The Banff International Research Station will host the "Equivariant Stable Homotopy Theory and p-adic Hodge Theory" workshop in Banff from March 1 to March 06, 2020.

Algebraic topology has had a long and fruitful collaboration with algebraic geometry, with each providing techniques and problems to the other. This workshop is aimed at an exciting, evolving incarnation of this story: applications of equivariant stable homotopy to number theory. Recent work on the foundations of equivariant stable homotopy theory (starting with the Hill--Hopkins--Ravenel work on the Kervaire invariant one problem) and Lurie's development of the foundations of ''derived algebraic geometry'' now allows systematic exploration and organization of ''equivariant derived algebraic geometry''. This allows us to do ordinary algebraic geometry in commutative ring spectra.

New foundations in this area have been spectacularly applied to phenomena seen in the trace methods approach to computing algebraic K -theory. For instance, although the theory of equivariant commutative ring spectra was described decades ago, few of the subtleties in the theory were understood or explored. The modern approaches to computing algebraic K-groups step through equivariant commutative ring spectra via the natural S1-action on topological Hochschild homology. Ongoing and transformative work by Bhatt--Morrow-Scholze in p-adic Hodge theory uses cyclotomic spectra and therefore subtle equivariant information. This workshop, at the vanguard of work in this area, seeks to bring together experts in algebraic topology, (derived) algebraic geometry, and number theory to explore these exciting new connections.

This Spring School will gather together PhD students and junior researchers who use category-theoretic ideas or techniques in their research. It will provide a forum to learn about important themes in contemporary category theory, both from experts and from each other.

Three invited speakers will each present a three-hour mini-course, accessible to non-specialists, introducing an area of active research. There will also be short talks contributed by PhD students and postdocs, and a poster session.

The focus of the Spring School is on aspects of pure category theory as they interact with research in other areas of algebra, geometry, topology and logic. Any "categorical thinker" - that is, any mathematician whose work makes use of categorical ideas - is welcome to participate.

The Southern Regional Algebra Conference is an annual weekend conference that has been in existence since 1988. It serves an important role as part of the algebra research community in the Gulf Coast Region. Graduate students are strongly encouraged to participate. There is no registration fee. Presentations will be 25 minutes in length. The deadline to submit abstracts for SRAC 2020 is February 1, 2020.

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.

The Mathematics Research Communities program, run by AMS, is a great opportunity for young researchers to get involved in new research projects. It is a professional development program offering a chance to be part of a network. The program is described at http://www.ams.org/programs/research-communities/mrc-20 .

Marni MISHNA, Stephen MELCZER, Robin PEMANTLE are organizing a MATHEMATICAL RESEARCH COMMUNITY the week of May 31 - June 6, 2020 on the theme of Combinatorial Applications of Computational Geometry and Algebraic Topology. Yuliy BARYSHNIKOV and Mark WILSON will be assisting as well in the running of the workshop and the applied mathematics mentoring activities.

A brief description of MRC is at the site: https://www.ams.org/programs/research-communities/2020MRC-CompGeom . It is a great chance to learn some new techniques and crossover to a new community. Note the cross-disciplinary nature: the topic draws on combinatorics, singularity theory, algebraic topology, and computational algebra.

Young researchers who will be between -2 and +5 years post Ph.D. in Summer 2020 are encouraged to apply.

Applications are being accepted from now through February at the site https://www.mathprograms.org/db/programs/826 .

The 37th Annual Workshop in Geometric Topology will be held June 4-6, 2020 at Texas Christian University in Fort Worth, Texas. The featured speaker will be Andy Putman of the University of Notre Dame, who will give a series of three one-hour lectures on the Topology of Moduli Spaces. Participants are invited to contribute talks of 20 to 30 minutes.

Full details can be found at the conference web site at http://faculty.tcu.edu/gfriedman/GTW2020

Financial support is available to help defer travel and local expenses. Graduate students, recent PhDs in geometric topology, and members of underrepresented groups in mathematics are especially encouraged to apply for support. Funding for the workshop is provided by a grant from the National Science Foundation (DMS-1764311), by the TCU College of Science and Engineering, and by the TCU Department of Mathematics.

Important deadlines: Requests for financial support (to receive full consideration): April 17 Reservation and payment for housing on TCU campus: May 1 Submission of contributed talks, including title and abstract: May 1

Please contact Greg Friedman (g.friedman@tcu.edu) if you have any questions.

Workshop Organizers: Fredric Ancel, University of Wisconsin-Milwaukee; Greg Friedman, Texas Christian University; Craig Guilbault, University of Wisconsin-Milwaukee; Molly Moran, Colorado College; Nathan Sunukjian, Calvin College; Eric Swenson, Brigham Young University; Frederick Tinsley, Colorado College; Gerard Venema, Calvin College

With this workshop we would like to promote the interaction between the following five fields:

• Berkovich spaces,
• Tropical geometry,
• p-adic differential equations,
• Arithmetic D-modules and representations of p-adic Lie groups,
• Arithmetic applications of p-adic local systems.

While the first two are already tightly linked, the role of Berkovich spaces in the last 3 topics is only emerging and within this, the role of tropical geometry has not yet been explored. More generally, we consider this conference to be a good opportunity to study new techniques recently introduced into the field. We are convinced that each of these areas has plenty of potential and that a fruitful interaction between them might nourish their development. The aim of the conference is precisely to give leading experts in these each of these domains the opportunity to meet, present their last results and open challenges, and encourage an exchange that will drive forward these exciting and rapidly developing subjects.

A poster session is planned. Students are welcome to submit posters.

Topic: A primary aim of chromatic homotopy theory is to understand the stable homotopy category by decomposing it into pieces (called chromatic localizations) which are, at least in principle, easier to understand. These chromatic localizations enjoy a certain duality property called ambidexterity, which guarantees that certain homotopy limits can be understood as homotopy colimits (and vice versa). The goal of this workshop is to explain the mathematics of ambidexterity and some of its applications.

A preliminary syllabus and live application is available at the website.

Suggested prerequisites: Some knowledge of chromatic homotopy theory will be expected; while the workshop will feature a review lecture on the topic, this will be insufficient if the topic is entirely new to participants. Additionally, participants should have familiarity with the language of infinity categories.

Mentors: The 2020 Talbot workshop will be mentored by Prof. Jacob Lurie of the IAS and Prof. Tomer Schlank of The Hebrew University of Jerusalem.

Format: The workshop discussions will have an expository character and most of the talks will be given by participants. The afternoon schedule will be kept clear for informal discussions and collaborations. The workshop will take place in a communal setting, with participants sharing living space and cooking and cleaning responsibilities.

Funding: We cover all local expenses, including lodging and food. We also have limited funding available for participant travel costs.

Who should apply: Talbot is meant to encourage collaboration among young researchers, particularly graduate students. To this end, the workshop aims 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. Our decisions are based not on applicants' credentials but on our assessment of how much they would benefit from the workshop. As we are committed to promoting diversity in mathematics, we also especially encourage women and minorities to apply.

The purpose of this meeting is to bring together a diverse range of experts and early-career researchers working in in a variety of aspects of the study of holomorphic curves and their applications to low-dimensional topology. Points of focus will include contact and symplectic structures and dynamics, Lagrangian cobordisms and Legendrian knots, and Floer–theoretic frameworks of study.

Andrew Ranicki and his theory of algebraic surgery played a central role in linking manifold theory, algebraic K-theory, and its close cousin L-theory. These areas have seen great developments and advances in the last decade from distinct research communities. This workshop will bring together mathematicians working on the topology of high-dimensional manifolds and their automorphisms with those working on the algebraic K-theory (and its cousins hermitian K-theory and L-theory) of rings and ring spectra, in order to share recent progress in these areas and kindle a fresh interaction between them.

The lecture series and research talks at the IHES Summer School will focus on presenting the latest developments in topics related to categories of motives, calculational and foundational aspects of motivic and equivariant homotopy theory, and the generalisations of these tools and techniques in the setting of non-commutative geometry.

See conference website

The goal of this summer school is to introduce participants to modern tools used in the study of fixed point theory in algebraic topology and homotopy theory. The workshop will be centered around mini-courses whose goal will be to introduce and apply tools such as categorical approaches to duality, spectra and trace methods in algebraic K-theory to the study of classical fixed point 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 from any PhD granting institution. The school will be structured around a few mini-courses which will run in an active-learning style.

Scientific Leaders

Jonathan Campbell, Vanderbilt University

Inbar Klang, École Polytechnique Fédérale de Lausanne

Kate Ponto, University of Kentucky

Cary Malkiewich, Binghamton University

John Lind, California State Chico

Sarah Yeakel, University of Maryland

Inna Zakharevich, Cornell University

Transchromatic phenomena appear in a variety of contexts. These include stable and unstable homotopy theory, higher category theory, topological field theories, and arithmetic geometry. The aim of the conference is to bring together people from all of these areas in order to understand the relationship between each others work and to further demystify the appearance of transchromatic patterns in such disparate areas.

Homotopical and higher categorical methods have seen increasing importance in mathematics, both as foundations and as computational tools. In fact, such methods merge two apparently distinct goals: understanding geometrical forms and classifying mathematical structures. This conference aims at gathering together under this perspective geometers in a rather broad sense. It seeks to foster the applications of these higher methods in the interplay between homotopy theory, arithmetic, and algebraic geometry.

The conference is supported by the SFB1085 "Higher Invariants -Interactions between Arithmetic Geometry and Global Analysis"

Applied and computational topology, one of the most rapidly growing branches of mathematics, is becoming a key tool in applied sciences. It is making impact not only in mathematics, but on the wide interdisciplinary environment including material and medical sciences, data science, robotics. Building upon successful conferences held in Bedlewo in 2013 and 2017, the next edition of Applied Topology in Bedlewo will take place in 2021. Similarly as before, our aim is to bring together scientists from all over the world working in various fields of applied topology. This time we will focus on:

• random topology,
• topological methods in combinatorics,
• topological data analysis and shape descriptors,
• topological analysis of time-varying data in biology, engineering and finance,
• topological and geometrical descriptors of porous materials.