Mohammadi-O. (for n=3) and by Minju Lee-O. (for n>3).
  • 5:00 - 6:30 pm EDT
    Reception
    11th Floor Collaborative Space
Tuesday, May 16, 2023
  • 9:30 - 10:00 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:00 - 10:45 am EDT
    Arithmeticity, superrigidity, and totally geodesic manifolds
    11th Floor Lecture Hall
    • Speaker
    • Nicholas Miller, University of Oklahoma
    • Session Chair
    • Alan Reid, Rice University
    Abstract
    In the 1970s seminal work of Margulis showed that higher rank lattices have superrigid representations, which in particular implies that all such lattices are arithmetic. Since then Gromov–Piatetski-Shapiro and Deligne–Mostow have shown that a similar superrigidity theorem cannot hold for all lattices in the isometry group of real or complex hyperbolic space, i.e., in the rank 1 setting. However in recent work joint with Bader, Fisher, and Stover we show that one can prove certain superrigidity/arithmeticity theorems provided the associated manifold satisfies the geometric condition that it contains infinitely many (maximal) totally geodesic submanifolds. Specifically, we show that this latter criteria forces a hyperbolic manifold to be arithmetic.
    The goal of this mini-course will be first to recount the work of Margulis on superrigidity of higher rank lattices and then to go on to discuss the proof of the aforementioned theorem. This will include a discussion of the connections between homogeneous dynamics and geodesic submanifolds, their interaction with superrigidity, and an introduction to techniques introduced by Bader and Furman for studying algebraic representations of ergodic actions. If time permits, we will also discuss the analogous theorem for complex hyperbolic manifolds and the key differences from the real hyperbolic setting.
  • 11:00 - 11:45 am EDT
    Rigidity and geodesic planes in infinite volume hyperbolic manifolds
    11th Floor Lecture Hall
    • Speaker
    • Hee Oh, Yale university
    • Session Chair
    • Alan Reid, Rice University
    Abstract
    The aim of this mini course is to discuss some basic theory of homogeneous dynamics on the quotient of SO(n,1) by a discrete subgroup and to explain the topological rigidity of geodesic planes in hyperbolic n-manifolds of Fuchsian ends which was proved by McMullen-Mohammadi-O. (for n=3) and by Minju Lee-O. (for n>3).
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:15 pm EDT
    Totally geodesic subvarieties via Hodge theory
    11th Floor Lecture Hall
    • Speaker
    • Gregorio Baldi, Institut des Hautes Études Scientifiques
    • Session Chair
    • Dubi Kelmer, Boston College
    Abstract
    In this Mini Course, following a joint work with E.Ullmo, I will explain how (integral) Hodge theory naturally comes up in the study of totally geodesic subvarieties of a complex hyperbolic ball quotient S. From such a point of view, the finiteness of the maximal totally geodesics of S becomes a consequence of a very general conjecture about 'unlikely intersections'. The two lectures will give some motivations and an introduction to such techniques (no prior knowledge in Hodge theory will be assumed).
  • 2:30 - 3:15 pm EDT
    Exponential mixing of frame flows for geometrically finite hyperbolic manifolds
    11th Floor Lecture Hall
    • Speaker
    • Pratyush Sarkar, UC San Diego
    • Session Chair
    • Dubi Kelmer, Boston College
    Abstract
    The frame bundle of an n-dimensional hyperbolic manifold X is the homogeneous space Γ\SO(n, 1)° for some discrete subgroup Γ and the frame flow is given by the right translation action by a one-parameter diagonalizable subgroup. We assume that Γ is Zariski dense and X is geometrically finite, i.e., it need not be compact but has at most finitely many ends consisting of cusps and funnels. We endow the frame bundle with the unique probability measure of maximal entropy called the Bowen-Margulis-Sullivan measure. In a joint work with Jialun Li and Wenyu Pan, we prove that the frame flow is exponentially mixing. The proof uses a countably infinite coding and the latest version of Dolgopyat's method. To overcome the difficulty in applying Dolgopyat's method due to the cusps of non-maximal rank, we prove a large deviation property for symbolic recurrence to certain large subsets of the limit set of Γ.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    Length functions in Lie groups and lattices.
    11th Floor Lecture Hall
    • Speaker
    • Sebastian Hurtado, Yale University
    • Session Chair
    • Dubi Kelmer, Boston College
    Abstract
    We will discuss the notion of length functions on groups, focusing on lattices in Lie groups of higher rank, and discuss how dynamics and ergodic theory can help to understand some questions about them.
Wednesday, May 17, 2023
  • 9:30 - 10:00 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:00 - 10:45 am EDT
    Rigidity and geodesic planes in infinite volume hyperbolic manifolds
    11th Floor Lecture Hall
    • Speaker
    • Hee Oh, Yale university
    • Session Chair
    • David Fisher, Rice University
    Abstract
    The aim of this mini course is to discuss some basic theory of homogeneous dynamics on the quotient of SO(n,1) by a discrete subgroup and to explain the topological rigidity of geodesic planes in hyperbolic n-manifolds of Fuchsian ends which was proved by McMullen-Mohammadi-O. (for n=3) and by Minju Lee-O. (for n>3).
  • 11:00 - 11:45 am EDT
    Arithmeticity, superrigidity, and totally geodesic manifolds
    11th Floor Lecture Hall
    • Speaker
    • Nicholas Miller, University of Oklahoma
    • Session Chair
    • David Fisher, Rice University
    Abstract
    "In the 1970s seminal work of Margulis showed that higher rank lattices have superrigid representations, which in particular implies that all such lattices are arithmetic. Since then Gromov–Piatetski-Shapiro and Deligne–Mostow have shown that a similar superrigidity theorem cannot hold for all lattices in the isometry group of real or complex hyperbolic space, i.e., in the rank 1 setting. However in recent work joint with Bader, Fisher, and Stover we show that one can prove certain superrigidity/arithmeticity theorems provided the associated manifold satisfies the geometric condition that it contains infinitely many (maximal) totally geodesic submanifolds. Specifically, we show that this latter criteria forces a hyperbolic manifold to be arithmetic.
    The goal of this mini-course will be first to recount the work of Margulis on superrigidity of higher rank lattices and then to go on to discuss the proof of the aforementioned theorem. This will include a discussion of the connections between homogeneous dynamics and geodesic submanifolds, their interaction with superrigidity, and an introduction to techniques introduced by Bader and Furman for studying algebraic representations of ergodic actions. If time permits, we will also discuss the analogous theorem for complex hyperbolic manifolds and the key differences from the real hyperbolic setting."
  • 11:55 am - 12:00 pm EDT
    Group Photo (Immediately After Talk)
    11th Floor Lecture Hall
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:15 pm EDT
    Discrete subgroups with finite Bowen-Margulis-Sullivan measure in higher rank
    11th Floor Lecture Hall
    • Speaker
    • Minju Lee, University of chicago
    • Session Chair
    • Julien Paupert, Arizona State University
    Abstract
    Let G be a connected semisimple real algebraic group and D be its Zariski dense discrete subgroup. We prove that if D\G admits any finite Bowen-Margulis-Sullivan measure, then D is virtually a product of higher rank lattices and discrete subgroups of rank one factors of G. This may be viewed as a measure-theoretic analogue of classification of convex cocompact actions by Kleiner-Leeb and Quint, which was conjectured by Corlette in 1994. This is joint work with Mikolaj Fraczyk. We will then discuss its application on the bottom of the L^2 spectrum, in joint work with Samuel Edwards, Mikolaj Fraczyk and Hee Oh.
  • 2:30 - 3:15 pm EDT
    Billiards and the arithmetic of non-arithmetic groups
    11th Floor Lecture Hall
    • Speaker
    • Curtis McMullen, Harvard University
    • Session Chair
    • Julien Paupert, Arizona State University
    Abstract
    We will survey new results and open problems on triangle groups in SL_2(R), and their connections to Abelian varieties, Teichmueller curves and billiards in polygons.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    Understanding geodesic planes in hyperbolic 3-manifolds via computations and visualization
    11th Floor Lecture Hall
    • Speaker
    • Yongquan Zhang, Stony Brook University
    • Session Chair
    • Julien Paupert, Arizona State University
    Abstract
    As a companion and complement to the mini-course on rigidity of geodesic planes in infinite volume hyperbolic manifolds, I will discuss several examples of rigidity and nonrigidity of geodesic planes in hyperbolic 3-manifolds. These results are orthogonal to the ones obtained by McMullen, Mohammadi and Oh, and illustrate what can happen if some of their assumptions are relaxed. Some of these examples were produced by explicit computations and can be visualized very nicely, and I will discuss these aspects as well.
Thursday, May 18, 2023
  • 9:30 - 10:00 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:00 - 10:45 am EDT
    Arithmeticity, superrigidity, and totally geodesic manifolds
    11th Floor Lecture Hall
    • Speaker
    • Nicholas Miller, University of Oklahoma
    • Session Chair
    • Jane Wang, University of Maine
    Abstract
    In the 1970s seminal work of Margulis showed that higher rank lattices have superrigid representations, which in particular implies that all such lattices are arithmetic. Since then Gromov–Piatetski-Shapiro and Deligne–Mostow have shown that a similar superrigidity theorem cannot hold for all lattices in the isometry group of real or complex hyperbolic space, i.e., in the rank 1 setting. However in recent work joint with Bader, Fisher, and Stover we show that one can prove certain superrigidity/arithmeticity theorems provided the associated manifold satisfies the geometric condition that it contains infinitely many (maximal) totally geodesic submanifolds. Specifically, we show that this latter criteria forces a hyperbolic manifold to be arithmetic.
    The goal of this mini-course will be first to recount the work of Margulis on superrigidity of higher rank lattices and then to go on to discuss the proof of the aforementioned theorem. This will include a discussion of the connections between homogeneous dynamics and geodesic submanifolds, their interaction with superrigidity, and an introduction to techniques introduced by Bader and Furman for studying algebraic representations of ergodic actions. If time permits, we will also discuss the analogous theorem for complex hyperbolic manifolds and the key differences from the real hyperbolic setting.
  • 11:00 - 11:45 am EDT
    Uniform spectral gap and orthogeodesic counting for Kleinian groups
    11th Floor Lecture Hall
    • Speaker
    • Beibei Liu, University of California, Davis
    • Session Chair
    • Jane Wang, University of Maine
    Abstract
    Strongly convergent sequences of hyperbolic manifolds arise naturally in the study of Kleinian group representations, for example, the Dehn surgeries on hyperbolic knots. It turns out that such sequences usually have uniform control on the geometry and dynamics, such as the uniform convergence of small eigenvalues of the Laplacian, and the Patterson-Sullivan measures. We will talk about the uniform convergence results in this talk and apply them to count uniformly along the sequence the number of simple closed geodesics and orthogeodesics. This is joint work with Franco Vargas Pallete.
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:15 pm EDT
    Lyapunov spectrum: simplicity and continuity beyond random products
    11th Floor Lecture Hall
    • Speaker
    • Alex Furman, University of Illinois at Chicago - UIC
    • Session Chair
    • Plinio Pino Murillo, Fluminense Federal University
  • 2:30 - 3:15 pm EDT
    Intersection number and intersection points of closed geodesics on hyperbolic surfaces
    11th Floor Lecture Hall
    • Speaker
    • Tina Torkaman, Harvard University
    • Session Chair
    • Plinio Pino Murillo, Fluminense Federal University
    Abstract
    In this talk, I will discuss the (geometric) intersection number between closed geodesics on finite volume hyperbolic surfaces. Specifically, I talk about the optimum upper bound on the intersection number in terms of the product of hyperbolic lengths. I also talk about the equidistribution of the intersection points between closed geodesics.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    Understanding geodesic planes in hyperbolic 3-manifolds via computations and visualization
    11th Floor Lecture Hall
    • Speaker
    • Yongquan Zhang, Stony Brook University
    • Session Chair
    • Plinio Pino Murillo, Fluminense Federal University
    Abstract
    As a companion and complement to the mini-course on rigidity of geodesic planes in infinite volume hyperbolic manifolds, I will discuss several examples of rigidity and nonrigidity of geodesic planes in hyperbolic 3-manifolds. These results are orthogonal to the ones obtained by McMullen, Mohammadi and Oh, and illustrate what can happen if some of their assumptions are relaxed. Some of these examples were produced by explicit computations and can be visualized very nicely, and I will discuss these aspects as well.
Friday, May 19, 2023
  • 9:30 - 10:00 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:00 - 10:45 am EDT
    Fourier decay of self-conformal measures for non-linear IFS’s
    11th Floor Lecture Hall
    • Speaker
    • Zhiren Wang, Penn State University
    • Session Chair
    • Bena Tshishiku, Brown University
    Abstract
    We show that for a C^2 IFS on R, either up to smooth conjugacy the IFS has vanishing second derivative on its attractor, or the self-conformal measure has polynomial decay of Fourier coefficients. A key argument is a cocycle version of Dolgopyat's method and resulting spectral gap-type estimates and renewal theorem. This is a joint work with Amir Algom and Federico Rodriguez Hertz.
  • 11:00 - 11:45 am EDT
    Central extensions of real and complex hyperbolic lattices
    11th Floor Lecture Hall
    • Speaker
    • Matthew Stover, Temple University
    • Session Chair
    • Bena Tshishiku, Brown University
    Abstract
    I will describe joint work with Domingo Toledo on residual finiteness for cyclic central extensions of fundamental groups of aspherical manifolds, its application to central extensions of (arithmetic) real and complex hyperbolic lattices, and connections to several open problems.
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:15 pm EDT
    Poisson-Voronoi tessellations in higher rank and the fixed price conjecture
    11th Floor Lecture Hall
    • Speaker
    • Mikolaj Fraczyk, University of Chicago
    • Session Chair
    • Dubi Kelmer, Boston College
    Abstract
    The cost of a probability measure preserving action of a countable group G on X is an invariant that generalizes the rank (minimal number of generators) of G and measures the “minimal average number of maps” needed to connect every pair of points of X in the same G orbit. The fixed price conjecture predicts that any two essentially free p.m.p. actions of the group G have the same cost. In my talk I will report on a joint work with Sam Mellick and Amanda Wilkens in which we prove fixed price one for higher ranks lattices in semisimple real or p-adic groups. As a corollary we obtain that the number of generators of index n subgroup of such a group grows like o(n) which implies new state of the art results on the growth of mod-p homology groups. The proof is based on certain miraculous properties of the Poisson-Voronoi tessellation of higher rank symmetric spaces (not present in rank 1) that might be of independent interest.
  • 2:30 - 3:15 pm EDT
    The arithmetic of totally geodesic surfaces on Bianchi orbifolds
    11th Floor Lecture Hall
    • Speaker
    • Junehyuk Jung, Brown University
    • Session Chair
    • Dubi Kelmer, Boston College
    Abstract
    Bianchi subgroups are cofinite non-cocompact lattices in PSL_2(C), defined by \Gamma_d = PSL_2(O_d), where O_d is the ring of integers of the imaginary quadratic field of discriminant -d. The Bianchi orbifold \Omega_d = \Gamma_d\H^3 is known to contain infinitely many immersed totally geodesic surfaces, which can be identified with integral binary hermitian forms over O_d. In this talk, I will show that some of these immersed totally geodesic surfaces are in fact orientable embedded closed totally geodesic surfaces using number theoretic ideas. I then present some numerical data concerning these surfaces. This talk is based on a joint work with Alan Reid and on an ongoing project with Sam Kim and James Rickards.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space

All event times are listed in ICERM local time in Providence, RI (Eastern Standard Time / UTC-5).

All event times are listed in .

Request Reimbursement

This section is for general purposes only and does not indicate that all attendees receive funding. Please refer to your personalized invitation to review your offer.

ORCID iD
As this program is funded by the National Science Foundation (NSF), ICERM is required to collect your ORCID iD if you are receiving funding to attend this program. Be sure to add your ORCID iD to your Cube profile as soon as possible to avoid delaying your reimbursement.
Acceptable Costs
  • 1 roundtrip between your home institute and ICERM
  • Flights on U.S. or E.U. airlines – economy class to either Providence airport (PVD) or Boston airport (BOS)
  • Ground Transportation to and from airports and ICERM.
Unacceptable Costs
  • Flights on non-U.S. or non-E.U. airlines
  • Flights on U.K. airlines
  • Seats in economy plus, business class, or first class
  • Change ticket fees of any kind
  • Multi-use bus passes
  • Meals or incidentals
Advance Approval Required
  • Personal car travel to ICERM from outside New England
  • Multiple-destination plane ticket; does not include layovers to reach ICERM
  • Arriving or departing from ICERM more than a day before or day after the program
  • Multiple trips to ICERM
  • Rental car to/from ICERM
  • Flights on a Swiss, Japanese, or Australian airlines
  • Arriving or departing from airport other than PVD/BOS or home institution's local airport
  • 2 one-way plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
Travel Maximum Contributions
  • New England: $250
  • Other contiguous US: $750
  • Asia & Oceania: $2,000
  • All other locations: $1,500
  • Note these rates were updated in Spring 2022 and superseded any prior invitation rates. Any invitations without travel support will still not receive travel support.
Reimbursement Requests

Request Reimbursement with Cube

Refer to the back of your ID badge for more information. Checklists are available at the front desk and in the Reimbursement section of Cube.

Reimbursement Tips
  • Scanned original receipts are required for all expenses
  • Airfare receipt must show full itinerary and payment
  • ICERM does not offer per diem or meal reimbursement
  • Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via pdf of Google Maps result
  • Keep all documentation until you receive your reimbursement!
Reimbursement Timing

6 - 8 weeks after all documentation is sent to ICERM. All reimbursement requests are reviewed by numerous central offices at Brown who may request additional documentation.

Reimbursement Deadline

Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. Submissions after thirty days will incur applicable taxes. No submissions are accepted more than six months after the program end.