Arithmetic groups provide a fruitful link between various areas, such as geometry, topology, representation theory and number theory. Methods from geometry and topology hinge on the fact that arithmetic groups are lattices in Lie groups, whereas the theory of automorphic forms establishes a connection to representation theory and number theory. This interplay is especially intriguing in the setting of hyperbolic 3-manifolds. Indeed many conjectures in 3-manifold theory tend to be much more accessible for hyperbolic 3-manifolds whose fundamental groups are arithmetic, and conversely such manifolds provide the simplest set-up in which some of the most exciting new phenomena in the Langlands program can be studied. This conference will bring together researchers with various backgrounds around links between number theory and 3-manifolds. Central topics of the conference are the cohomology of arithmetic groups, the relation between torsion and L²-torsion, profinite invariants of 3-manifolds, and number theoretic ramifications.

Limited funding to cover travel cost and accommodation is available for early carreer participants.

The conference is planned as a hybrid event. However, due to the still unpredictable situation regarding Covid, we reserve the right to change it to be held completely virtually. We will inform you when a final decision has been made.

Some datasets are too small for standard statistical/data analysis to accurately characterize the data. Others are extremely large and data size reduction methods may be needed. One solution is to use topological data analysis to simplify and/or visualize data. This workshop will include both tutorials and research talks on topological techniques for visualizing data.

In person workshop with hybrid component for those who wish to join virtually.

Signal processing and machine learning constitutes an important area for the application of mathematical concepts and techniques, in an era where learning algorithms must be transparent, robust, explainable and understandable, and ethical. It is a thriving area, as demonstrated by the success of the UK hosting the recent International Conference on Acoustics, Speech, and Signal Processing (ICASSP) in Brighton in 2019.

Signal and information processing is at the heart of our technological world, fuelled by developments in, for example, mobile communications, networks and graphs, multimedia systems, medical image analysis, genomics and bioengineering, neural signal processing, big data processing and internet of things. The aim of the conference is to bring together mathematicians, statisticians and engineers with a view to exploring recent developments in mathematics for signal processing and machine learning and identifying fruitful avenues for further research. It is hoped that the meeting will help to attract more mathematicians into this important and challenging field. The conference will follow the same successful format as our previous conferences, comprising tutorials, keynote addresses and non-overlapping technical sessions consisting of oral and poster presentations. A social programme will be organised and will include a reception to welcome delegates.

This will be a one-week conference highlighting recent advances in algebraic topology and related fields. The guiding theme will be the use of algebraic and categorical structure to better understand geometric contexts. We hope by bringing together mathematicians from diverse subfields in algebraic topology, who use similar techniques to achieve different goals, we can foster new ideas and perspectives. The event will feature invited talks, mini-courses, contributed talks, and time for informal interactions in a relaxed and tropical atmosphere.

This year's workshop will be completely online. Registrants will be sent connection details prior to the Workshop.

Deadlines

Submission of contributed talks, including title and abstract: May 6

Principal Speaker

The featured speaker is Jessica Purcell of Monash University, who will give a series of three one-hour lectures on using hyperbolic geometry as a tool to study 3-manifolds and knot theory. An abstract can be found below.

Contributed Talks

The workshop will also feature contributed talks of 20 minutes. Contributed talks need not be directly related to the topic of the principal lectures. If you wish to apply to give a contributed talk please submit a title and abstract on the registration form or send directly to Greg Friedman (send email). Talks will be selected in a way that provides a balanced collection of topics and respects the historical traditions of the workshop. Earlier responses may be given some preference. Applicants will be notified whether their talk has been accepted by May 23.

European Women in Mathematics/European Mathematical Society Mittag-Leffler Summer School Chromatic Homotopy Theory and Friends is scheduled to take place June 7 to 10, 2022 at the Mittag-Leffler Institute in Djursholm, Sweden.

The goal of this summer school is to increase the number of women mathematicians working in chromatic homotopy theory and adjacent areas. The summer school will be centered around a background lecture series by Constanze Roitzheim from the University of Kent on chromatic homotopy theory, with satellite talks in areas of active research related to the central topic.

As a European Women in Mathematics Summer School, we aim to have at least 50% women among the participants.

Please visit

https://docs.google.com/forms/d/e/1FAIpQLScQz5DZ2iFwHEWxs8CVMBa_xR77GxJpm3L3Z6wxu7J2Ukm0Xg/viewform

for more information and the application form.

The application deadline is December 15, 2021.

A conference bringing together established and junior researchers from the Langlands Program and Homotopy Theory.

This week-long workshop is designed to support women, particularly women of color, who have completed 1–3 years of graduate school and are considering research in algebra, combinatorics, geometry, topology, or number theory.

The transition to independent learning and research is a crucial and often jarring point in every graduate student's career. This transition is even more difficult for students from marginalized groups, who often have smaller support systems and may face an actively unsupportive environment at their institution. The goal of this workshop is to support, mentor, and guide students at this crucial stage in their career.

This workshop is open to anyone who identifies as a woman, nonbinary, and/or gender fluid and who has also completed 1-3 years of graduate education in mathematics. The program is tailored to support women of color, and our strategies reflect this priority.

The application for this year's Talbot workshop is now live.

2022 TALBOT WORKSHOP: SCISSORS CONGRUENCE AND ALGEBRAIC K-THEORY

Mentored by Inna Zakharevich and Jonathan Campbell

June 12 - 18, 2022

New York (to be confirmed)

What: The Talbot Workshop is a one week learning workshop for roughly 35 graduate students and a few postdocs. Most of the talks will be given by participants, and will be expository in nature. Due to the pandemic, the workshop will most likely utilize a virtual format, with half of the participants invited to join us in person.

Topic description: Hilbert’s third problem asked to produce two polyhedra of equal volume which are not scissors congruent, i.e. which cannot be decomposed into the same (finite) set of isomorphic sub-polygons. In 1901 Dehn showed that a second invariant, now called the Dehn invariant, was preserved under such decompositions, and that this invariant is zero for the cube but nonzero for the regular tetrahedron, thus providing the example Hilbert requested. In 1965 Sydler showed that no other invariants are necessary: if two polyhedra have the same volume and the same Dehn invariant, then they are scissors congruent. Analogs of this problem, in other geometries and in other dimensions, are still open.

By defining the sum of polytopes to be their disjoint union we can define a group structure on scissors congruence classes. Hilbert’s third problem can then be reinterpreted as the question of analyzing these scissors congruence groups. The first part of this course will focus on learning about computations and connections between scissors congruence and algebraic K-theory. The second part will discuss how to construct scissors congruence invariants using K-theory and various implications of these constructions. The third part dives deeper into the technical underpinnings of K-theory to illustrate how the algebraic approaches of classical K-theory can be expanded to include more combinatorial descriptions. More details can be found here. 

Applications close on Thursday, March 10 at 11:59PM Eastern Time. You can apply online here: http://math.mit.edu/events/talbot/index.php?pageID=application

Talbot is meant to encourage collaboration among young researchers, with an emphasis on graduate students. We also aim to gather participants with a diverse array of knowledge and interests, so applicants need not be an expert in the field -- in particular, students at all levels of graduate education are encouraged to apply. As we are committed to promoting diversity in mathematics, we also especially encourage women and minorities to apply.

We will cover all local expenses including lodging and food. We also offer partial funding for participants' travel costs.

If you have any questions, please do not hesitate to e-mail the organizers at talbotworkshop (at) gmail.com.

Organizers:

Adam Holeman

Liam Keenan

Lucy Yang

This conference will bring together experts in various aspects of four-dimensional topology. Themes include diffeomorphism groups of four-manifolds, construction and detection of exotic four-manifolds, and trisections of four-manifolds. In addition to standard plenary talks, there will be a lightning talk session open to submissions from all participants.

Registration space for this conference is limited. To apply to participate in this conference, please visit the conference website and fill out the application by April 10th, 2022.

Speakers include:
Samantha Allen (University of Georgia)
Gregory Arone^* (Stockholm University)
Irving Dai (Stanford University)
David Gabai (Princeton University)
Daniel Hartman (University of Georgia)
Kyle Hayden (Columbia University/Rutgers University-Newark)
Alexandra Kjuchukova (University of Notre Dame)
Robin Koytcheff (University of Louisiana at Lafayette)
Alexander Kupers (University of Toronto Scarborough)
Miriam Kuzbary (Georgia Institute of Technology)
Peter Lambert-Cole (University of Georgia)
Arunima Ray (Max Planck Institute for Mathematics)
Keiichi Sakai^* (Shinshu University)
Victor Turchin (Kansas State University)
Tadayuki Watanabe^* (Kyoto University)
Ian Zemke (Princeton University)

*virtual or potentially virtual

We anticipate limited funding to cover travel cost and accommodation, with priority given to early career participants.

The Summer School in Mathematics 2022 (Institut Fourier, Grenoble) will take place from June 13th to July 1st, 2022 and will be dedicated to Cohomology, Geometry and Explicit number theory (COGENT).

It will be a hybrid event with both in-person and online participation.

The goal of this school is to introduce young mathematicians to some recent developments in the field of cohomology of groups, with a focus on arithmetic groups, from geometrical, topological and computational aspects with applications to number theory. We also want to promote greater interaction among researchers and PhD students,​ and strengthen the COGENT network through new collaborations.

The first two weeks are dedicated to mini-courses and mini-workshops around some computational tools and new computational techniques, as well as short term team projects.

The third week will be devoted to a workshop on COGENT featuring both young researchers and leading specialists.

There will also be an "Illustrating mathematics'' event with an art exhibitions showcasing artistic visuals related to the geometries of arithmetic groups.

website: https://if-summer2022.sciencesconf.org/

We have partial funding for the accommodation of participants. Registration is mandatory for both on-site and online participation (including for the third week workshop). (see https://if-summer2022.sciencesconf.org/resource/page/id/1),

Registration for on-site participation will close on May 16, 2022. Registration for online participation is open and will close on June 6th, 2022.

We acknowledge the support of the Institut Fourier, of the CNRS, of the LabEx Persyval, of the GDR JC2A, of U. Grenoble Alpes and Grenoble-INP, of Grenoble-Alpes Métropole and of the MSTII Doctoral School for the organisation of this event.

Looking forward to seeing you in Grenoble.

The organizers: B. Eick (TU Braunschweig), Ph. Elbaz-Vincent (U.Grenoble Alpes), G. Ellis (NUI Galway), P. Gunnells (U. Massachusetts-Amherst), H. Sengun (U. Sheffield)

Contact organizer: [email protected] Contact staff: Géraldine Touvier ([email protected])

The ICM 2022 Satellite Conference "Hochschild (co)homology and derived categories" will be held at St Petersburg Department of Steklov Mathematical Institute from 20 to 24 June 2022.

The event will focus on presenting the latest developments in topics of homological and homotopical algebra related to Hochschild (co)homology.

Speakers will include:

Benjamin Briggs • University of Utah

Claude Cibils • Université de Montpellier

Karin Erdmann • Oxford University

Vincent Gélinas • Desjardins

Estanislao Herscovich • Université Grenoble Alpes

Srikanth Iyengar • University of Utah

Janina Letz • Universität Bielefeld

Markus Linckelmann • City University

Ayelet Lindenstrauss • Indiana University Bloomington

Maria Julia Redondo • Universidad Nacional del Sur

Travis Schedler • Imperial College London

Sibylle Schroll • Universität zu Köln

Greg Stevenson • University of Glasgow

Mariano Suárez-Álvarez • Universidad de Buenos Aires

Rachel Taillefer • Université Clermont Auvergne

Zhengfang Wang • Universität Stuttgart

Guodong Zhou • East China Normal University

Alexandra Zvonareva • Universität Stuttgart

For more details and to register see the webpage

https://indico.eimi.ru/event/315/.

Note that visa-free entry to the Russian Federation from 01.03.2022 to 01.09.2022 will be available to registered participants of the Congress, including those who plan to participate in satellite events.

To avail of that, one has to register at the Congress website and pay the registration fee. Please check the ICM webpage at https://icm2022.org/visa-free-entry for further details.

We plan to provide some financial support for participants from developing countries and young participants without access to travel funding.

Deadlines:

Proposals of contributed talks: March 15, 2022

Requests for financial support: March 15, 2022

General registration: April 15, 2022

Best wishes,

Organising Committee: Vladimir Dotsenko (Université de Strasbourg), Bernhard Keller (Université de Paris), Andrea Solotar (Universidad de Buenos Aires), Yury Volkov (St Petersburg University)

Scientific Committee: Luchezar Avramov (University of Nebraska - Lincoln), Yang Han (Chinese Academy of Sciences), Henning Krause (Universität Bielefeld), Wendy Lowen (Universiteit Antwerpen), Birgit Richter (Universität Hamburg)

The field of homotopy theory originated in the study of topological spaces up to deformation, but has since been applied effectively in several other disciplines. Indeed, homotopical ideas lead to the resolution of several long-standing open conjectures, for instance on smooth structures on spheres, the moduli of curves, and the cohomology of fields. More recently, Bhatt, Morrow, and Scholze used homotopical methods to compare different cohomology theories for algebraic varieties, thereby resolving open questions in arithmetic geometry. In a similarly arithmetic vein, Galatius and Venkatesh initiated the study of Galois representations with homotopical means, whereas Clausen and Scholze revisited the foundations of analytic topology. These and other recent developments in the interface of arithmetic and topology opened up new lines of attack towards classical open questions, which sparked a wide range of current research activities. This conference intends to survey some of the most spectacular recent advances in the fields, thereby paving the way to new developments and future interactions. Our goal is to foster scientific exchange and collaboration between established researchers, emerging leaders, early career mathematicians, and graduate students.

This will be a split transatlantic conference taking place at the Fields Institute in Canada and the Max Planck Institute for Mathematics in Germany, with videoconferencing connections in place to help collaboration.

The field of homotopy theory originated in the study of topological spaces up to deformation, but has since been applied effectively in several other disciplines. Indeed, homotopical ideas lead to the resolution of several long-standing open conjectures, for instance on smooth structures on spheres, the moduli of curves, and the cohomology of fields. More recently, Bhatt, Morrow, and Scholze used homotopical methods to compare different cohomology theories for algebraic varieties, thereby resolving open questions in arithmetic geometry. In a similarly arithmetic vein, Galatius and Venkatesh initiated the study of Galois representations with homotopical means, whereas Clausen and Scholze revisited the foundations of analytic topology. These and other recent developments in the interface of arithmetic and topology opened up new lines of attack towards classical open questions, which sparked a wide range of current research activities. This conference intends to survey some of the most spectacular recent advances in the fields, thereby paving the way to new developments and future interactions. Our goal is to foster scientific exchange and collaboration between established researchers, emerging leaders, early career mathematicians, and graduate students.

This will be a split transatlantic conference taking place at the Fields Institute in Canada and the Max Planck Institute for Mathematics in Germany, with videoconferencing connections in place to help collaboration.

Join us for a five-day workshop hosted by Western Washington University. Mornings will be dedicated to talks, and in the afternoons, participants will work on open problems related to 4-manifold trisections in small groups. The deadline to apply for support is April 22, 2022.

The official ICM 2022 has been reorganised as an online event. We will host some of the talks real life in Copenhagen, and attempt to salvage, on a smaller scale, some of the usual spirit of an ICM. The focus of the event in Copenhagen will be the Geometry and Topology sections, though it will not be restricted to those. See the webpage for more info.

Description The goal of this summer school is to introduce participants to tools and ideas from algebraic topology and homotopy theory that are used in the study of fixed point theory. The workshop will be centered around mini-courses, both on classical fixed-point theory and on modern techniques such as duality theory, spectra, and trace methods in algebraic K-theory.

The intended audience for this summer school should be familiar with the material in Hatcher (except the appendices). This reflects our goal that the school be accessible to second and third year students with an interest in algebraic topology. The school will be structured around a few mini-courses, which will run in an active-learning style.

The target audience is graduate students or other early career people in fields related to Floer Homotopy Theory, very broadly construed. Please tell anyone you know who might be interested.

The application to attend can also be found on the event page. The deadline to apply is 4 February 2022. Housing will be provided for at least the first 50 accepted applicants.

There is a registration fee (to be paid later) to discourage spurious registrations, but this can be waived if it is an obstacle to attendance.

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Speakers and Courses:

 Mohammed Abouzaid, Columbia University: Floer Homotopy
 Omar Antolín, UNAM: Introduction to Ring Spectra
 Nate Bottman, Max Planck: Floer Homology Fundamentals
 Catherine Cannizzo, SCGP: Floer Homology Fundamentals
 Jeff Hicks, University of Edinburgh: Applications
 Cary Malkiewich, Binghamton University: Spectra and Smash Products
 Katherine Poirier, New York City College of Technology: String Topology 
 Hiro Lee Tanaka, Texas State University: Operads

School Structure:

The summer school will consist of lecture courses with problem sessions; seminars on recent developments; and two panel discussions about professional development. The lecture courses will be:

Week 1

Fundamentals of Floer homology (9 lectures)

Introduction to ring spectra (3 lectures)

String topology (3 lectures)

Week 2

Spectra and smash products (4 lectures) Operads (4 lectures)

Applications of Floer homology (3 lectures)

Floer homotopy theory (4 lectures)

Most days, an hour and a half will be set aside for problem sessions. There will also be two seminars on recent developments and one panel discussion on professional development each week.

The Young Topologists Meeting (YTM) is an annual event that has previously been organised by the EPFL (Switzerland), the University of Copenhagen (Denmark), and jointly by Stockholm University and the Royal Institute of Technology (Sweden). The YTM 2022 it will take place on July 18-22, 2022 in Copenhagen. This yearly meeting is an opportunity for young researchers in topology to meet each other and share their work. In addition to short talks by the participants, the program for the meeting will include lectures by Andrew J. Blumberg (Columbia University), Natàlia Castellana Vila (Universitat Autònoma de Barcelona), and Robert Ghrist (University of Pennsylvania).

The conference mainly focuses on topics in pure and applied mathematics, related to the research areas mainly, Topology, Analysis and Functional Analysis, Sequences, Series, Summability, Fixed Point Theory, Differential Geometry, Algebra, Computer Science and Technology, Applied Statistics, Mathematical Methods in Physics.

The summer school will feature mini-courses by Joshua Greene, Jen Hom, Francesco Lin, John Pardon (to be confirmed) and Thomas Walpuski, covering topics in low-dimensional topology, Floer homology, and gauge theory. The school will be followed by a research conference the week after. The DEADLINE for applications is FEBRUARY 28, 2022. The application page is linked to from the conference webpage. Applicants are expected to provide a recommendation letter from their PhD advisor.

The conference will cover several areas of current research, including low-dimensional topology, gauge theory, and Floer homology in all its flavors. It is partly intended to celebrate the mathematical contributions of Tomasz Mrowka. The conference will be preceded by a summer school for graduate students (the week before). The list of speakers is on the event webpage. That webpage also contains a link to the application page. The DEADLINE for participants to apply is FEBRUARY 28, 2022.

The two-day conference Connections Workshop: Floer Homotopy Theory will run September 8th and 9th at the Mathematical Sciences Research Institute (MSRI). This workshop will feature talks by experts in Floer theory (and its applications to low-dimensional topology) and homotopy theory. It will include two expository lectures aimed at graduate students and other researchers who are new to the field, as well as a five research talks, given by the following speakers.

Expository Talks

• Jennifer Hom, Georgia Institute of Technology
• Mona Merling, University of Pennsylvania

Research Talks

• Po Hu, Wayne State University
• Xin Jin, Boston College
• Inbar Klang, Columbia University
• Shira Tanny, Institute for Advanced Study
• Melissa Zhang, University of Georgia

There will also be a contributed talks session and a panel discussion focusing on professional development. This workshop will highlight contributions by women and gender minorities, and members of these groups and of other underrepresented groups are especially encouraged to attend. This workshop is open to all mathematicians. The deadline for applying for funding is June 1; contributed talks will be solicited shortly thereafter.

This workshop precedes the weeklong Introductory Workshop: Floer Homotopy Theory, which may also be of interest to participants.

Over the last decade, there has been a wealth of new applications of homotopy-theoretic techniques to Floer homology in low-dimensional topology and symplectic geometry, including Manolescu’s disproof of the high-dimensional Triangulation Conjecture and Abouzaid-Blumberg’s proof of the Arnol’d Conjecture in finite characteristic. Conversely, results in Floer theory and categorification have opened new directions of research in homotopy theory, from string topology to S-Lie algebras. The goal of this workshop is to introduce researchers in Floer theory to modern techniques and questions in homotopy theory and, conversely, introduce researchers in homotopy theory to ideas underlying Floer theory and its applications.

The workshop will focus on the interaction between homotopy theory and symplectic topology and low dimensional topology that is mediated by Floer theory. Among the topics covered are foundational questions, applications to concrete geometric questions, and the relationship with finite dimensional approaches.

A conference on Homotopy theory at Northwestern to honor the contributions of Paul Goerss.